From b96a894344e557fb6b264678342f595c2915c0c5 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 00:08:37 +0800 Subject: [PATCH 01/19] Fix Rings paper accuracy and evaluation scope --- papers/rings.pdf | Bin 286104 -> 119046 bytes papers/rings.tex | 301 ++++++++++++++++++++++++----------------------- 2 files changed, 153 insertions(+), 148 deletions(-) diff --git a/papers/rings.pdf b/papers/rings.pdf index ebba74dc6ee6e07a73d96676500096ad51ba6557..c6e6e9f4b8659b7091b3ea9b2609913b86c0235e 100644 GIT binary patch delta 113597 zcmZshLy#s4)MU%HZQHiHY}>Z0tG}{s+qP}nwr$tEKVlX$F|*6v-Q?z;JZYWCAq9|e z8~`q6E&%};7guL9BRd$+jc&Zn7&^}T>{_fHcft~r)LWwlC=nte;iMxdBs_wdE7Jm^ z_&#EkgWGyNhR!SZ*(Wh7=@|Ep&W+TL-K|gn{*my|?@_<-mjRysuhZLc<{)Hm3S=i( z>DT`Bb6&Sj&@&`GhQ-nT^l>dEFo12QbXMCmW|e0szk4knvWoVf19| z^(D6~)F=9u^H}T!%LnfC?rFW^tZo1_-kTHsvR6b{R&@s|au19QXi1CVwd2u2W*H-4iYN+Ik zZI}{k32S(ZqATNMbAI*LE(=GHV-d1kXY0eIMFElHz8m!IS3DT#s%$He)!nnzaxhAI 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zKz}&*dQyGdPrg1*kkBsfs`ZW>sph6IyRvI+Cf2$xSIW1z79+ zD+^D~BsN7_<|rRB$b7>a*QcE`=HEM~qyOgRY&?@1v8m afupm#qlqar6FY!~2>?w-CL$*a{eJ)kK_kKd diff --git a/papers/rings.tex b/papers/rings.tex index 069bad3b0..28ed6f7c6 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -11,7 +11,6 @@ \usepackage{epsfig} \usepackage{epstopdf} \usepackage{url} -\usepackage{enumitem} \usepackage{array} \usepackage[utf8]{inputenc} \usepackage[english]{babel} @@ -26,6 +25,9 @@ \newtheorem{invariant}{Invariant} \newtheorem{obligation}{Obligation} +\newcommand{\RingsObj}{\mathsf{Rings}} +\newcommand{\SetOverR}{\mathbf{Set}/R} + \usetikzlibrary{shapes,arrows,positioning,patterns,through} \tikzset{ @@ -58,19 +60,21 @@ \parbox{0.90\textwidth}{% \centering\bfseries Abstract\\[0.5\baselineskip]% \normalfont -Rings is an implemented algebraic structured peer-to-peer network for -decentralized identity, resource ownership, transport, storage, and application -protocols. The project starts from a concrete failure mode in contemporary +Rings is an implemented structured peer-to-peer network whose design is stated +as algebraic carriers, ownership maps, protocol transitions, and explicit proof +obligations. The project starts from a concrete failure mode in contemporary Internet systems: application servers, DNS names, relay services, and platform accounts often become the authority that identities and data must trust. Rings -instead treats identities and resources as algebraic objects over a structured -CorrectChord overlay, with browser and native runtimes connected through -WebRTC/WebAssembly adapters and cryptographic protocols kept on carriers -separate from the routing identifier space. +instead places identities and resources over a CorrectChord overlay, connects +browser and native runtimes through WebRTC/WebAssembly adapters, and keeps +cryptographic protocols on carriers separate from the routing identifier space. +This paper distinguishes implemented mechanisms from scoped verification +evidence and from evaluation obligations that still require Rings-specific +measurement. The core object is \[ - \mathcal{Rings}= - (R,\mathcal{R}_N,\mathbf{Set}/R,\Omega_N, + \RingsObj= + (R,\mathcal{R}_N,\SetOverR,\Omega_N, \mathsf{T}^{\mathcal{E}}_A,\Pi,\mathbb{G},\mathcal{X}) \] with @@ -84,7 +88,7 @@ \end{array} \] \[ - \{D,V,M,H,Q,W\}\subset\operatorname{Obj}(\mathbf{Set}/R), + \{D,V,M,H,Q,W\}\subset\operatorname{Obj}(\SetOverR), \qquad \mathsf{CryptoCarrier}\cap R=\varnothing. \] @@ -109,9 +113,10 @@ \section{Introduction} authority. Rings is implemented as a network, but this paper is organized around the -algebraic structure that makes the implementation coherent. It states the -ideal carrier, ownership, transition, and safety laws that the implementation -realizes and continues to refine. The older intuition was that Decentralized +algebraic structure that makes the implementation coherent. It separates +implemented mechanisms from ideal carrier, ownership, transition, and safety +laws that remain obligations for stronger verification and evaluation. The +older intuition was that Decentralized Identifiers (DIDs) directly form a finite ring suitable for all routing and cryptographic operations. The refined model is more precise: Chord identifiers form an additive circular carrier for placement, interval order, replica @@ -140,31 +145,25 @@ \section{Problem Statement and Design Goals} message or storage operation would turn Rings into a ledger rather than an algebraic structured peer-to-peer substrate. -The problem is therefore to specify a network object -\[ - \mathcal{Rings} -\] -that simultaneously supports: -\begin{enumerate}[leftmargin=*,noitemsep,topsep=0pt] -\item self-certifying identity and delegated sessions; -\item structured lookup and resource ownership; -\item browser-native and native transport surfaces; -\item application protocols with typed side effects; -\item cryptographic protocols over correct carriers; -\item bounded algebraic and operational obligations for routing and state repair. -\end{enumerate} +The problem is therefore to specify a network object \(\RingsObj\) that +simultaneously supports self-certifying identity and delegated sessions, +structured lookup and resource ownership, browser-native and native transport +surfaces, application protocols with typed side effects, cryptographic protocols +over correct carriers, and bounded algebraic and operational obligations for +routing and state repair. This paper makes the following contributions. It presents Rings as an algebraic structured peer-to-peer network, not merely as an overlay lookup routine. It models the Rings identifier space as the additive cyclic group \(R=\mathbb{Z}/2^{160}\mathbb{Z}\), not as a general finite field. It lifts -resource placement into \(\mathbf{Set}/R\), so each protocol object carries an +resource placement into \(\SetOverR\), so each protocol object carries an explicit map into the overlay. It uses CorrectChord as the maintenance law before introducing Rings-specific replication, storage, mailbox, relay, and ranking semantics. It gives a writer effect monad for DHT transitions and a -TLA-style state relation for model checking and trace replay. These algebraic -and operational artifacts are the core of the paper; the surrounding text -explains why those artifacts exist and how they relate to prior systems. +TLA-style state relation for scoped model checking and trace replay. These +algebraic and operational artifacts are the core of the paper; the surrounding +text explains which parts are implemented, which parts are checked in bounded +models, and which parts remain future measurement obligations. \section{Algebraic System Model} @@ -232,24 +231,29 @@ \section{Algebraic System Model} \[ \begin{array}{rcl} \rho&\in&\mathbb{N}_{>0},\\ -\operatorname{rot}^{\rho}_i(k) +\operatorname{repkey}^{\rho}_i(k) &=&k+\left\lfloor M\cdot i/\rho\right\rfloor,\\[4pt] -\operatorname{Rep}^{\rho}_N(k) +\operatorname{RepKey}^{\rho}(k) &=& - \{\operatorname{owner}_N(\operatorname{rot}^{\rho}_i(k)): - 0\leq i<\rho\}. + \langle \operatorname{repkey}^{\rho}_i(k):0\leq i<\rho\rangle,\\[4pt] +\operatorname{RepOwner}^{\rho}_N(k) + &=& + \langle \operatorname{owner}_N(\operatorname{repkey}^{\rho}_i(k)): + 0\leq i<\rho\rangle. \end{array} \] -Storage redundancy uses affine rotations of the entry key. Successor lists -remain the CorrectChord safety root for topology maintenance, not the storage -replica set. +Storage redundancy is specified first as distinct placement keys. Effective +node-level redundancy depends on how those keys map through the live owner +function; two placement keys can collapse to the same live owner when the +topology is too small or poorly spaced. Successor lists remain the +CorrectChord safety root for topology maintenance, not the storage replica set. \end{definition} \begin{definition}[Rings overlay object] \[ \mathcal{R}_N= (R,N,\operatorname{owner}_N,\operatorname{pred}_N, - \operatorname{Succ}^r_N,\operatorname{Rep}^{\rho}_N,F,E), + \operatorname{Succ}^r_N,\operatorname{RepOwner}^{\rho}_N,F,E), \] \[ \begin{array}{rcl} @@ -287,7 +291,9 @@ \section{Algebraic System Model} \begin{array}{rcl} \mathsf{PlacementOps}&=& \{0,+,-,\delta_a,(a,b]_R\}\\ -&&\cup\{\operatorname{owner}_N,\operatorname{Rep}^r_N\},\\ +&&\cup\{\operatorname{owner}_N\}\\ +&&\cup\{\operatorname{RepKey}^{\rho}, + \operatorname{RepOwner}^{\rho}_N\},\\ \mathsf{CryptoOps}&=& \{\times,^{-1},\cdot_{scalar},\mathsf{interp}\}\\ &&\cup\{\mathsf{pair},\mathsf{subgroup}\},\\ @@ -299,20 +305,19 @@ \section{Algebraic System Model} \begin{table}[htbp] \centering -\small -\begin{tabular}{p{2.0cm}|p{4.8cm}} +\footnotesize +\begin{tabular}{p{1.65cm}|p{5.15cm}} \hline Object & Carrier or law \\ \hline Chord IDs & additive cyclic group $R$ \\ DID proof & signature verifier and transcript law \\ VID placement & $H_\nu:X_\nu\to R$ then owner map \\ Storage merge & join semilattice or explicit finalizer \\ -E2E encryption & finite field or curve group \\ +E2E encryption & group operation plus byte-to-point adapter \\ Sequencing & partial order over witness domains \\ Effects & writer monad over action lists \\ \hline \end{tabular} -\normalsize \caption{Carrier boundaries in the Rings model} \label{carrier-table} \end{table} @@ -479,7 +484,7 @@ \section{Category and Effects} \begin{array}{rcl} \nu&\in&\{D,V,M,H,U,Q,W\},\\ H_\nu&:&X_\nu\to R,\\ -(X_\nu,H_\nu)&\in&\mathbf{Set}/R. +(X_\nu,H_\nu)&\in&\SetOverR. \end{array} \] \end{definition} @@ -487,7 +492,7 @@ \section{Category and Effects} \begin{definition}[Placement functor] \[ \begin{array}{rcl} - \Omega_N&:&\mathbf{Set}/R\to\mathbf{Set}/N,\\ + \Omega_N&:&\SetOverR\to\mathbf{Set}/N,\\ (X,H)&\mapsto&(X,\operatorname{owner}_N\circ H). \end{array} \] @@ -612,27 +617,6 @@ \section{Chord Overlay} \] This section fixes Chord as the base protocol and CorrectChord as the maintenance law~\cite{Chord,ZaveChordCorrect}. -\begin{figure}[h] - \begin{center} - \begin{tikzpicture}[node distance=5cm,auto,>=latex'] - \xdef\N{16} - \xdef\S{3} - \xdef\deltadegree{360/\N} - \draw[thick] (0,0) circle (\S); - \foreach \i in {0,...,15} { - \foreach \j in {1,...,4}{ - \pgfmathsetmacro{\result}{mod(\i+2^\j,\N)} - \draw (-\i*\deltadegree+90:\S) -- (-1*\result*\deltadegree+90:\S); - } - } - \foreach \i in {0,...,15} - \node (\i) [circle,fill=white,draw=black,thick] at (-\i*\deltadegree+90:\S) {\i}; - \end{tikzpicture} - \end{center} - \caption{Chord algorithm, lookup protocol} - \label{dht} -\end{figure} - \begin{definition}[Local node state] \[ S_n=(p_n,L_n,F_n,E_n) @@ -728,7 +712,7 @@ \section{Chord Overlay} \node (\i) [circle,fill=white,draw=black,thick] at (-\i*\deltadegree+90:\S) {\i}; \end{tikzpicture} \end{center} - \caption{Chord algorithm, lookup protocol} + \caption{Chord finger targets from node 1 in a 16-node ring} \label{lookup-figure} \end{figure} @@ -859,11 +843,17 @@ \section{DID and Resource Algebra} \begin{invariant}[Placement] \[ - \operatorname{Inv}_{place}\equiv - \forall \nu,x.\; - \operatorname{replicas}(H_\nu(x)) - \subseteq - \operatorname{Rep}^{\rho}_N(H_\nu(x)). +\begin{array}{rcl} +K_{\nu,x}&=&\operatorname{replicaKeys}(H_\nu(x)),\\[2pt] +P_{\nu,x}&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(H_\nu(x))),\\[2pt] +O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(H_\nu(x))),\\[2pt] +U_{\nu,x}&=&\operatorname{owner}_N[K_{\nu,x}],\\[2pt] +\operatorname{Inv}_{place} +&\equiv& +\forall \nu,x.\; +K_{\nu,x}\subseteq P_{\nu,x} +\land U_{\nu,x}\subseteq O_{\nu,x}. +\end{array} \] \end{invariant} @@ -919,24 +909,31 @@ \section{Cryptographic Carriers and Traffic} \caption{ElGamal Encryption and Decryption} \label{alg:elgamal} \begin{algorithmic}[1] -\State \textbf{Input:} Message $m$, private key $x \in \mathbb{Z}_q$, public key $h = g^x$, generator $g$ -\State \textbf{Output:} Encrypted message $(c_1, c_2)$ +\State \textbf{Input:} Encoded group element $m_G\in\mathbb{G}$, private key $x \in \mathbb{Z}_q$, public key $h = g^x$, generator $g$ +\State \textbf{Output:} Group ciphertext $(c_1, c_2)$ \Procedure{Encryption}{} \State Choose a random integer $k \in \mathbb{Z}_q$ \State Compute $c_1 = g^k$ -\State Compute $c_2 = m\cdot h^k$ +\State Compute $c_2 = m_G\cdot h^k$ \State \Return $(c_1, c_2)$ \EndProcedure \Procedure{Decryption}{} -\State Compute $m = c_2\cdot(c_1)^{-x}$ -\State \Return $m$ +\State Compute $m_G = c_2\cdot(c_1)^{-x}$ +\State \Return $m_G$ \EndProcedure \end{algorithmic} \end{algorithm} +Algorithm~\ref{alg:elgamal} is the group-level carrier operation. Byte +payloads must first be encoded into curve points and split into bounded frames. +The direct ElGamal body is malleable when detached from its signed transport +envelope; Rings therefore treats message signatures, DID ownership of the +public key, stream identifiers, sequence numbers, and final-frame checks as +part of the security boundary rather than as optional metadata. + \begin{definition}[Signed encrypted frame] \[ - f=(sid,seq,last,cipher,pk_s,\sigma_s). + f=(sid,seq,last,cipher,pk_s,\sigma_s,win). \] \[ \begin{aligned} @@ -944,7 +941,9 @@ \section{Cryptographic Carriers and Traffic} \operatorname{FrameValid}(f) \Leftrightarrow\;&V(pk_s,\sigma_s,m_f)=\top\\ &\land\; - \operatorname{Session}(D(pk_s),sid,e). + \operatorname{Session}(D(pk_s),sid,e)\\ + &\land\; + \operatorname{SeqOK}(sid,seq,last,win). \end{aligned} \] \end{definition} @@ -1069,22 +1068,26 @@ \section{Ordering, Ranking, and Security} \begin{table}[htbp] \centering -\small +\footnotesize \setlength{\tabcolsep}{2pt} -\begin{tabular}{p{1.1cm}|p{2.1cm}|p{2.35cm}} +\begin{tabular}{p{1.05cm}|p{2.0cm}|p{2.45cm}} \hline -Attack & Predicate & Rings control \\ \hline -Sybil & many DIDs, one actor & admission cost, ranking, challenge \\ -Replay & stale valid $\sigma$ & nonce, TTL, session epoch \\ -MITM & wrong key for DID & DID proof, signed envelope, E2E \\ -DoS & unbounded resource use & quotas, ranking, chunk bounds \\ +Attack & Predicate & Required boundary \\ \hline +Sybil & many DIDs, one actor & admission and ranking policy \\ +Replay & stale valid $\sigma$ & TTL, stream order, final marker \\ +MITM & wrong key for DID & DID proof and signed envelope \\ +DoS & unbounded resource use & quotas and chunk bounds \\ \hline \end{tabular} -\normalsize -\caption{Security predicates and controls} +\caption{Security predicates and required controls} \label{security-table} \end{table} +Table~\ref{security-table} is a boundary summary, not a standalone proof of +Sybil resistance, anonymity, or denial-of-service tolerance. Those properties +depend on protocol-specific admission, ranking, relay, and resource-accounting +policies outside the base overlay. + \begin{obligation}[Replay rejection] \[ \begin{array}{rcl} @@ -1097,7 +1100,13 @@ \section{Ordering, Ranking, and Security} \] \end{obligation} -\section{Verification and Evaluation} +\section{Verification Evidence and Evaluation Scope} + +This section separates three things that are easy to conflate: algebraic +specification, scoped verification evidence, and performance evaluation. The +repository contains executable evidence for specific overlay, storage, and +message-flow obligations. It does not yet contain a wide-area Rings benchmark +that can replace a published Chord latency or churn experiment. \begin{definition}[State relation] \[ @@ -1113,9 +1122,13 @@ \section{Verification and Evaluation} } \] \[ - \mathsf{Explore}=\mathsf{TLAStyle}(\to) + \mathsf{Explore}_{scope}=\mathsf{ModelCheck}(\to,\Gamma) \] -The exploration relation follows TLA+ style and Stateright execution~\cite{LamportSpecifyingSystems,Stateright}. +The exploration relation follows TLA+ style and Stateright execution for a +finite scope \(\Gamma\)~\cite{LamportSpecifyingSystems,Stateright}. The scope +must state the node count, topology shape, message scheduler, and failure model; +otherwise the result is only an implementation test, not a model-checking +claim. \end{definition} \begin{invariant}[Effect refinement] @@ -1142,6 +1155,31 @@ \section{Verification and Evaluation} \] \end{obligation} +\begin{table}[htbp] +\centering +\footnotesize +\setlength{\tabcolsep}{2pt} +\begin{tabular}{p{1.35cm}|p{2.65cm}|p{2.45cm}} +\hline +Artifact & Checked scope & Limitation \\ \hline +Topology tests + & join, rectify, stabilize fixpoints on finite DID layouts + & not a parametric TLAPS proof \\ +Stateright + & predecessor update, small discovery abstraction, storage CRDT, handoff + & scoped models, not a full live network \\ +Trace replay + & deterministic delivery schedules over real routing code + & not an Internet latency benchmark \\ +E2E tests + & signed direct-ElGamal frame order, final marker, and replay behavior + & not a symbolic cryptographic proof \\ +\hline +\end{tabular} +\caption{Verification evidence and explicit limits} +\label{verification-table} +\end{table} + \begin{definition}[Latency decomposition] \[ T_{total} @@ -1157,25 +1195,6 @@ \section{Verification and Evaluation} \] \end{definition} -\begin{table}[htbp] -\centering -\begin{tabular}{l|l|l} -\cline{1-3} - \shortstack{Fraction of \\failed nodes} & \shortstack{Mean \\routing hops} &\shortstack{Mean num. of \\lookup timeouts} \\ \cline{1-3} -0 & 3.84 & 0.0 \\ \cline{1-3} -0.1 & 4.03 & 0.60 \\ \cline{1-3} -0.2 & 4.22 & 1.17 \\ \cline{1-3} -\end{tabular} -\caption{Latency on failed node rate of Chord \cite{Chord}} -\label{latency-table} -\end{table} - -\begin{figure}[htbp] - \includegraphics[width=\columnwidth]{imgs/rings/path.png} - \caption{Chord lookup path \cite{Chord}} - \label{path} -\end{figure} - \begin{definition}[Reliability baseline] \[ \begin{array}{rcl} @@ -1185,42 +1204,27 @@ \section{Verification and Evaluation} \] \end{definition} -\begin{table}[htpb] -\centering - \begin{tabular}{l|l|l|l} -\cline{1-4} - \shortstack{join/leave rate \\ (per sec./stab. \\ period)} - & \shortstack{Mean \\routing\\ hops} - &\shortstack{Mean \\num. of \\lookup \\timeouts} - &\shortstack{Lookup \\ failures \\ per 10k} \\ \cline{1-4} -0.05/1.5 & 3.90 & 0.5 & 0 \\ \cline{1-4} -0.10/2 & 3.83 & 0.11 & 0 \\ \cline{1-4} - 0.15/4.5 & 3.84 & 0.16 & 2 \\ \cline{1-4} - 0.20/6 & 3.81 & 0.23 & 5 \\ \cline{1-4} -0.25/7.5 & 3.83 & 0.30 & 6 \\ \cline{1-4} - 0.30/9 & 3.91 & 0.34 & 8 \\ \cline{1-4} - 0.35/10.5 & 3.94 & 0.42 & 16 \\ \cline{1-4} -0.40/12 & 4.06 & 0.46 & 15 \\ \cline{1-4} -\end{tabular} -\caption{Failure rate of Chord \cite{Chord}} -\label{failure} -\end{table} - -\begin{obligation}[Evaluation morphism] +\begin{obligation}[Benchmark report] \[ \begin{aligned} - \Phi_{eval}:& - (h,timeouts,failures)_{Chord}\\ - &\mapsto - (T_{total},timeoutMean,failrate)_{Rings}, + \mathsf{Report}_{Rings} = + (&N,\rho,r,\mathsf{transport},\mathsf{runtime},\\ + &\mathsf{scheduler},T_{total},timeoutMean,failrate). \end{aligned} \] \[ - \Delta\Phi= - T_{conn}+T_{crypto}+T_{witness}+T_{app}. + \mathsf{Baseline}_{Chord} + \not\equiv + \mathsf{Measurement}_{Rings}. \] \end{obligation} +Chord's published hop-count and churn measurements remain the baseline for the +underlying circular overlay~\cite{Chord}. A Rings performance claim must add +the measured cost of connection establishment, browser or native transport, +cryptographic framing, storage replication, and application witnesses on a +specified implementation build. + \section{Related Work} Distributed hash tables give Rings its closest technical ancestry. IPFS and @@ -1261,19 +1265,20 @@ \section{Related Work} \begin{table}[htbp] \centering -\small +\footnotesize \setlength{\tabcolsep}{2pt} -\begin{tabular}{p{1.35cm}|p{1.55cm}|p{2.25cm}} +\begin{tabular}{p{1.25cm}|p{1.25cm}|p{2.95cm}} \hline System & Metric & Ownership law \\ \hline -Kademlia fam. +Kademlia & XOR & bucket routing \\ Relay mixnets & path & no structured owner \\ Rings - & circular & owner, Succ, affine Rep \\ + & circular & clockwise owner, successor list, affine placement keys \\ \hline \end{tabular} +\vspace{2pt} \caption{Routing and ownership comparison \cite{Kademlia,IPFS,Libp2p,TorNetwork,NymNetwork}} \label{related-table} \end{table} @@ -1287,22 +1292,22 @@ \section{Conclusion} procedures. \[ - \mathsf{Rings}= - (R,\mathcal{R}_N,\mathbf{Set}/R,\Omega_N, + \RingsObj= + (R,\mathcal{R}_N,\SetOverR,\Omega_N, \mathsf{T}^{\mathcal{E}}_A,\Pi,\mathbb{G},\mathcal{X}). \] \[ \begin{array}{rcl} \mathsf{Overlay}&=&\mathsf{CorrectChord}(R,N,r),\\ -\mathsf{Resource}&=&(X_\nu,H_\nu)\in\mathbf{Set}/R,\\ +\mathsf{Resource}&=&(X_\nu,H_\nu)\in\SetOverR,\\ \mathsf{Placement}&=&\Omega_N(X_\nu,H_\nu),\\ \mathsf{Transition}&=&\tau_\nu:S_\nu\times I_\nu\to Y_\nu,\\ Y_\nu&=&\mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu),\\ \mathsf{Crypto}&=&\mathbb{G}\lor\mathbb{F}_q,\quad \mathsf{Crypto}\cap R=\varnothing,\\ \mathsf{Evidence}&=& - \{\mathsf{figures},\mathsf{tables},\mathsf{algorithms}\}\\ -&&\cup\{\mathsf{invariants},\mathsf{obligations}\}. + \{\mathsf{scopedModels},\mathsf{traceReplay}\}\\ +&&\cup\{\mathsf{invariants},\mathsf{benchmarkObligations}\}. \end{array} \] From 3743142956fc5af5fb1670d0163d59ce9bb7341e Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 00:56:25 +0800 Subject: [PATCH 02/19] Formalize Rings paper exposition --- papers/rings.pdf | Bin 119046 -> 116978 bytes papers/rings.tex | 314 +++++++++++++++++++++++++++-------------------- 2 files changed, 179 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zpL%H;?Wa@pEuE&rbcV+0EUl&Ww2}I0Gk-ECol0iR=2CGNi>7Lf`tOwlW7)x4IA9ooS~}rtgZnDmeh5$fi}?qZJ}-S5q(Ub&}X!hKBp1dO?zlBjRK>K z?kQsboa4vN$@k8g4Bf*UVD3=e2QqDLZ diff --git a/papers/rings.tex b/papers/rings.tex index 28ed6f7c6..be79252ab 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -60,18 +60,16 @@ \parbox{0.90\textwidth}{% \centering\bfseries Abstract\\[0.5\baselineskip]% \normalfont -Rings is an implemented structured peer-to-peer network whose design is stated -as algebraic carriers, ownership maps, protocol transitions, and explicit proof -obligations. The project starts from a concrete failure mode in contemporary -Internet systems: application servers, DNS names, relay services, and platform -accounts often become the authority that identities and data must trust. Rings -instead places identities and resources over a CorrectChord overlay, connects -browser and native runtimes through WebRTC/WebAssembly adapters, and keeps -cryptographic protocols on carriers separate from the routing identifier space. -This paper distinguishes implemented mechanisms from scoped verification -evidence and from evaluation obligations that still require Rings-specific -measurement. -The core object is +Rings is an implemented structured peer-to-peer network specified by carriers, +owner maps, protocol morphisms, and explicit obligations. Its motivating +failure mode is authority collapse: +\[ + \mathsf{root}(id,data,route) + \in\{\mathsf{server},\mathsf{dns},\mathsf{relay},\mathsf{platform}\}. +\] +Rings replaces that root with self-certifying identity and resource ownership +over a CorrectChord overlay, while keeping cryptographic carriers disjoint from +the routing carrier. The object studied here is \[ \RingsObj= (R,\mathcal{R}_N,\SetOverR,\Omega_N, @@ -92,6 +90,15 @@ \qquad \mathsf{CryptoCarrier}\cap R=\varnothing. \] +Claims are stratified as +\[ + \mathsf{Claim} + = + \mathsf{Spec} + \cup\mathsf{Impl} + \cup\mathsf{Evidence}_{\Gamma} + \cup\mathsf{Obligation}. +\] }% \hfill\mbox{}% \vspace{0.5\baselineskip}% @@ -102,68 +109,100 @@ \section{Introduction} -Centralized application platforms simplify deployment, but they also concentrate -identity, naming, storage, and traffic control at service operators. Cloud and -platform centralization therefore becomes a privacy, availability, and autonomy -risk for users who need direct communication and durable control over their -data~\cite{Kshetri2013,Zissis2012,KshetriMurugesan2013}. The Rings project is motivated by -this observation: a sovereign network should let a participant own an identity, -establish a session, route to another identity or resource, and run application -protocols without turning a single application server into the root of -authority. - -Rings is implemented as a network, but this paper is organized around the -algebraic structure that makes the implementation coherent. It separates -implemented mechanisms from ideal carrier, ownership, transition, and safety -laws that remain obligations for stronger verification and evaluation. The -older intuition was that Decentralized -Identifiers (DIDs) directly form a finite ring suitable for all routing and -cryptographic operations. The refined model is more precise: Chord identifiers -form an additive circular carrier for placement, interval order, replica -selection, and finger targets; threshold schemes, signatures, encryption, and -zero-knowledge protocols use their own fields or groups. - -The resulting design has three practical consequences. First, DIDs and virtual -DIDs (VIDs) share the same 160-bit placement surface, so identities, mailboxes, -service descriptors, chunks, subrings, and application rendezvous points can be -routed by one owner function. Second, Rings builds on Chord and CorrectChord -rather than replacing the overlay literature: successor lists, predecessor -relations, join, rectify, and stabilize are the maintenance substrate on which -Rings semantics are layered~\cite{Chord,ZaveChordCorrect}. Third, state -transitions return typed effects instead of directly performing network IO, -which allows the overlay to be reasoned about as a pure state machine and then -interpreted by browser or native runtimes. +Centralized platforms are efficient deployment mechanisms but poor authority +carriers: identity, naming, storage, and traffic control collapse to service +operators~\cite{Kshetri2013,Zissis2012,KshetriMurugesan2013}. Rings starts +from the opposite requirement: +\[ +\begin{array}{rcl} +\mathsf{Own}(d)&=&k_d,\\ +\mathsf{Route}(x)&=&\operatorname{owner}_N(H_\nu(x)),\\ +\mathsf{Run}(\mathcal{P}_\nu)&=& + \tau_\nu:S_\nu\times I_\nu\to + \mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu),\\ +\mathsf{RootOfAuthority}&\neq&\mathsf{ApplicationServer}. +\end{array} +\] + +The central modeling choice is carrier separation. The Chord identifier space +is the additive cyclic group for placement and interval order; signatures, +threshold schemes, encryption, and zero-knowledge protocols remain in their own +fields or groups: +\[ +\begin{array}{rcl} +R&=&\mathbb{Z}/2^{160}\mathbb{Z},\\ +\mathsf{CC}&\in&\{\mathbb{F}_q,\mathbb{G},\mathbb{Z}_q\},\\ +R\cap\mathsf{CC}&=&\varnothing. +\end{array} +\] +This paper studies the algebra that makes the implementation coherent, then +marks which claims are implemented, model checked in a finite scope, or still +benchmark obligations. \section{Problem Statement and Design Goals} -Rings addresses a narrow but recurring gap between existing decentralized -systems. Kademlia-derived systems provide scalable lookup, but the XOR metric -does not by itself give Rings the circular ownership law needed for successor -lists, replicated ownership, and interval-based placement. Relay networks and -mixnets improve metadata resistance, but they are not structured P2P ownership -systems. Blockchains provide global ordering, but embedding consensus in every -message or storage operation would turn Rings into a ledger rather than an -algebraic structured peer-to-peer substrate. - -The problem is therefore to specify a network object \(\RingsObj\) that -simultaneously supports self-certifying identity and delegated sessions, -structured lookup and resource ownership, browser-native and native transport -surfaces, application protocols with typed side effects, cryptographic protocols -over correct carriers, and bounded algebraic and operational obligations for -routing and state repair. - -This paper makes the following contributions. It presents Rings as an -algebraic structured peer-to-peer network, not merely as an overlay lookup -routine. It models the Rings identifier space as the additive cyclic group -\(R=\mathbb{Z}/2^{160}\mathbb{Z}\), not as a general finite field. It lifts -resource placement into \(\SetOverR\), so each protocol object carries an -explicit map into the overlay. It uses CorrectChord as the maintenance law -before introducing Rings-specific replication, storage, mailbox, relay, and -ranking semantics. It gives a writer effect monad for DHT transitions and a -TLA-style state relation for scoped model checking and trace replay. These -algebraic and operational artifacts are the core of the paper; the surrounding -text explains which parts are implemented, which parts are checked in bounded -models, and which parts remain future measurement obligations. +Existing decentralized systems supply only parts of the required object: +\[ +\begin{array}{rcl} +\mathsf{Kademlia}&\Rightarrow&\mathsf{lookup}_{XOR} + \not\Rightarrow\mathsf{clockwiseOwner},\\ +\mathsf{RelayMixnet}&\Rightarrow&\mathsf{pathPrivacy} + \not\Rightarrow\mathsf{structuredOwner},\\ +\mathsf{Ledger}&\Rightarrow&\mathsf{globalOrder} + \not\Rightarrow\mathsf{localOverlay}. +\end{array} +\] + +\begin{obligation}[Design target] +\[ +\begin{array}{rcl} +G_{id}&=&\mathsf{SelfCertID}\land\mathsf{DelegatedSession},\\ +G_{own}&=&\mathsf{StructuredOwner},\\ +G_{io}&=&\mathsf{BrowserNativeTransport},\\ +G_{eff}&=&\mathsf{TypedProtocolEffect},\\ +G_{cr}&=&\mathsf{CarrierCorrectCrypto},\\ +G_{rep}&=&\mathsf{BoundedRepairEvidence},\\ +\RingsObj&\models& +G_{id}\land G_{own}\land G_{io} +\land G_{eff}\land G_{cr}\land G_{rep}. +\end{array} +\] +\end{obligation} + +\begin{definition}[Methodology] +\[ +\begin{array}{rcl} +\mathsf{Method} +&=& +\mathsf{Mot} +\to\mathsf{Spec}_C +\to\mathsf{Alg}_P +\to\mathsf{ImplMap}\\ +&&{}\to\mathsf{Ev}_{\Gamma} +\to\mathsf{OpenObl},\\[3pt] +\Gamma&=&(|N|,\mathsf{topology},\mathsf{scheduler},\mathsf{fault}),\\[3pt] +\mathsf{Admit}(c) +&\Rightarrow& +c\in +\mathsf{Spec}\cup\mathsf{Impl}\\ +&&{}\cup\mathsf{Ev}_{\Gamma}\cup\mathsf{Obl}. +\end{array} +\] +The prose in this paper is used only where the construction needs motivation, +scope, or comparison; the claims themselves are carried by definitions, +constraints, invariants, algorithms, and obligations. +\end{definition} + +\[ +\begin{aligned} +\mathsf{Contribution}=\{& +R,\SetOverR,\Omega_N,\mathcal{R}_N, +\mathsf{RepKey}^{\rho},\\ +&\mathsf{T}^{\mathcal{E}}_A, +\mathsf{Explore}_{\Gamma}, +\mathsf{Report}_{Rings}\}. +\end{aligned} +\] \section{Algebraic System Model} @@ -242,11 +281,17 @@ \section{Algebraic System Model} 0\leq i<\rho\rangle. \end{array} \] -Storage redundancy is specified first as distinct placement keys. Effective -node-level redundancy depends on how those keys map through the live owner -function; two placement keys can collapse to the same live owner when the -topology is too small or poorly spaced. Successor lists remain the -CorrectChord safety root for topology maintenance, not the storage replica set. +\[ +\begin{array}{rcl} +P_k&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(k)),\\ +O_k&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(k)),\\ +|P_k|&=&\rho,\\ +|O_k|&\leq&\min(\rho,|N|),\\ +\mathsf{collapse}_{N,\rho}(k)&\Leftrightarrow&|O_k|<\rho. +\end{array} +\] +Thus replica keys specify redundancy intent; live owner images specify realized +redundancy. CorrectChord successor lists remain the topology safety root. \end{definition} \begin{definition}[Rings overlay object] @@ -1083,10 +1128,15 @@ \section{Ordering, Ranking, and Security} \label{security-table} \end{table} -Table~\ref{security-table} is a boundary summary, not a standalone proof of -Sybil resistance, anonymity, or denial-of-service tolerance. Those properties -depend on protocol-specific admission, ranking, relay, and resource-accounting -policies outside the base overlay. +\[ +\begin{array}{rcl} +\mathsf{Base}&\not\vdash& + \mathsf{Sybil}\land\mathsf{Anon}\land\mathsf{DoS},\\ +\mathsf{SecClaim}&\Rightarrow& + \mathsf{Adm}\land\mathsf{Rank} + \land\mathsf{Relay}\land\mathsf{Quota}. +\end{array} +\] \begin{obligation}[Replay rejection] \[ @@ -1102,11 +1152,11 @@ \section{Ordering, Ranking, and Security} \section{Verification Evidence and Evaluation Scope} -This section separates three things that are easy to conflate: algebraic -specification, scoped verification evidence, and performance evaluation. The -repository contains executable evidence for specific overlay, storage, and -message-flow obligations. It does not yet contain a wide-area Rings benchmark -that can replace a published Chord latency or churn experiment. +\[ + \mathsf{Spec}\neq\mathsf{Evidence}_{\Gamma}\neq\mathsf{Evaluation}. +\] +The repository contains executable evidence for finite overlay, storage, and +message-flow obligations; it does not yet contain a wide-area Rings benchmark. \begin{definition}[State relation] \[ @@ -1124,11 +1174,17 @@ \section{Verification Evidence and Evaluation Scope} \[ \mathsf{Explore}_{scope}=\mathsf{ModelCheck}(\to,\Gamma) \] -The exploration relation follows TLA+ style and Stateright execution for a -finite scope \(\Gamma\)~\cite{LamportSpecifyingSystems,Stateright}. The scope -must state the node count, topology shape, message scheduler, and failure model; -otherwise the result is only an implementation test, not a model-checking -claim. +\[ +\begin{array}{rcl} +\Gamma&=&(|N|,\mathsf{topology},\mathsf{scheduler},\mathsf{fault}),\\ +\mathsf{ModelClaim}(\Gamma) +&\Rightarrow& +\mathsf{finite}(\Gamma) +\land\mathsf{declared}(\Gamma). +\end{array} +\] +The relation follows TLA+ style and Stateright execution in the declared finite +scope~\cite{LamportSpecifyingSystems,Stateright}. \end{definition} \begin{invariant}[Effect refinement] @@ -1219,49 +1275,40 @@ \section{Verification Evidence and Evaluation Scope} \] \end{obligation} -Chord's published hop-count and churn measurements remain the baseline for the -underlying circular overlay~\cite{Chord}. A Rings performance claim must add -the measured cost of connection establishment, browser or native transport, -cryptographic framing, storage replication, and application witnesses on a -specified implementation build. +\[ +\begin{array}{rcl} +\vec{T}&=&(T_{conn},T_{hop},T_{crypto},T_{app},T_{witness}),\\ +\mathsf{PerfClaim}_{R}&\Rightarrow&\mathsf{Measure}_{build}(\vec{T}),\\ +\mathsf{Baseline}_{C}&=&\mathsf{hop/churn}. +\end{array} +\] +Chord remains the overlay baseline~\cite{Chord}; Rings performance requires +Rings-specific measurements. \section{Related Work} -Distributed hash tables give Rings its closest technical ancestry. IPFS and -libp2p use Kademlia-derived routing, where distance is measured by XOR and -routing state is organized into buckets~\cite{Kademlia,IPFS,Libp2p}. This is a -strong fit for content-addressed lookup, but Rings needs a different law: the -owner of a DID or VID is the first live node clockwise from that point, topology -repair follows successor-list maintenance, and storage redundancy places -affine rotations of an entry key around the ring. The paper therefore uses -Chord's circular order as the base model, then uses Zave's CorrectChord results -to avoid treating the original Chord maintenance protocol as already correct -under churn~\cite{Chord,ZaveChordCorrect}. - -Relay anonymity systems take a different route. Tor and Nym route traffic over -selected relay paths and focus on hiding communication metadata from local -observers or intermediate services~\cite{TorNetwork,NymNetwork}. Rings does -not replace these systems as anonymity systems. It instead specifies a -structured ownership substrate on which relay, mailbox, and hidden-service style -protocols can be written. This distinction matters: a relay path can carry -traffic, but it does not define the algebraic owner of a DID, mailbox, chunk, or -service descriptor. - -Blockchain and account-based decentralized systems provide another partial -answer. A ledger can publish names, order events, and make writes globally -auditable, but the price is global consensus on operations that often only need -local routing, replicated storage, or protocol-specific ordering. Rings keeps -global consensus outside the base overlay. When a protocol needs stronger -ordering evidence, it uses sidecar witnesses rather than changing the overlay -into a blockchain. - -Browser-native networking is also part of the design space. WebRTC gives -browsers a standardized peer transport, while WebAssembly gives portable code a -browser execution target~\cite{webrtc-standard,webassembly}. Rings treats -these as adapters for the same abstract protocol object, not as separate -networks. The same DID/session, Chord owner, effect, and resource-placement -laws should hold for browser nodes and native nodes; only the IO interpreter -changes. +Use the comparison coordinates +\[ + \mathsf{Axis}(S)= + (m,o,q,r). +\] +\[ +\begin{array}{c|c} +S&\mathsf{Axis}(S)\\ \hline +\mathsf{Kad}&(XOR,\mathsf{bucket},\bot,\mathsf{native})\\ +\mathsf{Chord}&(\mathsf{circ},\mathsf{succ},\bot,\mathsf{native})\\ +\mathsf{Tor/Nym}&(\mathsf{path},\bot,\bot,\mathsf{relay})\\ +\mathsf{Ledger}&(\bot,\mathsf{acct},\mathsf{global},\mathsf{repl})\\ +\mathsf{Rings}&(\mathsf{circ},\operatorname{owner}_N,\mathsf{sidecar}, + \mathsf{web}\cup\mathsf{native}) +\end{array} +\] +Kademlia/IPFS/libp2p supply scalable lookup but not the clockwise owner law +needed here~\cite{Kademlia,IPFS,Libp2p}. Tor and Nym supply relay-path +privacy, not structured ownership~\cite{TorNetwork,NymNetwork}. Ledgers +supply global order; Rings keeps ordering outside the base overlay. WebRTC and +WebAssembly are runtime adapters, so the same protocol object is interpreted in +browser and native environments~\cite{webrtc-standard,webassembly}. \begin{table}[htbp] \centering @@ -1285,11 +1332,8 @@ \section{Related Work} \section{Conclusion} -Rings is an algebraic structured peer-to-peer network: structured because -ownership, routing, affine storage replication, and repair are defined over -CorrectChord's circular overlay, and algebraic because each layer preserves an -explicit carrier or morphism rather than hiding semantics inside ad hoc network -procedures. +The paper's claim is the following structured object, not an informal bundle of +network mechanisms: \[ \RingsObj= From 890f635dd8266c351b4c6724d54576223541ce35 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 01:20:39 +0800 Subject: [PATCH 03/19] Address Rings paper review comments --- papers/README.md | 1 - papers/imgs/rings/path.png | Bin 150745 -> 0 bytes papers/rings.pdf | Bin 116978 -> 118719 bytes papers/rings.tex | 73 +++++++++++++++++++++++++++++-------- 4 files changed, 58 insertions(+), 16 deletions(-) delete mode 100644 papers/imgs/rings/path.png diff --git a/papers/README.md b/papers/README.md index b0071ac7b..57dbc9db3 100644 --- a/papers/README.md +++ b/papers/README.md @@ -5,7 +5,6 @@ This directory contains the repository-owned Rings whitepaper copy. - `rings.pdf`: compiled Rings whitepaper. - `rings.tex`: LaTeX source for the Rings whitepaper. - `cites.bib`: bibliography used by `rings.tex`. -- `imgs/rings/path.png`: image asset referenced by `rings.tex`. 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a/papers/rings.tex b/papers/rings.tex index be79252ab..8e56248d3 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -178,14 +178,14 @@ \section{Problem Statement and Design Goals} \to\mathsf{Spec}_C \to\mathsf{Alg}_P \to\mathsf{ImplMap}\\ -&&{}\to\mathsf{Ev}_{\Gamma} -\to\mathsf{OpenObl},\\[3pt] +&&{}\to\mathsf{Evidence}_{\Gamma} +\to\mathsf{Obligation},\\[3pt] \Gamma&=&(|N|,\mathsf{topology},\mathsf{scheduler},\mathsf{fault}),\\[3pt] \mathsf{Admit}(c) &\Rightarrow& c\in \mathsf{Spec}\cup\mathsf{Impl}\\ -&&{}\cup\mathsf{Ev}_{\Gamma}\cup\mathsf{Obl}. +&&{}\cup\mathsf{Evidence}_{\Gamma}\cup\mathsf{Obligation}. \end{array} \] The prose in this paper is used only where the construction needs motivation, @@ -891,17 +891,27 @@ \section{DID and Resource Algebra} \begin{array}{rcl} K_{\nu,x}&=&\operatorname{replicaKeys}(H_\nu(x)),\\[2pt] P_{\nu,x}&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(H_\nu(x))),\\[2pt] -O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(H_\nu(x))),\\[2pt] -U_{\nu,x}&=&\operatorname{owner}_N[K_{\nu,x}],\\[2pt] \operatorname{Inv}_{place} &\equiv& -\forall \nu,x.\; -K_{\nu,x}\subseteq P_{\nu,x} -\land U_{\nu,x}\subseteq O_{\nu,x}. +\forall \nu,x.\;K_{\nu,x}\subseteq P_{\nu,x}. \end{array} \] \end{invariant} +\begin{obligation}[Replica realization] +\[ +\begin{array}{rcl} +O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(H_\nu(x))),\\ +L_{\nu,x}&=&|O_{\nu,x}|,\\ +\mathsf{FullRed}_{\nu,x}&\Leftrightarrow&L_{\nu,x}=\min(\rho,|N|),\\ +\mathsf{Collapse}_{\nu,x}&\Leftrightarrow&L_{\nu,x}<\min(\rho,|N|),\\ +\mathsf{LiveClaim}_{\nu,x}(\rho)&\Rightarrow&\mathsf{FullRed}_{\nu,x},\\ +\mathsf{Report}_{Rings}&\ni& + |\{(\nu,x):\mathsf{Collapse}_{\nu,x}\}|. +\end{array} +\] +\end{obligation} + \begin{definition}[Mailbox] \[ \begin{array}{rcl} @@ -978,21 +988,46 @@ \section{Cryptographic Carriers and Traffic} \begin{definition}[Signed encrypted frame] \[ - f=(sid,seq,last,cipher,pk_s,\sigma_s,win). + f=(sid,seq,last,cipher,pk_s,\sigma_s). \] \[ \begin{aligned} m_f&=sid\Vert seq\Vert last\Vert cipher,\\ - \operatorname{FrameValid}(f) + \operatorname{FrameValid}_{\Delta}(f) \Leftrightarrow\;&V(pk_s,\sigma_s,m_f)=\top\\ &\land\; \operatorname{Session}(D(pk_s),sid,e)\\ &\land\; - \operatorname{SeqOK}(sid,seq,last,win). + \operatorname{SeqOK}_{\Delta}(seq,last). \end{aligned} \] \end{definition} +\begin{definition}[Receiver sequence policy] +\[ + \Delta=(next,final,closed,pending,seen,w). +\] +\[ +\begin{array}{rcl} +\mathsf{NoFuture}_{\Delta}(seq)&\Leftrightarrow& + \neg\exists p\in pending.\;p>seq,\\ +\mathsf{Dup}_{\Delta}(seq)&\Leftrightarrow& + seq\in seen\cup pending,\\ +\mathsf{New}_{\Delta}(seq,last)&\Leftrightarrow& + seq\notin seen\cup pending\\ +&&{}\land\neg closed\\ +&&{}\land seq-next\leq w\\ +&&{}\land(final=\bot\lor seq\leq final)\\ +&&{}\land(last\Rightarrow\mathsf{NoFuture}_{\Delta}(seq)),\\ +\operatorname{SeqOK}_{\Delta}(seq,last)&\Leftrightarrow& + \mathsf{Dup}_{\Delta}(seq)\\ +&&{}\lor\mathsf{New}_{\Delta}(seq,last),\\ +\mathsf{Dup}_{\Delta}(seq)&\Rightarrow&\mathsf{emit}=\epsilon. +\end{array} +\] +Here \(w\) is receiver policy, not a signed wire field. +\end{definition} + \begin{definition}[Secret sharing placement] \[ \begin{array}{rcl} @@ -1119,7 +1154,7 @@ \section{Ordering, Ranking, and Security} \hline Attack & Predicate & Required boundary \\ \hline Sybil & many DIDs, one actor & admission and ranking policy \\ -Replay & stale valid $\sigma$ & TTL, stream order, final marker \\ +Replay & stale valid $\sigma$ & TTL, nonce cache, stream/final \\ MITM & wrong key for DID & DID proof and signed envelope \\ DoS & unbounded resource use & quotas and chunk bounds \\ \hline @@ -1131,7 +1166,7 @@ \section{Ordering, Ranking, and Security} \[ \begin{array}{rcl} \mathsf{Base}&\not\vdash& - \mathsf{Sybil}\land\mathsf{Anon}\land\mathsf{DoS},\\ + \mathsf{SybilResist}\land\mathsf{Anon}\land\mathsf{DoSResist},\\ \mathsf{SecClaim}&\Rightarrow& \mathsf{Adm}\land\mathsf{Rank} \land\mathsf{Relay}\land\mathsf{Quota}. @@ -1172,7 +1207,7 @@ \section{Verification Evidence and Evaluation Scope} } \] \[ - \mathsf{Explore}_{scope}=\mathsf{ModelCheck}(\to,\Gamma) + \mathsf{Explore}_{\Gamma}=\mathsf{ModelCheck}(\to,\Gamma) \] \[ \begin{array}{rcl} @@ -1290,7 +1325,15 @@ \section{Related Work} Use the comparison coordinates \[ \mathsf{Axis}(S)= - (m,o,q,r). + (\mu,\omega,\chi,\lambda). +\] +\[ +\begin{array}{rcl} +\mu&=&\mathsf{metric},\\ +\omega&=&\mathsf{owner},\\ +\chi&=&\mathsf{order},\\ +\lambda&=&\mathsf{runtime}. +\end{array} \] \[ \begin{array}{c|c} From 0950d50a518f50de6967c1f70f2418b3fb5e44d0 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 02:18:28 +0800 Subject: [PATCH 04/19] Restore formal Chord performance baseline --- papers/rings.pdf | Bin 118719 -> 119467 bytes 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Kung can be reached at ryankung@ieee.org. Manuscript created February 8, 2023; last updated July 4, 2026.}} +\thanks{Ryan J. Kung can be reached at ryankung@ieee.org. Manuscript created February 8, 2023; last updated July 5, 2026.}} \title{\huge Rings: An Algebraic Structured Peer-to-Peer Network\\ for Decentralized Identity and Resource Ownership} \date{} @@ -1286,53 +1286,141 @@ \section{Verification Evidence and Evaluation Scope} \] \end{definition} -\begin{definition}[Chord performance baseline] +\begin{definition}[Benchmark data model] \[ \begin{array}{rcl} -\operatorname{fail}(Q,F)&=&\dfrac{|F|}{|Q|},\\[8pt] -\operatorname{timeout}(Q)&=&\dfrac{1}{|Q|}\sum_{q\in Q}to(q),\\[8pt] -\eta&=&(|N|,\mathsf{churn},\mathsf{stabilize},\mathsf{loss}),\\[4pt] -B_C(\eta)&=& - (\mathbb{E}[h_C], - \operatorname{timeout}(Q_C), - \operatorname{fail}(Q_C,F_C)),\\[4pt] -\mathbb{E}[h_C]&\in&O(\log |N|). +F_X(\eta;D)&\subseteq&Q_X(\eta;D),\\ +to_X&:&Q_X(\eta;D)\to\mathbb{N},\\ +\phi_X(\eta;D)&=&|F_X(\eta;D)|/|Q_X(\eta;D)|,\\[3pt] +\bar{to}_X(\eta;D)&=&|Q_X|^{-1}\sum_{q\in Q_X}to_X(q),\\[3pt] +B_X(\eta;D)&=& + (\mathbb{E}[h_X^f\mid\eta,D], + \mathbb{E}[h_X^r\mid\eta,D],\\ +&& \bar{to}_X(\eta;D),\phi_X(\eta;D)),\\ +h_X^r&=&h_X^f+1. \end{array} \] +\[ +\begin{array}{rcl} +D_{656}&=&D_C^{paper}\cup D_C^{1600}\cup D_R^{docker},\\ +D_C^{paper}&=&\{C_{II},C_{III},C_{IV},C_{8},C_{9},C_{10}\},\\ +D_C^{1600}&=&\{\mathsf{maintained},\mathsf{stale}\},\\ +D_R^{docker}&=&\{\mathsf{convergence},\mathsf{transport}\}. +\end{array} +\] +\[ +\begin{array}{rcl} +C_{II}&:&(N,r,|Q|)=(1000,20,10^4),\\ +C_{III}&:&(N,r,\lambda) \simeq (1000,20,0.05..0.40),\\ +D_C^{1600}&:&(N,r,m,L)=(1600,3,160,64). +\end{array} +\] +\[ + D_C^{paper}\not\subset\mathsf{Impl}_{Rings}, + \qquad + D_R^{docker}\subset\mathsf{Impl}_{Rings}. +\] \end{definition} +\begin{table}[htbp] +\centering +\scriptsize +\setlength{\tabcolsep}{2pt} +\begin{tabular}{c|c|c|c|c} +\hline +$\eta$ & $N,r$ & $\mathbb{E}[h_C^f]$ & +$\operatorname{timeout}_C$ & $10^4\operatorname{fail}_C$ \\ \hline +$C_{II},f=0$ & $1000,20$ & 3.815 & 0.000 & 0.0 \\ +$C_{II},f=.10$ & $1000,20$ & 4.007 & 0.522 & 0.0 \\ +$C_{II},f=.20$ & $1000,20$ & 4.177 & 1.071 & 0.0 \\ +$C_{II},f=.30$ & $1000,20$ & 4.354 & 1.830 & 0.0 \\ +$C_{II},f=.40$ & $1000,20$ & 4.791 & 3.700 & 0.0 \\ +$C_{II},f=.50$ & $1000,20$ & 5.345 & 6.565 & 0.0 \\ +$C_{III},\lambda=.05$ & $\simeq1000,20$ & 3.905 & 0.076 & 7.0 \\ +$C_{III},\lambda=.10$ & $\simeq1000,20$ & 3.949 & 0.168 & 19.0 \\ +$C_{III},\lambda=.15$ & $\simeq1000,20$ & 4.044 & 0.272 & 18.0 \\ +$C_{III},\lambda=.20$ & $\simeq1000,20$ & 4.094 & 0.335 & 35.0 \\ +$C_{III},\lambda=.25$ & $\simeq1000,20$ & 4.128 & 0.405 & 36.0 \\ +$C_{III},\lambda=.30$ & $\simeq1000,20$ & 4.221 & 0.501 & 47.0 \\ +$C_{III},\lambda=.35$ & $\simeq1000,20$ & 4.308 & 0.599 & 60.0 \\ +$C_{III},\lambda=.40$ & $\simeq1000,20$ & 4.345 & 0.656 & 58.0 \\ +\hline +\end{tabular} +\caption{Chord-paper-aligned rows in +\texttt{chord-paper-sim-2026-07-05.jsonl}.} +\label{chord-paper-data-table} +\end{table} + +\begin{table}[htbp] +\centering +\scriptsize +\setlength{\tabcolsep}{1.5pt} +\begin{tabular}{c|c|c|c|c|c} +\hline +$\eta$ & $M$ & $\bar h^f/\bar h^r$ & +$ok$ & $\bar{to}$ & $10^4\phi$ \\ \hline +stable & m & $4.469/5.469$ & 1.000 & 0.000 & 0.0 \\ +$f=.10$ & m & $4.394/5.394$ & 1.000 & 0.000 & 0.0 \\ +$f=.20$ & m & $4.316/5.316$ & 1.000 & 0.000 & 0.0 \\ +$\chi=.05$ & m & $4.465/5.465$ & 1.000 & 0.000 & 0.0 \\ +$\chi=.40$ & m & $4.470/5.470$ & 1.000 & 0.000 & 0.0 \\ +$f=.10$ & s & $4.758/5.758$ & .990 & .734 & 98.2 \\ +$f=.20$ & s & $5.186/6.186$ & .969 & 1.890 & 314.7 \\ +$\chi=.05$ & s & $4.617/5.617$ & .945 & .361 & 546.2 \\ +$\chi=.40$ & s & $5.746/6.746$ & .484 & 4.604 & 5161.1 \\ +\hline +\end{tabular} +\caption{Current Rings-parameter Chord baselines +($m=$maintained, $s=$stale; churn endpoints) from +\texttt{dummy-paper-scale-2026-07-05.jsonl}.} +\label{rings-param-chord-data-table} +\end{table} + \begin{obligation}[Benchmark report] \[ \begin{aligned} \mathsf{Report}_{Rings} = (&N,\rho,r,\mathsf{transport},\mathsf{runtime},\\ - &\mathsf{scheduler},\vec{T}_R, - \operatorname{timeout}(Q_R), - \operatorname{fail}(Q_R,F_R)). + &\mathsf{scheduler},\vec{T}_{total}, + B_R(\eta_R;D_R^{docker})). \end{aligned} \] \[ - B_C(\eta) + B_C(\eta;D_C^{paper}) \not\equiv - \mathsf{Report}_{Rings}. + B_R(\eta_R;D_R^{docker}). \] \end{obligation} \[ \begin{array}{rcl} -\vec{T}_R&=&(T_{conn},h_R T_{hop},T_{crypto},\\ +\vec{T}_{total}&=&(T_{conn},hT_{hop},T_{crypto},\\ &&T_{app},T_{witness}),\\ +\sum_i\vec{T}_{total,i}&=&T_{total},\\ \mathsf{Overhead}_{R/C} &=&(T_{conn},T_{crypto},T_{app},\\ &&T_{witness},\mathsf{runtime}),\\ \mathsf{PerfClaim}_{R} &\Rightarrow& - \mathsf{Measure}_{build}(\mathsf{Report}_{Rings})\\ -&&{}\wedge\mathsf{Cite}(B_C). + \mathsf{Measure}_{build}(B_R)\\ +&&{}\wedge\mathsf{Cite}(B_C^p),\\ +D_C^p&=&D_C^{paper},\\ +B_C^p&=&B_C(\eta;D_C^p). +\end{array} +\] +\[ +\begin{array}{rcl} +D_R^{conv}&=& + (16,309.532s,0/16,3/16,\\ +&& .194,1.026,8058.6),\\ +D_R^{tx}&=& +\{(1,10.46),(16,107.35),\\ +&& (64,90.36)\}_{\mathrm{KiB},\mathrm{Mbps}}. \end{array} \] -Chord supplies the lookup/churn baseline~\cite{Chord}; Rings performance -requires Rings-specific measurements. +Chord supplies the lookup/churn baseline~\cite{Chord}; Rings supplies runtime +evidence only through Rings measurements. The fresh Docker/WebRTC cluster above +is convergence evidence, not a steady-state lookup result. \section{Related Work} From c7df04ee69bfa3fd360b9fa658dd6d1a59454740 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 21:30:10 +0800 Subject: [PATCH 06/19] Explain benchmark formulas and tables --- papers/rings.pdf | Bin 131569 -> 132947 bytes papers/rings.tex | 18 ++++++++++++++++-- 2 files changed, 16 insertions(+), 2 deletions(-) diff --git a/papers/rings.pdf b/papers/rings.pdf index 0ba1c55d159dc6e0d125f20588089f904dd58fd1..44266ce2ab42a3c706ccd498c73c446a27fb137e 100644 GIT binary patch delta 82082 zcmY&xI0!BIq6-Q59Rebm5|hx;(?zhw6ltn|viW={`>l#$t?EWE-L^e4dOSw(l|_xynu{qE1J z&0qR&k4C>JD^mL&J$aP+T|H1{%51B+iRUt}f*PMU`&$jK6Ih?KkV$q*x<~?bQGV$6 zvYzEg!3x$)J?X$%Apj>c>G)GmZ1+TcoZS7%w-Zmh*#vv2Uz?6;0_;ME7E$T>UFu#m zgD=_G5>s-o>fJ!npi^sls!==tuLNbAK1%&g-c43-hmX?*PEIk$A&TEv*Lb+)GeYPH zlF#S!^W5~(6jG|@*Q&a=vP$bl 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znp2O5aBI5bTTdsAsY&%Wsd`-Z&1U_dF+e*rhEdfK=I+~G>U4anJgJRH4wSk>`%0%d> Date: Tue, 7 Jul 2026 04:24:05 +0800 Subject: [PATCH 07/19] Strengthen Rings paper review response --- papers/cites.bib | 137 +++++++ papers/rings.pdf | Bin 132947 -> 150829 bytes papers/rings.tex | 1017 +++++++++++++++++++++++++++------------------- 3 files changed, 747 insertions(+), 407 deletions(-) diff --git a/papers/cites.bib b/papers/cites.bib index cf83b9b6b..8fbbd5814 100644 --- a/papers/cites.bib +++ b/papers/cites.bib @@ -162,3 +162,140 @@ @misc{webassembly year = {2019}, note = {\url{https://www.w3.org/TR/2019/REC-wasm-core-1-20191205/}} } + +@inproceedings{SFS, + author = {David Mazi{\`e}res and Michael Kaminsky and M. Frans Kaashoek and Emmett Witchel}, + title = {Separating Key Management from File System Security}, + booktitle = {Proceedings of the 17th ACM Symposium on Operating Systems Principles}, + pages = {124--139}, + year = {1999}, + doi = {10.1145/319151.319160} +} + +@misc{DIDCore, + author = {{W3C Decentralized Identifier Working Group}}, + title = {Decentralized Identifiers ({DIDs}) v1.0: Core Architecture, Data Model, and Representations}, + howpublished = {W3C Recommendation}, + year = {2022}, + note = {\url{https://www.w3.org/TR/2022/REC-did-core-20220719/}} +} + +@inproceedings{Pastry, + author = {Antony Rowstron and Peter Druschel}, + title = {Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems}, + booktitle = {Middleware 2001}, + series = {Lecture Notes in Computer Science}, + volume = {2218}, + pages = {329--350}, + year = {2001}, + doi = {10.1007/3-540-45518-3_18} +} + +@article{Tapestry, + author = {Ben Y. Zhao and Ling Huang and Jeremy Stribling and Sean C. Rhea and Anthony D. Joseph and John Kubiatowicz}, + title = {Tapestry: A Resilient Global-Scale Overlay for Service Deployment}, + journal = {IEEE Journal on Selected Areas in Communications}, + volume = {22}, + number = {1}, + pages = {41--53}, + year = {2004} +} + +@inproceedings{CAN, + author = {Sylvia Ratnasamy and Paul Francis and Mark Handley and Richard Karp and Scott Shenker}, + title = {A Scalable Content-Addressable Network}, + booktitle = {Proceedings of ACM SIGCOMM}, + pages = {161--172}, + year = {2001}, + doi = {10.1145/383059.383072} +} + +@inproceedings{SitMorrisDHTSecurity, + author = {Emil Sit and Robert Morris}, + title = {Security Considerations for Peer-to-Peer Distributed Hash Tables}, + booktitle = {Peer-to-Peer Systems}, + series = {Lecture Notes in Computer Science}, + volume = {2429}, + pages = {261--269}, + year = {2002}, + doi = {10.1007/3-540-45748-8_25} +} + +@inproceedings{SecureRoutingOverlays, + author = {Miguel Castro and Peter Druschel and Ayalvadi Ganesh and Antony Rowstron and Dan S. Wallach}, + title = {Secure Routing for Structured Peer-to-Peer Overlay Networks}, + booktitle = {5th USENIX Symposium on Operating Systems Design and Implementation}, + year = {2002}, + doi = {10.1145/844128.844156} +} + +@inproceedings{SybilDouceur, + author = {John R. Douceur}, + title = {The Sybil Attack}, + booktitle = {Peer-to-Peer Systems}, + series = {Lecture Notes in Computer Science}, + volume = {2429}, + pages = {251--260}, + year = {2002}, + doi = {10.1007/3-540-45748-8_24} +} + +@inproceedings{EclipseOverlay, + author = {Atul Singh and Tsuen-Wan J. Ngan and Peter Druschel and Dan S. Wallach}, + title = {Eclipse Attacks on Overlay Networks: Threats and Defenses}, + booktitle = {25th IEEE International Conference on Computer Communications}, + pages = {1--12}, + year = {2006} +} + +@misc{WebRTCMeasurement, + author = {Kosuke Nakagawa and Manabu Tsukada and Keiichi Shima and Hiroshi Esaki}, + title = {{WebRTC}-based Measurement Tool for Peer-to-Peer Applications and Preliminary Findings with Real Users}, + howpublished = {arXiv:2112.02163}, + year = {2021}, + note = {\url{https://arxiv.org/abs/2112.02163}} +} + +@article{LampsonProtection, + author = {Butler W. Lampson}, + title = {Protection}, + journal = {ACM SIGOPS Operating Systems Review}, + volume = {8}, + number = {1}, + pages = {18--24}, + year = {1974}, + doi = {10.1145/775265.775268} +} + +@article{AbadiAccessControl, + author = {Mart{\'i}n Abadi and Michael Burrows and Butler Lampson and Gordon Plotkin}, + title = {A Calculus for Access Control in Distributed Systems}, + journal = {ACM Transactions on Programming Languages and Systems}, + volume = {15}, + number = {4}, + pages = {706--734}, + year = {1993}, + doi = {10.1145/155183.155225} +} + +@article{MoggiMonads, + author = {Eugenio Moggi}, + title = {Notions of Computation and Monads}, + journal = {Information and Computation}, + volume = {93}, + number = {1}, + pages = {55--92}, + year = {1991}, + doi = {10.1016/0890-5401(91)90052-4} +} + +@inproceedings{PlotkinPretnarEffects, + author = {Gordon Plotkin and Matija Pretnar}, + title = {Handlers of Algebraic Effects}, + booktitle = {Programming Languages and Systems}, + series = {Lecture Notes in Computer Science}, + volume = {5502}, + pages = {80--94}, + year = {2009}, + doi = {10.1007/978-3-642-00590-9_7} +} diff --git a/papers/rings.pdf b/papers/rings.pdf index 44266ce2ab42a3c706ccd498c73c446a27fb137e..53190d4b6959468b6b8aefe1a43cdb400813886d 100644 GIT binary patch delta 146063 zcmZsiQ*)pVw5%t#F|j!l+qP}nw%$x^+qP}nwmIR%#`#XwzStMLuhuW$8pt5n;eD<#p zf|_$9N2d;SAymPXP@JH22Z#2zgGiXk=r_RgK6!A_2tA7#g_MGN4W+=UK=M`xxCCtCQ=`V`a8&=` z+S6jklQRCi2Jb*6BxS{pcquOFmhpKY_1G|`9?0PL9{HIBuZD9`9KcymWOpo0Nu6~^ z^E3Td37G63S4FIWgqPa|{&>iepG*KMrYN;6Ii_1(L^%;)v?s&;Y8*IK^(2G=9^O0^ zMFN&tG!RC<9C&P_;?nq1Phv+SDEefo*i#0xlJ)q$)fn$p(#&1sYtw^xB#f2-1zY|^*pdxI%MB~ z9N2PAqV2Fva;uI9pRSQ)3pW zG+`Ty-G;E~T-VL*qIJJ_eG4!IRKAs6{DH9__VD%f_5s}9%@l6z5Xl@E z)iIoEo6vpZq`kcE*9hr5)j;aP1@k*oz#1Z}6~`7hh!R&eX)ECDvvyVu@l>AOOys6{ zR50CCK-;Qp-h}8a74i^d--2Ishd0%`ezIts$P%=JlEXojbNME4^2@YGEE7FN}vJIffpew&vQh<}rRXQfM zQg*ahx!H;o)??xnr>V~uevZ665zWWLt8-puWYsO04##5?67i!2RyHbSq(hz 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+&&{}\land\mathsf{EffectTyped},\\ +\mathsf{Claim}_{ledger} +&=&\mathsf{EvidenceScoped}_{\Gamma}\land\mathsf{LedgerDisc}_{Rings},\\ \mathsf{CryptoCarrier}\cap R&=&\varnothing. \end{array} \] @@ -259,21 +260,21 @@ \section{Problem Statement and Design Goals} \mathsf{WebRTC},\mathsf{CRDT}\},\\ \mathsf{New}_{Rings} &=(\Omega_N,\mathsf{PMor},\mathsf{CarrierSep}, - \mathsf{Ledger}_{\Gamma}). + \mathsf{LedgerDisc}_{Rings}). \end{aligned} \] \[ +\begin{aligned} \mathsf{Contribution}_{Rings} -\equiv -\mathsf{Reuse}_{Rings} -\oplus -\mathsf{New}_{Rings} -\models -\mathsf{Main}_{Rings}. +&\equiv +\mathsf{Reuse}_{Rings}\oplus\mathsf{New}_{Rings}\\ +&\models +\mathsf{Core}_{Rings}\land\mathsf{LedgerDisc}_{Rings}. +\end{aligned} \] -The formal content of \(\mathsf{Main}_{Rings}\) is -Theorem~\ref{thm:carrier-separated-ownership}; all performance claims remain -outside it unless admitted by the evidence ledger. +The formal theorem is Theorem~\ref{thm:carrier-separated-ownership}; +\(\mathsf{LedgerDisc}_{Rings}\) is the admission discipline, not a performance +theorem. \end{definition} \section{Algebraic System Model} @@ -774,30 +775,38 @@ \section{Category and Effects} &\equiv \forall\nu,s,i.\;\tau_\nu(s,i)\in \mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu),\\ -\mathsf{LedgerLaw} -&\equiv -\forall c.\;c\in\mathsf{Evidence}_\Gamma -\Rightarrow \mathsf{finite}(\Gamma)\land\mathsf{declared}(\Gamma),\\ -\mathsf{Main}_{Rings} +\mathsf{Core}_{Rings} &\equiv \mathsf{OwnerLaw}\land\mathsf{MorphLaw} -\land\mathsf{EffectLaw}\land\mathsf{LedgerLaw}. +\land\mathsf{EffectLaw}. \end{aligned} \] -Furthermore, -\[ - \forall c\in\NonClaim.\quad \mathsf{Main}_{Rings}\not\vdash c . -\] \end{theorem} \begin{proof} OwnerLaw is Lemma~\ref{lem:owner-totality}; MorphLaw is Lemma~\ref{lem:morphism-preservation}; EffectLaw is -Lemma~\ref{lem:effect-confinement}. LedgerLaw follows from the claim-ledger -methodology. \(\NonClaim\) is disjoint from -\(\mathsf{Spec}\cup\mathsf{Impl}\cup\mathsf{Evidence}_\Gamma\); therefore no -non-claim follows from the theorem. +Lemma~\ref{lem:effect-confinement}. \end{proof} +\begin{constraint}[Claim ledger discipline] +\label{constraint:claim-ledger} +\[ +\begin{array}{rcl} +\mathsf{Admit}_{R}(c,k)&\Rightarrow& +k\in\mathsf{ClaimKind},\\ +\mathsf{Admit}_{R}(c,\mathsf{Evidence}_{\Gamma})&\Rightarrow& +\mathsf{finite}(\Gamma)\land\mathsf{declared}(\Gamma),\\ +\mathsf{Reject}_{R}(c)&\Leftrightarrow&c\in\NonClaim,\\ +\mathsf{Reject}_{R}(c)&\Rightarrow& +\neg\exists k.\;\mathsf{Admit}_{R}(c,k),\\ +\mathsf{LedgerDisc}_{Rings} +&=&\mathsf{Admit}_{R}\land\mathsf{Reject}_{R}. +\end{array} +\] +Thus non-claims are excluded by the admission judgment; they are not proved +unreachable by Theorem~\ref{thm:carrier-separated-ownership}. +\end{constraint} + \section{Chord Overlay} \[ @@ -1373,6 +1382,12 @@ \section{Ordering, Ranking, and Security} \begin{definition}[Security and policy boundary] \[ \begin{array}{rcl} +\mathsf{AllowedRelay}&\subseteq&\mathsf{Path},\\ +\operatorname{use},\operatorname{limit} +&:&\mathsf{User}\times\mathsf{Epoch}\to\mathbb{N},\\ +\mathsf{SecEvent}&\subseteq& +X_D\times\mathsf{Epoch}\times\mathsf{RankEvent}\\ +&&{}\times\mathsf{RelayFrame}\times\mathsf{User},\\ \mathsf{P}_{adm}&:&X_D\times\mathsf{Epoch}\to\{\top,\bot\},\\ \mathsf{P}_{rank}(q)&\Leftrightarrow& \operatorname{RankValid}(q)\land weight(q)\leq W_{max},\\ @@ -1383,8 +1398,10 @@ \section{Ordering, Ranking, and Security} \operatorname{use}(u,e)\leq \operatorname{limit}(u,e),\\ z&=&(d,e,q,r,u),\\ \mathsf{Policy}_{R}(z)&\Leftrightarrow& - \mathsf{P}_{adm}(d,e)\land\mathsf{P}_{rank}(q)\\ -&&{}\land\mathsf{P}_{relay}(r)\land\mathsf{P}_{quota}(u,e). + \mathsf{P}_{adm}(d,e)\\ +&&{}\land\mathsf{P}_{rank}(q)\\ +&&{}\land\mathsf{P}_{relay}(r)\\ +&&{}\land\mathsf{P}_{quota}(u,e). \end{array} \] \[ @@ -1580,8 +1597,8 @@ \section{Verification Evidence and Evaluation Scope} \begin{definition}[Benchmark data model] \[ \begin{array}{rcl} -\eta&=&(N,r,m,L,f,\lambda,\chi,M),\\ -M&\in&\{\mathsf{maintained},\mathsf{stale}\},\\ +\eta&=&(N,r,m,L,f,\lambda,\gamma,\mu_B),\\ +\mu_B&\in&\{\mathsf{maintained},\mathsf{stale}\},\\ \pi(d)&\in&\mathsf{Prov},\\ \mathsf{Regen}(d)&\Rightarrow& \mathsf{src}(d)\neq\bot\land\mathsf{rev}(d)\neq\bot\\ @@ -1608,8 +1625,14 @@ \section{Verification Evidence and Evaluation Scope} D_{reported}&=&D_C^{656}\uplus D_R^{docker},\\ D_{all}&=&D_{external}\uplus D_{reported},\\ D_{admit}&=&\{d\in D_{all}:\mathsf{AdmittedEval}(d)\},\\ -D_C^{paper}&=&\{C_{II},C_{III},C_{IV},C_{8},C_{9},C_{10}\},\\ -D_C^{656}&=&\{\mathsf{maintained},\mathsf{stale}\},\\ +\mathcal{F}_{II}&=&\{0,.10,.20,.30,.40,.50\},\\ +\Lambda_{III}&=&\{.05,.10,.15,.20,.25,.30,.35,.40\},\\ +D_C^{paper}&=&\{C_{II}(f):f\in\mathcal{F}_{II}\}\\ +&&{}\uplus\{C_{III}(\lambda):\lambda\in\Lambda_{III}\},\\ +D_{maint}^{656}&=&\{stable,f_{.10},f_{.20},\gamma_{.05},\gamma_{.40}\},\\ +D_{stale}^{656}&=&\{f_{.10},f_{.20},\gamma_{.05},\gamma_{.40}\},\\ +D_C^{656}&=&(D_{maint}^{656}\times\{\mathsf{maintained}\})\\ +&&{}\uplus(D_{stale}^{656}\times\{\mathsf{stale}\}),\\ D_R^{docker}&=&\{D_R^{conv},D_R^{tx}\}. \end{array} \] @@ -1683,12 +1706,12 @@ \section{Verification Evidence and Evaluation Scope} stable & maint. & $4.469/5.469$ & 1.000 & 0.000 & 0.0 \\ $f=.10$ & maint. & $4.394/5.394$ & 1.000 & 0.000 & 0.0 \\ $f=.20$ & maint. & $4.316/5.316$ & 1.000 & 0.000 & 0.0 \\ -$\chi=.05$ & maint. & $4.465/5.465$ & 1.000 & 0.000 & 0.0 \\ -$\chi=.40$ & maint. & $4.470/5.470$ & 1.000 & 0.000 & 0.0 \\ +\(\gamma=.05\) & maint. & $4.465/5.465$ & 1.000 & 0.000 & 0.0 \\ +\(\gamma=.40\) & maint. & $4.470/5.470$ & 1.000 & 0.000 & 0.0 \\ $f=.10$ & stale & $4.758/5.758$ & .990 & .734 & 98.2 \\ $f=.20$ & stale & $5.186/6.186$ & .969 & 1.890 & 314.7 \\ -$\chi=.05$ & stale & $4.617/5.617$ & .945 & .361 & 546.2 \\ -$\chi=.40$ & stale & $5.746/6.746$ & .484 & 4.604 & 5161.1 \\ +\(\gamma=.05\) & stale & $4.617/5.617$ & .945 & .361 & 546.2 \\ +\(\gamma=.40\) & stale & $5.746/6.746$ & .484 & 4.604 & 5161.1 \\ \hline \end{tabular} \caption{Chord-only baselines at Rings parameters @@ -1702,8 +1725,8 @@ \section{Verification Evidence and Evaluation Scope} Thus stale rows explain sensitivity, not the maintained Chord baseline: \[ \begin{array}{rcl} -M=\mathsf{stale}&\Rightarrow&\neg\mathsf{maintenance},\\ -M=\mathsf{maintained}&\Rightarrow&\mathsf{Baseline}_{C}^{656}. +\mu_B=\mathsf{stale}&\Rightarrow&\neg\mathsf{maintenance},\\ +\mu_B=\mathsf{maintained}&\Rightarrow&\mathsf{Baseline}_{C}^{656}. \end{array} \] @@ -1758,16 +1781,21 @@ \section{Verification Evidence and Evaluation Scope} \[ \begin{array}{rcl} D_R^{conv}&=& - \mathsf{raw}(16,309.532s,0/16,3/16,\\ -&&.194,1.026,8058.6),\\ + \mathsf{conv}(n=16,T_{wall}=309.532\,\mathrm{s},\\ +&&fail=0/16,partial=3/16,\\ +&&t_{p50}=.194,t_{p95}=1.026,\mathsf{msg}_s=8058.6),\\ D_R^{tx}&=& - \{(1,10.46),(16,107.35),\\ -&& (64,90.36)\}\subset \mathrm{KiB}\times\mathrm{Mbps}. + \{\mathsf{tx}(1,10.46),\mathsf{tx}(16,107.35),\\ +&& \mathsf{tx}(64,90.36)\}. \end{array} \] -The Docker/WebRTC cluster tuple is convergence evidence, not a steady-state -lookup benchmark. \(D_R^{tx}\) is payload throughput; it must not be compared -to Chord forwarding hops or timeout rates. +\[ +\mathsf{tx}:\mathrm{KiB}\to\mathrm{Mbps},\qquad +\mathsf{msg}_s:\mathrm{messages}/\mathrm{s}. +\] +The Docker/WebRTC tuple is convergence evidence, not a steady-state lookup +benchmark. \(D_R^{tx}\) is payload throughput; it must not be compared to +Chord forwarding hops or timeout rates. \noindent\textbf{Artifact provenance.} \[ From 167d92301933bc7e4f2e7f96ef192a955143cc48 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Tue, 7 Jul 2026 17:17:12 +0800 Subject: [PATCH 10/19] Tighten paper claim 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&&{}\land pending(seq(f))\neq f,\\ \mathsf{New}_{\Delta}(f)&\Leftrightarrow& - seq(f)\notin seen\cup\operatorname{dom}(pending)\\ + seq(f)\notin seen_{seq}\cup\operatorname{dom}(pending)\\ +&&{}\land \operatorname{fid}(f)\notin seen_{fid}\\ &&{}\land\neg closed\\ &&{}\land seq(f)-next\leq w\\ &&{}\land(final=\bot\lor seq(f)\leq final)\\ @@ -1510,9 +1596,11 @@ \section{Ordering, Ranking, and Security} \operatorname{SessionValid}(sid(f))\\ &&{}\land t Date: Tue, 7 Jul 2026 20:42:45 +0800 Subject: [PATCH 12/19] Clarify paper subject for Rings implementation --- papers/rings.pdf | Bin 178950 -> 178985 bytes papers/rings.tex | 23 +++++++++++------------ 2 files changed, 11 insertions(+), 12 deletions(-) diff --git a/papers/rings.pdf b/papers/rings.pdf index 60943040daf5e09ce48211537f0e11e43854b29c..0edfb6e3168b2d95e555dab5fcb7f188a00f26c7 100644 GIT binary patch delta 92560 zcmV(bhIApJ#MN;6FOk4E`sx z)$Q!ttJzoI(V6P3=4N)aoe85mqRdQ?PD?twTL0^e5XsK}ef8IW+4HLa&t{BwmJ;q> 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which claims the paper admits: \[ \begin{array}{rcl} -\mathsf{Established} -&=&\mathsf{Core}_{Rings}\land\mathsf{LedgerDisc}_{Rings},\\ +\mathsf{Formalized}_{paper} +&=&\mathsf{Core}_{Rings},\\ +\mathsf{Admitted}_{paper} +&\subseteq&\mathsf{Spec}\uplus\mathsf{Artifact}_{R},\\ \mathsf{Eval}_{reported} &\subset&\mathsf{ReportedOnly},\\ \mathsf{PerfClaim}_{R}&\in&\mathsf{Obligation}. @@ -213,7 +216,7 @@ \section{Problem Statement and Design Goals} G_{cr}&=&\mathsf{CarrierCorrectCrypto},\\ G_{rep}&=&\mathsf{BoundedRepairEvidence},\\ G_{bd}&=&\mathsf{ExplicitClaimBoundary},\\ -\RingsObj&\models& +G_*&=& G_{id}\land G_{own}\land G_{io}\land G_{eff}\\ &&{}\land G_{cr}\land G_{rep}\land G_{bd}. \end{array} @@ -237,9 +240,20 @@ \section{Problem Statement and Design Goals} \mathsf{Spec}\cup\mathsf{Impl} \cup\mathsf{Evidence}_{\Gamma}\cup\mathsf{Obligation},\\ \mathsf{Ev}_{\Gamma}&=&\mathsf{Evidence}_{\Gamma},\\ -\mathsf{Prop}_{R}&=&\operatorname{dom}(\mathsf{Ledger}_{R}),\\ +\mathsf{Anchor}&=&\mathsf{Label}\cup\mathsf{Path}\cup\mathsf{ArtifactId},\\ +\mathsf{Scope}&=&\mathsf{Finite}\cup\mathsf{AllModel}\cup\mathsf{Open},\\ +\mathsf{Ledger}_{R} +&\subseteq& +\mathsf{Prop}_{R}\times\mathsf{ClaimKind}\times\mathsf{Anchor}\times\mathsf{Scope},\\ +\mathsf{row}_{R}(c,k,a,\sigma) +&\Leftrightarrow& +(c,k,a,\sigma)\in\mathsf{Ledger}_{R},\\ +\mathsf{Prop}_{R}&=&\{c:\exists k,a,\sigma.\mathsf{row}_{R}(c,k,a,\sigma)\},\\ \mathsf{Support}_{R} &:&\mathsf{Prop}_{R}\times\mathsf{ClaimKind}\to\{\top,\bot\},\\ +\mathsf{Support}_{R}(c,k) +&\Leftrightarrow& +\exists a,\sigma.\mathsf{row}_{R}(c,k,a,\sigma),\\ \mathsf{Admit}(c) &\Leftrightarrow& \exists k\in\mathsf{ClaimKind}.\ \mathsf{Admit}_{R}(c,k). @@ -280,9 +294,9 @@ \section{Problem Statement and Design Goals} \centering \scriptsize \setlength{\tabcolsep}{2.5pt} -\begin{tabular}{p{1.8cm}|p{1.6cm}|p{3.4cm}} +\begin{tabular}{p{1.7cm}|p{1.55cm}|p{3.6cm}} \hline -Claim family & Ledger class & Carrier in this paper \\ \hline +Claim family & Ledger class & Anchor and scope \\ \hline \(\Omega_N,\mathsf{PMor}\) & \(\mathsf{Spec}\) & Definitions and Theorem~\ref{thm:carrier-separated-ownership} \\ Chord state & \(\mathsf{Spec}\cup\mathsf{Ev}_{\Gamma}\) & Algorithms~\ref{alg:join}--\ref{alg:stabilize}; finite checks \\ DID/session & \(\mathsf{Impl}\) & signed session and context predicates \\ @@ -291,15 +305,30 @@ \section{Problem Statement and Design Goals} Chunking & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & Algorithm~\ref{alg:e2e_chunking}; bounded reassembly \\ Deferred APIs & \(\mathsf{Spec}\cup\mathsf{Obligation}\) & mailbox, hidden descriptor, secret sharing \\ Wit/rank/sec. & \(\mathsf{Spec}\cup\mathsf{Obligation}\) & policy predicates, no global security theorem \\ -Benchmark rows & \(\mathsf{ReportedOnly}\) & baseline/runtime coordinates, not admitted eval \\ +Benchmark rows & \(\notin\mathsf{ClaimKind}\) & baseline/runtime coordinates, not admitted eval \\ \hline \end{tabular} \caption{Claim-ledger instantiation. Rows inside \(\mathsf{ClaimKind}\) may be -admitted at the listed classes; \(\mathsf{ReportedOnly}\) rows are coordinates, -not claim evidence.} +admitted only through an explicit ledger row \((c,k,a,\sigma)\); +\(\mathsf{ReportedOnly}\) rows are coordinates, not claim evidence.} \label{claim-ledger-table} \end{table} +\[ +\begin{array}{rcl} +\ell_{own}&=&(\mathsf{OwnerLaw},\mathsf{Spec}, + \mathrm{Thm}\,\ref{thm:carrier-separated-ownership},\mathsf{AllModel}),\\ +\ell_{mor}&=&(\mathsf{MorphLaw},\mathsf{Spec}, + \mathrm{Thm}\,\ref{thm:carrier-separated-ownership},\mathsf{AllModel}),\\ +\ell_{eff}&=&(\mathsf{EffectLaw},\mathsf{Spec}, + \mathrm{Lem}\,\ref{lem:effect-confinement},\mathsf{AllModel}),\\ +\ell_{car}&=&(\mathsf{CarrierLaw},\mathsf{Spec}, + \mathrm{Lem}\,\ref{lem:carrier-noninterference},\mathsf{AllModel}),\\ +\mathsf{Ledger}_{core}&=&\{\ell_{own},\ell_{mor},\ell_{eff},\ell_{car}\},\\ +\mathsf{Ledger}_{R}&\supseteq&\mathsf{Ledger}_{core}. +\end{array} +\] + \begin{definition}[Contribution boundary] \[ \begin{aligned} @@ -313,16 +342,17 @@ \section{Problem Statement and Design Goals} \] \[ \begin{aligned} -\mathsf{Contribution}_{Rings} -&\equiv -\mathsf{Reuse}_{Rings}\oplus\mathsf{New}_{Rings}\\ -&\models -\mathsf{Core}_{Rings}\land\mathsf{LedgerDisc}_{Rings}. +\mathsf{Contribution}_{paper} +&=(\mathsf{Reuse}_{Rings},\mathsf{New}_{Rings}),\\ +\mathsf{TheoremTarget}_{paper} +&=\mathsf{Core}_{Rings},\\ +\mathsf{LedgerTarget}_{paper} +&=\mathsf{LedgerDisc}_{Rings}. \end{aligned} \] The formal theorem is Theorem~\ref{thm:carrier-separated-ownership}; -\(\mathsf{LedgerDisc}_{Rings}\) is the admission discipline, not a performance -theorem. +\(\mathsf{LedgerDisc}_{Rings}\) is an admission discipline, not a semantic +entailment from \(\mathsf{Reuse}_{Rings}\) and not a performance theorem. \end{definition} \section{Algebraic System Model} @@ -493,11 +523,21 @@ \section{Algebraic System Model} \mathsf{CryptoOps}&=& \{\times,^{-1},\cdot_{scalar},\mathsf{interp}\}\\ &&\cup\{\mathsf{pair},\mathsf{subgroup}\},\\ +\mathsf{TransportOps}&=& + \{\mathsf{offer},\mathsf{answer},\mathsf{send},\mathsf{recv}\},\\ +\mathsf{EffectOps}&=& + \{\mathsf{emit},\mathsf{defer},\mathsf{store},\mathsf{load}, + \mathsf{schedule}\},\\ \mathsf{RunOps}&=&\mathsf{TransportOps}\cup\mathsf{EffectOps},\\ +\mathsf{Ops}&=& +\mathsf{PlacementOps}\uplus\mathsf{CryptoOps}\uplus\mathsf{RunOps},\\ \mathsf{PlacementOps}&\cap&\mathsf{CryptoOps}=\varnothing,\\ \mathsf{PlacementOps}&\cap&\mathsf{RunOps}=\varnothing,\\ \mathsf{CryptoCarrier}&\in&\{\mathbb{F}_q,\mathbb{G},\mathbb{Z}_q\},\\ \pi_R&:&\mathsf{Ops}\to\operatorname{End}(R),\\ +a\in\mathsf{PlacementOps} +&\Rightarrow& +\pi_R(a)\in\operatorname{End}(R),\\ a\in\mathsf{CryptoOps}\cup\mathsf{RunOps} &\Rightarrow& \left\{\begin{array}{l} @@ -507,6 +547,10 @@ \section{Algebraic System Model} \end{array} \] \end{constraint} +Thus a concrete operation can affect placement only through a member of +\(\mathsf{PlacementOps}\). Transport, effect, and cryptographic operations may +alter runtime state, payloads, or cryptographic carriers, but their induced +endomorphism on \(R\) is the identity. \begin{table}[htbp] \centering @@ -845,10 +889,27 @@ \section{Category and Effects} =\operatorname{owner}_N\circ H\). \end{proof} +\begin{definition}[Correct base predicate] +\label{def:correct-base} +\[ +\begin{array}{rcl} +\mathsf{CorrectBase}(N,S) +&\Rightarrow& +\left\{\begin{array}{l} +1\le |N|<\infty,\\ +\forall k\in R.\operatorname{owner}_N(k)\in N,\\ +\mathsf{CorrectChord}(N,S). +\end{array}\right. +\end{array} +\] +The theorem below uses only the displayed total-owner consequence. The stronger +steady-state lookup obligation is stated in the Chord section as +\(\operatorname{Inv}_{ring}(N,S)\land\mathsf{FingerInv}(N,S)\). +\end{definition} + \begin{theorem}[Carrier-separated ownership theorem] \label{thm:carrier-separated-ownership} -Assume \(1\le |N|<\infty\), CorrectChord stable-base obligations, -carrier separation, and protocol morphisms satisfying +Assume \(\mathsf{CorrectBase}(N,S)\), carrier separation, and protocol morphisms satisfying Definition~\ref{def:protocol-morphism}. Then \[ \begin{array}{rcl} @@ -869,7 +930,8 @@ \section{Category and Effects} \] \end{theorem} \begin{proof} -OwnerLaw is Lemma~\ref{lem:owner-totality}; MorphLaw is +OwnerLaw follows from Definition~\ref{def:correct-base} and +Lemma~\ref{lem:owner-totality}; MorphLaw is Lemma~\ref{lem:morphism-preservation}; EffectLaw is Lemma~\ref{lem:effect-confinement}; CarrierLaw is Lemma~\ref{lem:carrier-noninterference}. @@ -880,21 +942,24 @@ \section{Category and Effects} \begingroup\small \[ \begin{array}{rl} -\mathsf{Admit}_{R}(c,k)\Rightarrow& -k\in\mathsf{ClaimKind}\land\mathsf{Support}_{R}(c,k),\\ +\mathsf{Admit}_{R}(c,k)\Leftrightarrow& +k\in\mathsf{ClaimKind}\land +\exists a,\sigma.\mathsf{row}_{R}(c,k,a,\sigma),\\ \mathsf{Admit}_{R}(c,\mathsf{Ev}_{\Gamma})\Rightarrow& \mathsf{finite}(\Gamma)\land\mathsf{declared}(\Gamma),\\ -\mathsf{Support}_{R}(c,\mathsf{Spec})\Rightarrow& +\mathsf{row}_{R}(c,\mathsf{Spec},a,\sigma)\Rightarrow& c\in\left\{\begin{array}{l} \mathsf{OwnerLaw},\mathsf{MorphLaw},\\ \mathsf{EffectLaw},\mathsf{CarrierLaw} -\end{array}\right\},\\ -\mathsf{Support}_{R}(c,\mathsf{Impl})\Rightarrow& -\mathsf{Anchor}_{R}(c)\in\mathsf{Manifest}_{R},\\ -\mathsf{Support}_{R}(c,\mathsf{Ev}_{\Gamma})\Rightarrow& -\mathsf{Witness}_{R}(c,\Gamma),\\ -\mathsf{Support}_{R}(c,\mathsf{Obligation})\Rightarrow& -c\in\mathsf{Obligation},\\ +\end{array}\right.\\ +&{}\land a\in\mathsf{Anchor},\\ +\mathsf{row}_{R}(c,\mathsf{Impl},a,\sigma)\Rightarrow& +a\in\mathsf{Manifest}_{R},\\ +\mathsf{row}_{R}(c,\mathsf{Ev}_{\Gamma},a,\sigma)\Rightarrow& +\mathsf{Witness}_{R}(c,\Gamma)\land a\in\mathsf{Manifest}_{R},\\ +\mathsf{row}_{R}(c,\mathsf{Obligation},a,\sigma)\Rightarrow& +c\in\mathsf{Obligation}\land\sigma=\mathsf{Open},\\ +\multicolumn{2}{l}{\mathsf{ReportedOnly}\notin\mathsf{ClaimKind},}\\ \mathsf{Reject}_{R}(c)\Leftrightarrow&c\in\NonClaim,\\ \mathsf{Reject}_{R}(c)\Rightarrow& \neg\exists k.\;\mathsf{Admit}_{R}(c,k),\\ @@ -911,8 +976,12 @@ \section{Category and Effects} \[ \begin{array}{rl} \mathsf{Admit}_{R}(c,k)\Rightarrow& -k\in\mathsf{ClaimKind}\land\mathsf{Support}_{R}(c,k),\\ +\exists a,\sigma.\mathsf{row}_{R}(c,k,a,\sigma),\\ +\mathsf{row}_{R}(c,k,a,\sigma)\Rightarrow& +\mathsf{Support}_{R}(c,k),\\ c\in\NonClaim\Rightarrow&\neg\mathsf{Admit}(c),\\ +\mathsf{ReportedOnly}\notin\mathsf{ClaimKind}\Rightarrow& +\neg\mathsf{Admit}_{R}(c,\mathsf{ReportedOnly}),\\ \mathsf{Admit}_{R}(c,\mathsf{Ev}_{\Gamma}) \Rightarrow& \left\{\begin{array}{l} @@ -923,8 +992,9 @@ \section{Category and Effects} \] \end{proposition} \begin{proof} -Immediate from Constraint~\ref{constraint:claim-ledger} and -Table~\ref{claim-ledger-table}. +The first and third lines are Constraint~\ref{constraint:claim-ledger}. The +second line unfolds the definition of \(\mathsf{Support}_{R}\). The fourth line +follows because admission quantifies only over \(\mathsf{ClaimKind}\). \end{proof} \section{Chord Overlay} @@ -1632,8 +1702,9 @@ \section{Verification Evidence and Evaluation Scope} This section separates executable artifact evidence from reported coordinates. The repository contains finite-scope evidence for overlay, storage, and message-flow obligations. It does not yet contain a wide-area Rings benchmark, -committed benchmark-table regeneration data, or committed seeds sufficient to -regenerate the tables below. Tables~\ref{verification-table} and +or a paper-branch manifest entry with source revision, command, seed, and host +metadata sufficient to regenerate the comparison tables below. +Tables~\ref{verification-table} and \ref{artifact-manifest-table} are the artifact ledger; reported comparison coordinates are isolated in Table~\ref{reported-coordinate-table}. \[ @@ -1883,6 +1954,9 @@ \section{Verification Evidence and Evaluation Scope} PR~656 Chord-only coordinate at current Rings overlay parameters, and \(D_R^{docker}\) is reported Rings runtime evidence. The sets are disjoint by claim role: external baseline, reported Chord baseline, reported Rings runtime. +At this paper revision, \(D_C^{656}\) is not an artifact-ledger row because the +paper branch records the numbers but does not admit a manifest row +\((d,\mathsf{Ev}_{\Gamma},a,\sigma)\) with regeneration metadata. Unless \(\mathsf{AdmittedEval}(d)\) holds, a tuple is a reported coordinate only; it is not used to prove \(\mathsf{Core}_{Rings}\) or any Rings performance claim. @@ -1951,8 +2025,8 @@ \section{Verification Evidence and Evaluation Scope} \caption{Chord-only baselines at Rings parameters (\(N=1600,r=3,m=160,L=64\)). Maintained rows are the baseline; stale rows are no-maintenance sensitivity. These are PR~656 reported coordinates, not -admitted current-artifact evidence until generator, revision, seed, command, and -host are shipped.} +admitted current-artifact evidence in this paper branch until generator, +revision, seed, command, and host enter \(\mathsf{Manifest}_{R}\).} \label{rings-param-chord-data-table} \end{table} @@ -2044,6 +2118,8 @@ \section{Verification Evidence and Evaluation Scope} \] No CI command currently regenerates Table~\ref{chord-paper-data-table}, Table~\ref{rings-param-chord-data-table}, \(D_R^{conv}\), or \(D_R^{tx}\). +Therefore PR~656 maintained-Chord rows are useful comparison coordinates, but +they are not admitted evidence for a Rings performance theorem in this revision. \noindent\textbf{Limitations.} The current artifact supports finite model/test evidence and reported baseline @@ -2109,8 +2185,8 @@ \section{Conclusion} \] \[ \begin{array}{rcl} -\mathsf{Established}&=& -\mathsf{Core}_{Rings}\land\mathsf{LedgerDisc}_{Rings},\\ +\mathsf{Formalized}_{paper}&=&\mathsf{Core}_{Rings},\\ +\mathsf{LedgerRule}_{paper}&=&\mathsf{LedgerDisc}_{Rings},\\ \mathsf{ScopedEv}&=& \{a:a\in\mathsf{Artifact}_{R}\\ &&{}\land\mathsf{AdmittedArtifact}(a)\},\\ @@ -2125,7 +2201,9 @@ \section{Conclusion} The scientific contribution is the composition law and its claim ledger: CorrectChord supplies the overlay safety root, \(\Omega_N\) lifts resource namespaces into live owners, protocol morphisms preserve placement, and runtime -effects remain typed. Implementation evidence supports only the entries +effects remain typed. \(\mathsf{Formalized}_{paper}\) is a theorem inside the +stated model; \(\mathsf{LedgerRule}_{paper}\) is the admission rule for paper +claims. Implementation evidence supports only the entries admitted by Table~\ref{artifact-manifest-table}; coordinates in Table~\ref{reported-coordinate-table} are not proof evidence. Benchmark and security claims outside that ledger remain obligations. 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z59l3mOMiwf3xNmq*15o7u{(X?wZ#v-Y;eo#I$QF9H(hRdKWxh);A56`KJX>UoeuxA zB>?=awJrcgK3OjY{+3x60;Bh>mq7KMbrCc%c7Jch(3Hp4OQC6f?w^+a+?HifPwak{ zL%qMOOQ6}0tb{+aU26Egx6nwR%6k3>S9fB6+S(ibBxz=G?L08i?w3@D^>u4?A zKsV7XbQ|44chUyhNcYla+Cp3DL3)@TrN?O-Jqazn=e|pMoHP8}S>c|MR{HJEJD^pc ztu{|VoBFLgq0M4_2HMtceSW;(TAzhRA6j36cEb7s^!7LF%g{SD)?LsiAKa%8<%|3W YS7LA+mwMd-9t$%#H8Bb$B}Gq03QK~Cs{jB1 diff --git a/papers/rings.tex b/papers/rings.tex index 7d28c3cbe..931dc0b98 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -84,6 +84,8 @@ \begin{array}{rcl} R&=&\mathbb{Z}/2^{160}\mathbb{Z},\\ \mathcal{R}_N&=&\text{Correct-Chord overlay object},\\ + v_0&\in&\{1,\ldots,256\},\\ + \operatorname{StoreOwner}^{v_0}_N:R\to N,\\ \Omega_N(X,H)&=&(X,\operatorname{owner}_N\circ H),\\ \tau_\nu&:&S_\nu\times I_\nu \to\mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu). @@ -285,7 +287,9 @@ \section{Problem Statement and Design Goals} \{\mathsf{Novel}(\mathsf{CRDT}), \mathsf{Novel}(\mathsf{Crypto})\}\\ &\quad{}\cup -\{\mathsf{ByzLive},\mathsf{Consensus},\mathsf{WANPerf}\}. +\{\mathsf{ByzLive},\mathsf{Consensus},\mathsf{WANPerf}\}\\ +&\quad{}\cup +\{\mathsf{FullVNodeRouting},\mathsf{VNodePerf}\}. \end{aligned} \] \end{definition} @@ -300,7 +304,7 @@ \section{Problem Statement and Design Goals} \(\Omega_N,\mathsf{PMor}\) & \(\mathsf{Spec}\) & Definitions and Theorem~\ref{thm:carrier-separated-ownership} \\ Chord state & \(\mathsf{Spec}\cup\mathsf{Ev}_{\Gamma}\) & Algorithms~\ref{alg:join}--\ref{alg:stabilize}; finite checks \\ DID/session & \(\mathsf{Impl}\) & signed session and context predicates \\ -Affine storage & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & replica-key invariant and storage tests \\ +Storage VNs & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & affine keys, virtual owners, storage tests \\ E2E frames & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & signed frame and receiver policy \\ Chunking & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & Algorithm~\ref{alg:e2e_chunking}; bounded reassembly \\ Deferred APIs & \(\mathsf{Spec}\cup\mathsf{Obligation}\) & mailbox, hidden descriptor, secret sharing \\ @@ -445,40 +449,63 @@ \section{Algebraic System Model} initialization edge case, not evidence for \(r\) distinct live successors. \end{assumption} -\begin{definition}[Affine replica set] +\begin{definition}[Affine replica set and storage VNODE ownership] +Write \(S^v_N=\operatorname{StoreOwner}^{v}_N\) and +\(Q^{\rho,v}_N=\operatorname{RepOwner}^{\rho,v}_N\). \[ \begin{array}{rcl} 1\le\rho&\le&M,\\ +v_0&\in&\{1,\ldots,256\},\\ \operatorname{repkey}^{\rho}_i(k) &=&(k+\left\lfloor M\cdot i/\rho\right\rfloor)\bmod M,\quad 0\le i<\rho,\\[4pt] \operatorname{RepKey}^{\rho}(k) &=& \langle \operatorname{repkey}^{\rho}_i(k):0\leq i<\rho\rangle,\\[4pt] -\operatorname{RepOwner}^{\rho}_N(k) +z^v_{n,i}&=&H(\mathtt{rings{:}vnode},net,n,i),\\ +\operatorname{vnode}^{v}_{net}(n,i) +&=&z^v_{n,i},\\ +V^v_N&=& +\{(n,z^v_{n,i}):n\in N,0\le i0),\\ +r_i&=&\operatorname{repkey}^{\rho}_i(k),\\ +q_i &=& - \langle \operatorname{owner}_N(\operatorname{repkey}^{\rho}_i(k)): - 0\leq i<\rho\rangle. + S^{v}_N(r_i),\\ +Q^{\rho,v}_N(k) + &=& + \langle q_i:0\leq i<\rho\rangle. \end{array} \] \[ \begin{array}{rcl} P_k&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(k)),\\ -O_k&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(k)),\\ +O_k&=&\operatorname{set}(Q^{\rho,v_0}_N(k)),\\ |P_k|&=&\rho,\\ 1\le |O_k|&\leq&\min(\rho,|N|),\\ -\mathsf{collapse}_{N,\rho}(k)&\Leftrightarrow&|O_k|<\min(\rho,|N|). +\mathsf{collapse}_{N,\rho,v_0}(k)&\Leftrightarrow&|O_k|<\min(\rho,|N|). \end{array} \] -Replica keys specify intended placement cardinality; live owner images specify -realizable redundancy under the current live topology. CorrectChord successor -lists remain the topology safety root. +Replica keys specify intended placement cardinality; storage VNODE ownership +maps each placement key to a physical owner through derived virtual positions. +The paper's default storage mode has \(v_0>0\); \(v=0\) is the legacy off-switch. +Virtual positions are not signing identities and do not own transport sessions. +CorrectChord successor lists remain the topology safety root. \end{definition} \begin{definition}[Rings overlay model] \[ - \mathcal{R}_N= - (R,N,\operatorname{owner}_N,\operatorname{pred}_N, - \operatorname{Succ}^r_N,\operatorname{RepOwner}^{\rho}_N,F,E), +\begin{array}{rcl} + \mathcal{R}_N&=& + (R,N,\operatorname{owner}_N,\operatorname{pred}_N,\\ + &&\operatorname{Succ}^r_N,\operatorname{StoreOwner}^{v_0}_N,\\ + &&\operatorname{RepOwner}^{\rho,v_0}_N,F,E). +\end{array} \] \[ \begin{array}{rcl} @@ -513,36 +540,39 @@ \section{Algebraic System Model} \begin{constraint}[Carrier separation] \label{constraint:carrier-separation} +Write \(P_o=\mathsf{PlacementOps}\), \(C_o=\mathsf{CryptoOps}\), and +\(R_o=\mathsf{RunOps}\). \[ \begin{array}{rcl} \mathsf{PlacementOps}&=& \{0,+,-,\delta_a,(a,b]_R,(a,b)_R\}\\ &&\cup\{\operatorname{owner}_N\}\\ &&\cup\{\operatorname{RepKey}^{\rho}\}\\ -&&\cup\{\operatorname{RepOwner}^{\rho}_N\},\\ +&&\cup\{\mathsf{vnode},\mathsf{StoreOwner},\mathsf{RepOwner}\},\\ \mathsf{CryptoOps}&=& \{\times,^{-1},\cdot_{scalar},\mathsf{interp}\}\\ &&\cup\{\mathsf{pair},\mathsf{subgroup}\},\\ \mathsf{TransportOps}&=& \{\mathsf{offer},\mathsf{answer},\mathsf{send},\mathsf{recv}\},\\ \mathsf{EffectOps}&=& - \{\mathsf{emit},\mathsf{defer},\mathsf{store},\mathsf{load}, - \mathsf{schedule}\},\\ + \{\mathsf{emit},\mathsf{defer},\mathsf{store}\}\\ +&&\cup\{\mathsf{load},\mathsf{schedule}\},\\ \mathsf{RunOps}&=&\mathsf{TransportOps}\cup\mathsf{EffectOps},\\ \mathsf{Ops}&=& -\mathsf{PlacementOps}\uplus\mathsf{CryptoOps}\uplus\mathsf{RunOps},\\ -\mathsf{PlacementOps}&\cap&\mathsf{CryptoOps}=\varnothing,\\ -\mathsf{PlacementOps}&\cap&\mathsf{RunOps}=\varnothing,\\ +\mathsf{PlacementOps}\uplus\mathsf{CryptoOps}\\ +&&{}\uplus\mathsf{RunOps},\\ +P_o\cap C_o&=&\varnothing,\\ +P_o\cap R_o&=&\varnothing,\\ \mathsf{CryptoCarrier}&\in&\{\mathbb{F}_q,\mathbb{G},\mathbb{Z}_q\},\\ \pi_R&:&\mathsf{Ops}\to\operatorname{End}(R),\\ -a\in\mathsf{PlacementOps} +a\in P_o &\Rightarrow& \pi_R(a)\in\operatorname{End}(R),\\ -a\in\mathsf{CryptoOps}\cup\mathsf{RunOps} +a\in C_o\cup R_o &\Rightarrow& \left\{\begin{array}{l} \pi_R(a)=\operatorname{id}_R,\\ -a\notin\mathsf{PlacementOps}. +a\notin P_o. \end{array}\right. \end{array} \] @@ -1307,13 +1337,13 @@ \section{DID and Resource Algebra} \begin{obligation}[Replica realization] \[ \begin{array}{rcl} -O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(H_\nu(x))),\\ +O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho,v_0}_N(H_\nu(x))),\\ L_{\nu,x}&=&|O_{\nu,x}|,\\ \mathsf{FullRed}_{\nu,x}&\Leftrightarrow&L_{\nu,x}=\min(\rho,|N|),\\ \mathsf{Collapse}_{\nu,x}&\Leftrightarrow&L_{\nu,x}<\min(\rho,|N|),\\ -\mathsf{LiveClaim}_{\nu,x}(\rho)&\Leftrightarrow& +\mathsf{LiveClaim}_{\nu,x}(\rho,v_0)&\Leftrightarrow& \mathsf{Admit}_{R}(\mathsf{FullRed}_{\nu,x},\mathsf{Evidence}_{\Gamma}),\\ -\mathsf{LiveClaim}_{\nu,x}(\rho)&\Rightarrow& +\mathsf{LiveClaim}_{\nu,x}(\rho,v_0)&\Rightarrow& \operatorname{Inv}_{place}\land\mathsf{FullRed}_{\nu,x},\\ \mathsf{ReplicaGap}_{R}&=& \{(\nu,x):\mathsf{Collapse}_{\nu,x}\},\\ @@ -1323,6 +1353,9 @@ \section{DID and Resource Algebra} \] When \(|N|<\rho\), fewer than \(\rho\) distinct live owners is not collapse; collapse means fewer owners than the live topology can realize. +For the paper default \(v_0>0\), \(O_{\nu,x}\) is the image of the storage +VNODE owner map. This is a placement claim, not a full routing-VNODE or +load-balance theorem. \end{obligation} \begin{definition}[Mailbox] @@ -1819,6 +1852,9 @@ \section{Verification Evidence and Evaluation Scope} E2E tests & signed frames, ordering, replay & no symbolic crypto proof \\ +Storage VNODE + & owner derivation, route, sync, repair + & no full routing-VNODE or perf theorem \\ CI witness & build, test, lint, doc, package & no benchmark regeneration \\ @@ -1851,6 +1887,12 @@ \section{Verification Evidence and Evaluation Scope} \(\mathsf{ChunkImpl}\) & \texttt{chunk.rs} & bounded whole-message reassembly \\ +\(\mathsf{VNodeImpl}\) + & \texttt{virtual\_node.rs} + & storage owner derivation \\ +\(\mathsf{SyncImpl}\) + & \texttt{storage/*.rs} + & additive repair, guarded cleanup \\ \hline \end{tabular} \caption{Artifact manifest for the current paper claim ledger. Each row names @@ -2122,10 +2164,11 @@ \section{Verification Evidence and Evaluation Scope} they are not admitted evidence for a Rings performance theorem in this revision. \noindent\textbf{Limitations.} -The current artifact supports finite model/test evidence and reported baseline -coordinates. It does not yet support claims about wide-area latency, NAT -population behavior, adversarial churn beyond the scoped models, symbolic -cryptographic security, or steady-state Rings lookup performance. +The current artifact supports finite model/test evidence, storage-VNODE +implementation evidence, and reported baseline coordinates. It does not yet +support claims about wide-area latency, NAT population behavior, adversarial +churn beyond the scoped models, symbolic cryptographic security, full routing +VNODEs, VNODE load balance, or steady-state Rings lookup performance. \section{Related Work} @@ -2193,18 +2236,22 @@ \section{Conclusion} \mathsf{RepCoord}&=& D_C^{paper}\uplus D_C^{656}\uplus D_R^{docker},\\ \mathsf{Obligation}&=& -\mathsf{wideAreaBenchmark}\cup\mathsf{adversarialLiveness}\\ -&&{}\cup\mathsf{fullReplicaRealization},\\ +\mathsf{wideAreaBenchmark}\\ +&&{}\cup\mathsf{adversarialLiveness}\\ +&&{}\cup\mathsf{fullReplicaRealization}\\ +&&{}\cup\mathsf{VNodeLoadBenchmark},\\ \mathsf{NonClaim}&=&\NonClaim . \end{array} \] The scientific contribution is the composition law and its claim ledger: -CorrectChord supplies the overlay safety root, \(\Omega_N\) lifts resource -namespaces into live owners, protocol morphisms preserve placement, and runtime -effects remain typed. \(\mathsf{Formalized}_{paper}\) is a theorem inside the -stated model; \(\mathsf{LedgerRule}_{paper}\) is the admission rule for paper -claims. Implementation evidence supports only the entries -admitted by Table~\ref{artifact-manifest-table}; coordinates in +CorrectChord supplies the overlay safety root, storage VNODEs instantiate the +default \(\operatorname{StoreOwner}^{v_0}_N\) placement map, \(\Omega_N\) lifts +resource namespaces into live owners, protocol morphisms preserve placement, and +runtime effects remain typed. Virtual positions are storage coordinates, not +authority principals or transport endpoints. \(\mathsf{Formalized}_{paper}\) +is a theorem inside the stated model; \(\mathsf{LedgerRule}_{paper}\) is the +admission rule for paper claims. Implementation evidence supports only the +entries admitted by Table~\ref{artifact-manifest-table}; coordinates in Table~\ref{reported-coordinate-table} are not proof evidence. Benchmark and security claims outside that ledger remain obligations. 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\mathsf{Eval}_{reported} &\subset&\mathsf{ReportedOnly},\\ -\mathsf{OnionImpl}_{R}&\in&\mathsf{Artifact}_{R},\\ +\mathsf{OnionImpl}_{R}&=&\mathsf{OnionReg}\cup\mathsf{OnionCircuit},\\ +\mathsf{OnionImpl}_{R}&\subseteq&\mathsf{Artifact}_{R},\\ \mathsf{OnionImpl}_{R}&\not\Rightarrow&\mathsf{Anon},\\ \mathsf{OnionImpl}_{R}&\not\Rightarrow&\mathsf{WANPerf},\\ \mathsf{PerfClaim}_{R}&\in&\mathsf{Obligation}. @@ -1459,22 +1460,34 @@ \section{Cryptographic Carriers and Traffic} \[ \begin{array}{rcl} \mathsf{Topic}_{onion}&=&\mathtt{onion\_exits},\\ -e&=&(d,k_d,s,nt,net,svc,\pi,t_0,t_h,t_x,\sigma),\\ +e&=&(d,k_d,s,nt,net,svc,tr,\pi,\\ +&&{}t_0,t_h,t_x,\sigma),\\ +p&=&(svc,tr,\chi),\\ \operatorname{ExitOK}(e,t)&\Leftrightarrow& V(k_d,\sigma,e\setminus\sigma)=\top\\ &&{}\land\operatorname{did}(k_d)=d \land t Date: Wed, 8 Jul 2026 22:39:51 +0800 Subject: [PATCH 19/19] Tighten paper VNODE and route claims --- papers/rings.pdf | Bin 205593 -> 208056 bytes papers/rings.tex | 155 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zRD$bPShk+sugAPkaR!&~wO1jPj5G?sQ?`KuJ`5h9nKE&~wL1b~gTeD^(Stg6E>T4h z!5)Z%DHUA^-^HuC2)@669Ck|VBtAL8zH@nEL%3+Sl17a``C~V4ja1~R7{E|eF_^O$ z`Fh2w7!-EPt|*fx=EOcrM>;!O(M39Yt1W^wD^#A1c5piFJtx+fNH}9*D2+8c(D;L* zc*O2~bzbTId;e5GcLwbmx4J}cpU+U?=s?v!lYiDG#%FcI(xs_s%JSsR{su!I$>YX! zl}g>zwnZ`u1#XxYxKQpssl?c23Et7x{m%jn?M>$#E+e3vezg93~pCfB+XN9i5!IJnDY|>dztD diff --git a/papers/rings.tex b/papers/rings.tex index b51fcf840..a43c7de08 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -85,7 +85,8 @@ R&=&\mathbb{Z}/2^{160}\mathbb{Z},\\ \mathcal{R}_N&=&\text{Correct-Chord overlay object},\\ v_0&\in&\{1,\ldots,256\},\\ - \operatorname{StoreOwner}^{v_0}_N:R\to N,\\ + \Theta&\subseteq&N,\qquad + \operatorname{StoreOwner}^{v_0}_{\Theta}:R\to\Theta,\\ \Omega_N(X,H)&=&(X,\operatorname{owner}_N\circ H),\\ \tau_\nu&:&S_\nu\times I_\nu \to\mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu). @@ -458,12 +459,15 @@ \section{Algebraic System Model} \end{assumption} \begin{definition}[Affine replica set and storage VNODE ownership] -Write \(S^v_N=\operatorname{StoreOwner}^{v}_N\) and -\(Q^{\rho,v}_N=\operatorname{RepOwner}^{\rho,v}_N\). +Write \(S^v_{\Theta}=\operatorname{StoreOwner}^{v}_{\Theta}\) and +\(Q^{\rho,v}_{\Theta}=\operatorname{RepOwner}^{\rho,v}_{\Theta}\), where +\(\Theta\subseteq N\) is the storage-owner view used for one owner decision. \[ \begin{array}{rcl} 1\le\rho&\le&M,\\ v_0&\in&\{1,\ldots,256\},\\ +\Theta_n(t)&=&\{n\}\cup\operatorname{Succ}_n(t)\\ +&&{}\cup\operatorname{Pred}_n(t)\cup\operatorname{Finger}_n(t),\\ \operatorname{repkey}^{\rho}_i(k) &=&(k+\left\lfloor M\cdot i/\rho\right\rfloor)\bmod M,\quad 0\le i<\rho,\\[4pt] \operatorname{RepKey}^{\rho}(k) @@ -472,20 +476,20 @@ \section{Algebraic System Model} z^v_{n,i}&=&H(\mathtt{rings{:}vnode},net,n,i),\\ \operatorname{vnode}^{v}_{net}(n,i) &=&z^v_{n,i},\\ -V^v_N&=& -\{(n,z^v_{n,i}):n\in N,0\le i0),\\ r_i&=&\operatorname{repkey}^{\rho}_i(k),\\ q_i &=& - S^{v}_N(r_i),\\ -Q^{\rho,v}_N(k) + S^{v}_{\Theta}(r_i),\\ +Q^{\rho,v}_{\Theta}(k) &=& \langle q_i:0\leq i<\rho\rangle. \end{array} @@ -493,15 +497,18 @@ \section{Algebraic System Model} \[ \begin{array}{rcl} P_k&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(k)),\\ -O_k&=&\operatorname{set}(Q^{\rho,v_0}_N(k)),\\ +O^\Theta_k&=&\operatorname{set}(Q^{\rho,v_0}_{\Theta}(k)),\\ |P_k|&=&\rho,\\ -1\le |O_k|&\leq&\min(\rho,|N|),\\ -\mathsf{collapse}_{N,\rho,v_0}(k)&\Leftrightarrow&|O_k|<\min(\rho,|N|). +1\le |O^\Theta_k|&\leq&\min(\rho,|\Theta|),\\ +\mathsf{collapse}_{\Theta,\rho,v_0}(k) +&\Leftrightarrow&|O^\Theta_k|<\min(\rho,|\Theta|). \end{array} \] Replica keys specify intended placement cardinality; storage VNODE ownership maps each placement key to a physical owner through derived virtual positions. The paper's default storage mode has \(v_0>0\); \(v=0\) is the legacy off-switch. +The implementation instantiates \(\Theta\) as \(\Theta_n(t)\), an authenticated +local topology view; \(\Theta=N\) is an offline global-coordinate model. Virtual positions are not signing identities and do not own transport sessions. CorrectChord successor lists remain the topology safety root. \end{definition} @@ -511,8 +518,8 @@ \section{Algebraic System Model} \begin{array}{rcl} \mathcal{R}_N&=& (R,N,\operatorname{owner}_N,\operatorname{pred}_N,\\ - &&\operatorname{Succ}^r_N,\operatorname{StoreOwner}^{v_0}_N,\\ - &&\operatorname{RepOwner}^{\rho,v_0}_N,F,E). + &&\operatorname{Succ}^r_N,\operatorname{StoreOwner}^{v_0}_{\Theta},\\ + &&\operatorname{RepOwner}^{\rho,v_0}_{\Theta},F,E). \end{array} \] \[ @@ -1345,25 +1352,34 @@ \section{DID and Resource Algebra} \begin{obligation}[Replica realization] \[ \begin{array}{rcl} -O_{\nu,x}&=&\operatorname{set}(\operatorname{RepOwner}^{\rho,v_0}_N(H_\nu(x))),\\ -L_{\nu,x}&=&|O_{\nu,x}|,\\ -\mathsf{FullRed}_{\nu,x}&\Leftrightarrow&L_{\nu,x}=\min(\rho,|N|),\\ -\mathsf{Collapse}_{\nu,x}&\Leftrightarrow&L_{\nu,x}<\min(\rho,|N|),\\ -\mathsf{LiveClaim}_{\nu,x}(\rho,v_0)&\Leftrightarrow& -\mathsf{Admit}_{R}(\mathsf{FullRed}_{\nu,x},\mathsf{Evidence}_{\Gamma}),\\ -\mathsf{LiveClaim}_{\nu,x}(\rho,v_0)&\Rightarrow& - \operatorname{Inv}_{place}\land\mathsf{FullRed}_{\nu,x},\\ -\mathsf{ReplicaGap}_{R}&=& - \{(\nu,x):\mathsf{Collapse}_{\nu,x}\},\\ -\mathsf{ReplicaGap}_{R}\neq\varnothing&\Rightarrow& -\mathsf{fullReplicaRealization}\in\mathsf{Obligation}. -\end{array} -\] -When \(|N|<\rho\), fewer than \(\rho\) distinct live owners is not collapse; -collapse means fewer owners than the live topology can realize. -For the paper default \(v_0>0\), \(O_{\nu,x}\) is the image of the storage -VNODE owner map. This is a placement claim, not a full routing-VNODE or -load-balance theorem. +\Theta&\in&\{\Theta_n(t),N\},\\ +O^\Theta_{\nu,x}&=& +\operatorname{set}(Q^{\rho,v_0}_{\Theta}(H_\nu(x))),\\ +L^\Theta_{\nu,x}&=&|O^\Theta_{\nu,x}|,\\ +\mathsf{FR}^{\Theta}_{\nu,x} +&\Leftrightarrow&L^\Theta_{\nu,x}=\min(\rho,|\Theta|),\\ +\mathsf{Col}^{\Theta}_{\nu,x} +&\Leftrightarrow&L^\Theta_{\nu,x}<\min(\rho,|\Theta|),\\ +\mathsf{LC}^{\Theta}_{\nu,x}&\Leftrightarrow& +\mathsf{Admit}_{R}(\mathsf{FR}^{\Theta}_{\nu,x}, +\mathsf{Evidence}_{\Gamma}),\\ +\mathsf{LC}^{\Theta}_{\nu,x}&\Rightarrow& + \operatorname{Inv}_{place}\land\mathsf{FR}^{\Theta}_{\nu,x},\\ +G_R^\Theta&=& + \{(\nu,x):\mathsf{Col}^{\Theta}_{\nu,x}\},\\ +G_R^\Theta\neq\varnothing&\Rightarrow& +\mathsf{FullReplica}_{R}\in\mathsf{Obligation}. +\end{array} +\] +Here \(\mathsf{FR}\), \(\mathsf{Col}\), and \(\mathsf{LC}\) abbreviate full +redundancy, collapse, and live claim; \(G_R^\Theta\) is the replica gap set and +\(\mathsf{FullReplica}_{R}\) is the full-replica-realization obligation. When +\(|\Theta|<\rho\), fewer than \(\rho\) distinct owners is not collapse; +collapse means fewer owners than the selected view can realize. For runtime +claims, \(\Theta=\Theta_n(t)\); reported coordinates may use \(\Theta=N\). +For the paper default \(v_0>0\), \(O^\Theta_{\nu,x}\) is the image of the +storage VNODE owner map. This is a placement claim, not a full routing-VNODE +or load-balance theorem. \end{obligation} \begin{definition}[Mailbox] @@ -1395,7 +1411,7 @@ \section{DID and Resource Algebra} \begin{definition}[Subring] \[ - \mathsf{Class}(\mathsf{Subring})=\mathsf{Impl}. + \mathsf{Class}(\mathsf{Subring})=\{\mathsf{Impl}\}. \] \[ \mathcal{S}_u=(u,N_u,\operatorname{owner}_{N_u}, @@ -1463,6 +1479,9 @@ \section{Cryptographic Carriers and Traffic} e&=&(d,k_d,s,nt,net,svc,tr,\pi,\\ &&{}t_0,t_h,t_x,\sigma),\\ p&=&(svc,tr,\chi),\\ +\operatorname{svc}(p)&=&svc,\quad +\operatorname{tr}(p)=tr,\quad +\operatorname{target}(p)=\chi,\\ \operatorname{ExitOK}(e,t)&\Leftrightarrow& V(k_d,\sigma,e\setminus\sigma)=\top\\ &&{}\land\operatorname{did}(k_d)=d @@ -1471,25 +1490,26 @@ \section{Cryptographic Carriers and Traffic} \operatorname{SvcOK}(e,svc)&\Leftrightarrow& \operatorname{offers}(e,svc),\\ \operatorname{ProxyOK}(e,p)&\Leftrightarrow& -\operatorname{SvcOK}(e,svc)\\ -&&{}\land\operatorname{transport}(e)=tr\\ -&&{}\land\operatorname{allows}(\pi(e),\chi),\\ -q&=&(d,s),\\ -\operatorname{RelayOK}(q,t)&\Leftrightarrow& +\operatorname{SvcOK}(e,\operatorname{svc}(p))\\ +&&{}\land\operatorname{transport}(e)=\operatorname{tr}(p)\\ +&&{}\land\operatorname{allows}(\pi(e),\operatorname{target}(p)),\\ +r_o&=&(d,s),\\ +\operatorname{RelayOK}(r_o,t)&\Leftrightarrow& \operatorname{Online}(d,s,t)\\ &&{}\land\mathtt{onion\mbox{-}relay}\in cap(d,t),\\ -\rho&=&(q_1,\ldots,q_{h-1},e),\\ +\omega&=&(r_1,\ldots,r_h),\quad r_h=e,\\ &&{}1\leq h\leq 8,\\ h_0&=&3,\\ -\operatorname{RouteOK}(\rho,svc,t)&\Leftrightarrow& -\operatorname{NoRepeat}(d(q_1),\ldots,d(e))\\ -&&{}\land\operatorname{ExitOK}(e,t) -\land\operatorname{SvcOK}(e,svc),\\ -\operatorname{PRouteOK}(\rho,p,t)&\Leftrightarrow& -\operatorname{RouteOK}(\rho,svc,t)\\ -&&{}\land\operatorname{ProxyOK}(e,p),\\ +\operatorname{exit}(\omega)&=&r_h,\\ +\operatorname{RouteOK}(\omega,svc,t)&\Leftrightarrow& +\operatorname{NoRepeat}(d(r_1),\ldots,d(r_h))\\ +&&{}\land\operatorname{ExitOK}(\operatorname{exit}(\omega),t)\\ +&&{}\land\operatorname{SvcOK}(\operatorname{exit}(\omega),svc),\\ +\operatorname{PRouteOK}(\omega,p,t)&\Leftrightarrow& +\operatorname{RouteOK}(\omega,\operatorname{svc}(p),t)\\ +&&{}\land\operatorname{ProxyOK}(\operatorname{exit}(\omega),p),\\ L_h&=&\operatorname{AEAD}_{s(e)}(ret,svc,m),\\ -L_i&=&\operatorname{AEAD}_{s(q_i)}(d(q_{i+1}),cid_{i+1},\\ +L_i&=&\operatorname{AEAD}_{s(r_i)}(d(r_{i+1}),cid_{i+1},\\ &&{}L_{i+1}),\quad i

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zy3og&nRk+YN!uw~W`5Qg26i!E;}k(#&c^chb*ay({L5iPoA))NscQW%LT#V78;OX~V%4w#J4eeQ{q3DJKQZgd$)6cLWrbLo z_nVzynfg|GFi&mTb)gV|?gbst=`Slih-pOax)6-x_LG{`t}wT`MEi@Uxk&yCXUme8 zL)(DRZk9Eu8t*fHqD>swShB`&V4Z6XKTKeaS#+Z7`P z5#ATqrifYwfe3J#FXSI-Ziue8IZyDX3&a-}b1!w9ZE-0PpOAsTPUmTy_@KD(Oq^WI OENn1jWMT^9F#iF*qg7V` diff --git a/papers/rings.tex b/papers/rings.tex index 62586b422..724fce0e6 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -54,7 +54,7 @@ } \author{Ryan~J.~Kung% -\thanks{Ryan J. Kung can be reached at ryankung@ieee.org. Manuscript created February 8, 2023; last updated July 7, 2026.}} +\thanks{Ryan J. Kung can be reached at ryankung@ieee.org. Manuscript created February 8, 2023; last updated July 8, 2026.}} \title{Rings: An Algebraic Structured Peer-to-Peer Network\\ for Decentralized Identity and Resource Ownership} \date{} @@ -114,6 +114,9 @@ &\subseteq&\mathsf{Spec}\uplus\mathsf{Artifact}_{R},\\ \mathsf{Eval}_{reported} &\subset&\mathsf{ReportedOnly},\\ +\mathsf{OnionImpl}_{R}&\in&\mathsf{Artifact}_{R},\\ +\mathsf{OnionImpl}_{R}&\not\Rightarrow&\mathsf{Anon},\\ +\mathsf{OnionImpl}_{R}&\not\Rightarrow&\mathsf{WANPerf},\\ \mathsf{PerfClaim}_{R}&\in&\mathsf{Obligation}. \end{array} \] @@ -289,6 +292,8 @@ \section{Problem Statement and Design Goals} &\quad{}\cup \{\mathsf{ByzLive},\mathsf{Consensus},\mathsf{WANPerf}\}\\ &\quad{}\cup +\{\mathsf{Anon},\mathsf{Unlinkability},\mathsf{OnionPerf}\}\\ +&\quad{}\cup \{\mathsf{FullVNodeRouting},\mathsf{VNodePerf}\}. \end{aligned} \] @@ -306,6 +311,7 @@ \section{Problem Statement and Design Goals} DID/session & \(\mathsf{Impl}\) & signed session and context predicates \\ Storage VNs & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & affine keys, virtual owners, storage tests \\ E2E frames & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & signed frame and receiver policy \\ +Onion circuits & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & exit registry, route builder, layered AEAD tests \\ Chunking & \(\mathsf{Impl}\cup\mathsf{Ev}_{\Gamma}\) & Algorithm~\ref{alg:e2e_chunking}; bounded reassembly \\ Deferred APIs & \(\mathsf{Spec}\cup\mathsf{Obligation}\) & mailbox, hidden descriptor, secret sharing \\ Wit/rank/sec. & \(\mathsf{Spec}\cup\mathsf{Obligation}\) & policy predicates, no global security theorem \\ @@ -338,7 +344,8 @@ \section{Problem Statement and Design Goals} \begin{aligned} \mathsf{Reuse}_{Rings} &=\{\mathsf{Chord},\mathsf{CorrectChord},\mathsf{DID}, - \mathsf{WebRTC},\mathsf{CRDT}\},\\ + \mathsf{WebRTC},\\ +&\quad{}\mathsf{CRDT},\mathsf{OnionRouting}\},\\ \mathsf{New}_{Rings} &=(\Omega_N,\mathsf{PMor},\mathsf{CarrierSep}, \mathsf{LedgerDisc}_{Rings}). @@ -1442,6 +1449,53 @@ \section{Cryptographic Carriers and Traffic} final-frame checks into the security boundary rather than treating them as optional metadata. +\begin{definition}[Onion exit registry and circuit] +\label{def:onion-circuit} +\[ + \mathsf{Class}(\mathsf{OnionImpl}_{R}) + \subseteq\{\mathsf{Impl},\mathsf{Evidence}_{\Gamma}\}. +\] +\begingroup\small +\[ +\begin{array}{rcl} +\mathsf{Topic}_{onion}&=&\mathtt{onion\_exits},\\ +e&=&(d,k_d,s,nt,net,svc,\pi,t_0,t_h,t_x,\sigma),\\ +\operatorname{ExitOK}(e,t)&\Leftrightarrow& +V(k_d,\sigma,e\setminus\sigma)=\top\\ +&&{}\land\operatorname{did}(k_d)=d +\land t Date: Wed, 8 Jul 2026 22:09:39 +0800 Subject: [PATCH 18/19] Fix paper artifact ledger consistency --- papers/rings.pdf | Bin 204385 -> 205593 bytes papers/rings.tex | 41 ++++++++++++++++++++++++++++++----------- 2 files changed, 30 insertions(+), 11 deletions(-) diff --git a/papers/rings.pdf b/papers/rings.pdf index 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z*%@$lum}6OS3>yclLe{wrf-@}RsP5^`Ty!l{;r8x(O1>V%2CG@#x&t@K8Tk3TJzfl z$jD(U1o|Ud!Ip+wW5kp|pOUQ11=h$1F-&(Jf7TZtQeS9=>2Y>6;|JR_c5KtysLKJY zJK=hBTQ)MFbDw2uKjttzby3R?xl!mn<^IH{u;)Ew>t&2K7lAVnEl>qcxqH6ccc&oa zd5Za?c|EB5!(k&-u>IKOcmH4y8y2,\bot\},\\ +\mathsf{Prov}&=&(\mathsf{src},\mathsf{rev},\mathsf{cmd}, + \mathsf{seed},\mathsf{host}),\\ +\mathsf{Limit}&=&\NonClaim\cup\mathsf{Obligation}. +\end{array} +\] +\[ +\begin{aligned} +\NonClaim +&=\mathsf{new}\{\mathsf{DHT},\mathsf{DID},\mathsf{WebRTC}, +\mathsf{CRDT},\mathsf{Crypto}\}\\ +&\quad{}\cup +\{\mathsf{ByzLive},\mathsf{Consensus},\mathsf{WANPerf}\}. +\end{aligned} +\] +\end{definition} + +\begin{definition}[Contribution] \[ \begin{aligned} -\mathsf{Contribution}=\{& -R,\SetOverR,\Omega_N,\mathcal{R}_N, +\mathsf{Contribution}_{Rings}=\{& +(R,\SetOverR,\Omega_N),\; +\mathcal{R}_N,\; \mathsf{RepKey}^{\rho},\\ -&\mathsf{T}^{\mathcal{E}}_A, -\mathsf{Explore}_{\Gamma}, +&\mathsf{T}^{\mathcal{E}}_A,\; +\mathsf{CarrierSep},\; +\mathsf{Explore}_{\Gamma},\; \mathsf{Report}_{Rings}\}. \end{aligned} \] +\[ +\mathsf{Reuse}_{Rings} += +\{\mathsf{Chord},\mathsf{CorrectChord},\mathsf{DID}, + \mathsf{WebRTC},\mathsf{CRDT}\}. +\] +\end{definition} + +\begin{proposition}[Main property boundary] +\label{prop:main-boundary} +Assume \(N\neq\varnothing\), the CorrectChord stable-base obligations for +\(\mathcal{R}_N\), carrier separation, and typed protocol morphisms. Write +\(\Sigma_{\nu\mu}=(\sigma_X,\sigma_S,\sigma_I,\sigma_O, +\sigma_{\mathcal{E}},\sigma_A^*)\) and +\(\mathsf{PMor}_{\nu\mu}(\Sigma_{\nu\mu})\) for the laws of +Definition~\ref{def:protocol-morphism}. The main claim is: +\[ +\begin{aligned} +\mathsf{OwnerLaw} +&\equiv +\forall\nu\in\NS.\forall x\in X_\nu.\; +P^N_\nu(x)=\operatorname{owner}_N(H_\nu(x))\in N,\\ +\mathsf{MorphLaw} +&\equiv +\forall\nu,\mu\in\NS.\forall\Sigma_{\nu\mu}.\\ +&\quad +\mathsf{PMor}_{\nu\mu}(\Sigma_{\nu\mu}) +\Rightarrow P^N_\mu\circ\sigma_X=P^N_\nu,\\ +\mathsf{EffectLaw} +&\equiv +\forall\nu\in\NS.\forall s,i.\;\tau_\nu(s,i)\in Y_\nu,\\ +Y_\nu&=\mathsf{T}^{\mathcal{E}_\nu}_{A_\nu}(S_\nu\times O_\nu),\\ +\mathsf{LedgerLaw} +&\equiv +\forall c.\;c=\mathsf{Evidence}_{\Gamma} +\Rightarrow \mathsf{finite}(\Gamma)\land\mathsf{declared}(\Gamma),\\ +\mathsf{Main}_{Rings} +&\equiv +\mathsf{OwnerLaw}\land\mathsf{MorphLaw} +\land\mathsf{EffectLaw}\land\mathsf{LedgerLaw}. +\end{aligned} +\] +It does not entail any \(c\in\NonClaim\): +\[ +\forall c\in\NonClaim.\quad \mathsf{Main}_{Rings}\not\vdash c. +\] +\end{proposition} \section{Algebraic System Model} -\begin{assumption}[System scope] +\begin{assumption}[System and adversary scope] \[ \begin{array}{rcl} -\mathsf{fault}&=&\mathsf{fail\mbox{-}stop},\\ -\mathsf{auth}(m,\sigma,k)&=&V(k,\sigma,m),\\ -\mathsf{net}&=&\mathsf{async},\\ -\mathsf{io}&=&I_X:A_X^*\to\mathsf{IO},\\ +\mathsf{fault}_{overlay}&=&\mathsf{fail\mbox{-}stop},\\ +\mathsf{Adv}_{net}&=&\{\mathsf{delay},\mathsf{drop},\mathsf{dup}, + \mathsf{reorder},\mathsf{replay}\},\\ +\mathsf{Adv}_{id}&=&\{\mathsf{manyDID},\mathsf{stolenSession}, + \mathsf{staleProof}\},\\ +\mathsf{Forge}_{\Pi}&=&\bot,\qquad \mathsf{Preimage}_{H}=\bot,\\ \mathsf{consensus}&\notin&\mathsf{Overlay},\\ \mathsf{order}&=&\mathsf{SidecarWitness},\\ \mathsf{crypto\_ops}&\cap&\mathsf{route\_ops}=\varnothing. \end{array} \] -The fail-stop clause scopes overlay maintenance; identity, ranking, and -application protocols still carry adversarial predicates at their own layer. +Thus CorrectChord is the safety root only for crash-scoped overlay maintenance. +Byzantine routing, Eclipse resistance, Sybil resistance, anonymity, and +denial-of-service resistance are not inherited from Chord; they must be +discharged by admission, session typing, ranking, relay, quota, and measurement +predicates at their own layers. \end{assumption} \begin{definition}[Identifier carrier] @@ -238,40 +350,52 @@ \section{Algebraic System Model} \begin{definition}[Live topology] \[ \begin{array}{rcl} - N&\subset&R,\quad N\neq\varnothing,\\[2pt] + N&\subset&R,\quad 1\le |N|<\infty,\\[2pt] \operatorname{owner}_N(k) - &=&\arg\min_{u\in N}\delta_k(u),\\[6pt] + &=&\arg\min_{u\in N}\delta_k(u),\\[4pt] + \operatorname{cw}_N(n) + &=&\operatorname{sort}_{\delta_n}(N\setminus\{n\})\cdot\langle n\rangle,\\[4pt] + \operatorname{succ}_N(n) + &=&\operatorname{head}(\operatorname{cw}_N(n)),\\[4pt] \operatorname{pred}_N(n) - &=&\arg\min_{p\in N\setminus\{n\}}\delta_p(n),\\[6pt] - \operatorname{Succ}^q_N(n) &=& - \operatorname{take}_q - \bigl(\operatorname{sort}_{\delta_n}(N\setminus\{n\})\bigr),\\[6pt] - \delta_a|_N&=&\mathsf{injective}. + \begin{cases} + \bot,& |N|=1,\\ + \arg\min_{p\in N\setminus\{n\}}\delta_p(n),& |N|>1, + \end{cases}\\[8pt] + \operatorname{Succ}^q_N(n) + &=&\operatorname{take}_{\min(q,|N|)}(\operatorname{cw}_N(n)). \end{array} \] +The list \(\operatorname{cw}_N(n)\) contains strictly clockwise live nodes and +uses \(n\) only as the wrap-around sentinel. Hence a singleton ring has +\(\operatorname{Succ}^q_N(n)=\langle n\rangle\) and +\(\operatorname{pred}_N(n)=\bot\). \end{definition} \begin{assumption}[Correct-Chord stable base] \[ \begin{array}{rcl} -r&=&|\operatorname{Succ}^r_N(n)|,\\ -\mathsf{Steady}(N)&\Rightarrow&|N|\geq r+1,\\ -|N|0},\\ +\mathsf{Steady}(N,r)&\Rightarrow&|N|\geq r+1,\\ +\mathsf{Init}(N,r)&\Leftrightarrow&1\le |N|\le r,\\ +|\operatorname{Succ}^r_N(n)|&=&\min(r,|N|),\\ \mathsf{Maintain}&=& \{\mathsf{join},\mathsf{rectify}\}\\ &&\cup\{\mathsf{stabilize}\}_{CorrectChord}. \end{array} \] -This is the CorrectChord stable base of Zave~\cite{ZaveChordCorrect}. +CorrectChord claims in this paper are stable-ring claims under +\(\mathsf{Steady}(N,r)\); singleton and small-ring behavior is an explicit +initialization edge case, not evidence for \(r\) distinct live successors. \end{assumption} \begin{definition}[Affine replica set] \[ \begin{array}{rcl} -\rho&\in&\mathbb{N}_{>0},\\ +1\le\rho&\le&M,\\ \operatorname{repkey}^{\rho}_i(k) - &=&k+\left\lfloor M\cdot i/\rho\right\rfloor,\\[4pt] + &=&(k+\left\lfloor M\cdot i/\rho\right\rfloor)\bmod M,\quad 0\le i<\rho,\\[4pt] \operatorname{RepKey}^{\rho}(k) &=& \langle \operatorname{repkey}^{\rho}_i(k):0\leq i<\rho\rangle,\\[4pt] @@ -286,12 +410,13 @@ \section{Algebraic System Model} P_k&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(k)),\\ O_k&=&\operatorname{set}(\operatorname{RepOwner}^{\rho}_N(k)),\\ |P_k|&=&\rho,\\ -|O_k|&\leq&\min(\rho,|N|),\\ -\mathsf{collapse}_{N,\rho}(k)&\Leftrightarrow&|O_k|<\rho. +1\le |O_k|&\leq&\min(\rho,|N|),\\ +\mathsf{collapse}_{N,\rho}(k)&\Leftrightarrow&|O_k|<\min(\rho,|N|). \end{array} \] -Thus replica keys specify redundancy intent; live owner images specify realized -redundancy. CorrectChord successor lists remain the topology safety root. +Replica keys specify intended placement cardinality; live owner images specify +realizable redundancy under the current live topology. CorrectChord successor +lists remain the topology safety root. \end{definition} \begin{definition}[Rings overlay object] @@ -303,7 +428,7 @@ \section{Algebraic System Model} \[ \begin{array}{rcl} F&\subseteq&N\times\mathbb{N}\times N,\\ -E&=&\prod_{v\in VID}E_v,\\ +E&=&\prod_{\nu\in\NS}E_\nu,\\ \mathsf{SafetyRoot}(\mathcal{R}_N)&=& (\operatorname{pred}_N,\operatorname{Succ}^r_N),\\ \mathsf{PerfWitness}(\mathcal{R}_N)&=&F. @@ -379,52 +504,53 @@ \section{Architecture As Interfaces} T & (C,A_T,\mathsf{offer},\mathsf{answer},\mathsf{send},\mathsf{recv})\\ O & \mathcal{R}_N\\ X & (S_X,A_X,\mathsf{cap},I_X)\\ -P & \{\mathcal{P}_\nu\}_{\nu\in Namespace}\\ +P & \{\mathcal{P}_\nu\}_{\nu\in\NS}\\ L & \mathsf{App}\circ P \end{array} \] \end{definition} -\begin{figure}[htbp] -\centering -\begin{tikzpicture}[every node/.style={draw,minimum width=5.1cm,minimum height=.55cm,align=center,font=\bfseries}] -\node (1) at (4.5,0) {Identity Layer}; -\node (2) at (4.5,0.7) {Transport Layer}; -\node (3) at (4.5,1.4) {Overlay Layer}; -\node (4) at (4.5,2.1) {Extension Runtime Layer}; -\node (5) at (4.5,2.8) {Protocol Layer}; -\node (6) at (4.5,3.5) {Application Layer}; -\end{tikzpicture} -\caption{Layers of Rings Network} -\label{layers} -\end{figure} +The interface tuple \(\mathcal{A}\) separates identity, transport, overlay, +extension runtime, protocol, and application layers. Only the overlay owns +\(\mathcal{R}_N\); the other layers discharge typed obligations through +\(I,T,X,P\). \begin{definition}[Identity proof] \[ - \Pi=(K,\Sigma,V,D,\mathsf{enc},\mathsf{ttl}) + \Pi=(K,\Sigma,V,\operatorname{did},\mathsf{enc},\mathsf{ttl}) \] \[ \begin{array}{rcl} V&:&K\times\Sigma\times B^*\to\{\top,\bot\},\\ -D&:&K\to R,\\ +\operatorname{did}&:&K\to X_D,\\ \mathsf{enc}&:&\Sigma\to B^*,\\ -\mathsf{ttl}&:&\Sigma\to Time. +\mathsf{ttl}&:&\Sigma\to \mathsf{Time}. \end{array} \] \end{definition} -\begin{invariant}[Session authority] +\begin{invariant}[Typed session authority] \[ - d\in X_D,\qquad s\in K. + sid=(d,s,e,ctx,cap),\qquad d\in X_D,\quad s\in K,\quad now=latex'] - \node (A) {Node 1}; - \node (B) [right of=A] {Node 2}; - \draw[->] (A |-, -1) -- node[above] {Offer} (B |-, -1); - \draw[->] (B |-, -2) -- node[above] {Answer} (A|-, -2 ); - \draw[->] (A |-, -3) -- node[above] {Accept Offer} (B |-, -3); - \draw[->] (A |-, -4) -- node[above] {Send ICE Candidate} (B |-, -4); - \draw[->] (B |-, -5) -- node[above] {Send ICE Candidate} (A |-, -5); - \draw[->,dashed] (B) -- (A); - \draw[pattern=north east lines, pattern color=red] (A.south west) -- (A.south east) -- (A.north east) -- (A.north west) -- cycle; - \draw[pattern=north east lines, pattern color=blue] (B.south west) -- (B.south east) -- (B.north east) -- (B.north west) -- cycle; - \draw[red, thick] (A.south) -- ++(0,-5.2cm); - \draw[blue, thick] (B.south) -- ++(0,-5.2cm); -\end{tikzpicture} -\caption{Standard SDP/ICE exchange} -\label{webrtc-standard-sdp} -\end{figure} - -\begin{figure}[htbp] -\begin{tikzpicture}[node distance=5cm,auto,>=latex'] - \node (A) {Node 1}; - \node (B) [right of=A] {Node 2}; - \draw[->] (A |-, -1) -- node[above] {Offer And ICE} (B |-, -1); - \draw[->] (B |-, -2) -- node[above] {Answer and ICE} (A|-, -2 ); - \draw[->,dashed] (B) -- (A); - \draw[pattern=north east lines, pattern color=red] (A.south west) -- (A.south east) -- (A.north east) -- (A.north west) -- cycle; - \draw[pattern=north east lines, pattern color=blue] (B.south west) -- (B.south east) -- (B.north east) -- (B.north west) -- cycle; - \draw[red, thick] (A.south) -- ++(0,-2.2cm); - \draw[blue, thick] (B.south) -- ++(0,-2.2cm); -\end{tikzpicture} -\caption{Rings single round-trip SDP/ICE exchange} -\label{webrtc-rings-sdp} -\end{figure} +WebRTC signaling is a runtime adapter rather than a new overlay primitive. +Rings may batch offer, answer, and ICE material into fewer protocol actions, +but correctness remains delegated to the WebRTC/ICE state machines; evaluation +therefore reports connection setup separately from overlay lookup. \begin{definition}[Runtime interpreter] \[ @@ -490,27 +586,8 @@ \section{Architecture As Interfaces} \] \end{definition} -\begin{figure}[htbp] - \begin{tikzpicture}[node distance=3cm,auto,>=latex'] - \node (A) {Browser}; - \node (B) [right of=A] {Wasm Module}; - \node (C) [right of=B] {Js Runtime}; - \draw (A) -- (A |-, -5.5); - \draw (B) -- (B |-, -5.5); - \draw (C) -- (C |-, -5.5); - \draw[->] (A |-, -1) -- node[midway, above] {Download Module} (B |-, -1); - \draw[->] (B |-, -2) -- node[midway, above] {Decode Binary} (C |-, -2); - \draw[->] (C|-, -3) -- node[midway, above] {Compile} (B|-, -3); - \draw[->] (B|-,-4) -- node[midway, above] {Execute} (C|-, -4); - \draw[->] (C|-,-5) -- node[midway, above] {Call} (B|-,-5); - \draw[pattern=north east lines, pattern color=gray] (A.south west) -- (A.south east) -- (A.north east) -- (A.north west) -- cycle; - \draw[pattern=north east lines, pattern color=gray] (B.south west) -- (B.south east) -- (B.north east) -- (B.north west) -- cycle; - \draw[pattern=north east lines, pattern color=gray] (C.south west) -- (C.south east) -- (C.north east) -- (C.north west) -- cycle; - \draw[->,dashed] (B) -- (C); -\end{tikzpicture} -\caption{Wasm module execution boundary} -\label{wasm-boundary} -\end{figure} +WebAssembly is modeled only through \(I_X\) and \(\mathsf{cap}\): it interprets +effect lists under runtime capabilities and does not change the overlay object. \begin{obligation}[Runtime confinement] \[ @@ -527,7 +604,7 @@ \section{Category and Effects} \begin{definition}[Namespace object] \[ \begin{array}{rcl} -\nu&\in&\{D,V,M,H,U,Q,W\},\\ +\nu&\in&\NS,\\ H_\nu&:&X_\nu\to R,\\ (X_\nu,H_\nu)&\in&\SetOverR. \end{array} @@ -616,6 +693,7 @@ \section{Category and Effects} \end{definition} \begin{definition}[Protocol morphism] +\label{def:protocol-morphism} \[ \Sigma:\mathcal{P}_\nu\to\mathcal{P}_\mu = @@ -635,20 +713,6 @@ \section{Category and Effects} \] \end{definition} -\begin{figure}[htpb] - \begin{center} -\begin{tikzpicture} -\node[rectangle, draw] (actor) {Actor}; -\node[rectangle, draw, below of=actor] (mailbox) {Mailbox}; -\node[rectangle, draw, below of=mailbox] (message) {Message}; -\draw[->] (actor) -- (mailbox); -\draw[->] (mailbox) -- (message); -\end{tikzpicture} -\end{center} -\caption{Actor Model} -\label{actor-model} -\end{figure} - \section{Chord Overlay} \[ @@ -662,58 +726,69 @@ \section{Chord Overlay} \] This section fixes Chord as the base protocol and CorrectChord as the maintenance law~\cite{Chord,ZaveChordCorrect}. -\begin{definition}[Local node state] -\[ - S_n=(p_n,L_n,F_n,E_n) -\] +\begin{definition}[Local node state and Chord auxiliaries] \[ \begin{array}{rcl} -p_n&\in&N\cup\{\bot\},\\ -L_n&\in&N^{\leq r},\\ -F_n&:&\mathbb{N}\rightharpoonup N,\\ -E_n&\subseteq&E,\\ - p_n=\operatorname{pred}_N(n), -&& - L_n=\operatorname{Succ}^r_N(n). +S_n&=&(p_n,L_n,F_n,E_n),\\ +p_n&\in&N\cup\{\bot\},\quad L_n\in N^{\le r},\\ +F_n&:&\{0,\ldots,159\}\rightharpoonup N. \end{array} \] -\end{definition} - -\begin{definition}[Finger target] \[ \begin{array}{rcl} - \operatorname{target}_i(n)&=&n+2^i,\\ - \operatorname{finger}_i(n)&=& - \operatorname{owner}_N(\operatorname{target}_i(n)),\\ - F_n(i)&\in&\{\bot,\operatorname{finger}_i(n)\}. +\mathsf{head}(\langle\rangle)&=&\bot,\\ +\mathsf{Normalize}_r(n,X) +&=&\operatorname{take}_{\min(r,|N|)}(U_n(X)),\\ +U_n(X)&=&\operatorname{uniq}(\operatorname{filter}_N(X)\cdot\operatorname{cw}_N(n)),\\ +\operatorname{target}_i(n)&=&n+2^i \bmod M,\\ +\operatorname{finger}_i(n)&=&\operatorname{owner}_N(\operatorname{target}_i(n)),\\ +\mathsf{Cand}_S(n,k)&=& +(\operatorname{rng}(F_n)\cup\operatorname{set}(L_n))\cap(n,k)_R,\\ +\mathsf{ClosestPreceding}_S(n,k) +&=&\max_{\delta_n}\mathsf{Cand}_S(n,k). \end{array} \] +Here \(\mathsf{ClosestPreceding}_S(n,k)=\bot\) when the displayed set is empty. \end{definition} \begin{algorithm} -\caption{DHT Join Transitions} +\caption{DHT Join and Rectify Transitions} \label{alg:join} \begin{algorithmic}[1] \Function{BeginJoin}{$n, known$} -\State $pred[n]\gets none$ -\State $a\gets FindSuccessor(n.did)$ -\State \Return $Remote(known, a)$ +\State $pred[n]\gets \bot$ +\If{$known=\bot$} + \State $succ[n]\gets \langle n.did\rangle$ + \State \Return $Done$ +\EndIf +\State \Return $Remote(known, FindSuccessor(n.did))$ \EndFunction \Function{InstallSuccessor}{$n, s$} -\State $succ[n]\gets take(r, [s])$ -\State \Return $Remote(s, QuerySuccList(s))$ +\If{$s=\bot$} + \State \Return $Repair(DiscoverSuccessor(n.did))$ +\EndIf +\State $succ[n]\gets \mathsf{Normalize}_r(n,\langle s\rangle)$ +\State \Return $Remote(s, QuerySuccList)$ \EndFunction \Function{InstallSuccList}{$n, s, list$} -\State $succ[n]\gets take(r, s :: list)$ -\If{$head(succ[n]) \neq none$} +\State $succ[n]\gets \mathsf{Normalize}_r(n,\langle s\rangle\cdot list)$ \State $h\gets head(succ[n])$ -\State $notify\gets Notify(h, n.did)$ -\State $sync\gets SyncStorage(h)$ -\State \Return $Multi(notify, sync)$ +\If{$h=\bot$} + \State \Return $Repair(DiscoverSuccessor(n.did))$ +\ElsIf{$h=n.did$} + \State \Return $Done$ \Else -\State \Return $Noop$ + \State $a\gets Remote(h, Notify(n.did))$ + \State $b\gets Remote(h, SyncStorage(n.did))$ + \State \Return $Multi(a,b)$ \EndIf \EndFunction +\Function{HandleNotify}{$n, q$} +\If{$q\neq n.did \land (pred[n]=\bot \lor q\in(pred[n],n.did)_R)$} + \State $pred[n]\gets q$ +\EndIf +\State \Return $Noop$ +\EndFunction \end{algorithmic} \end{algorithm} @@ -721,21 +796,23 @@ \section{Chord Overlay} \caption{DHT Lookup Algorithm} \label{alg:lookup} \begin{algorithmic}[1] -\Function{Lookup}{$key, node$} - \State $s\gets head(succ[node])$ - \If{$s = none$} - \State \Return $Repair(QuerySuccList(node))$ - \EndIf - \If{$key \in (node.did, s]$} - \State \Return $Local(s)$ - \EndIf - \State $next\gets closest\_preceding\_node(node, key)$ - \If{$next = none$} - \State \Return $Repair(QuerySuccList(s))$ - \Else - \State $a\gets FindSuccessor(key)$ - \State \Return $Remote(next, a)$ - \EndIf +\Function{FindSuccessor}{$key, n$} +\If{$key=n.did$} + \State \Return $Found(n.did)$ +\EndIf +\State $s\gets head(succ[n])$ +\If{$s=\bot$} + \State \Return $Repair(QuerySuccList(n.did))$ +\ElsIf{$s=n.did$} + \State \Return $Found(n.did)$ +\ElsIf{$key\in(n.did,s]_R$} + \State \Return $Found(s)$ +\EndIf +\State $next\gets \mathsf{ClosestPreceding}_S(n.did,key)$ +\If{$next=\bot$ or $next=n.did$} + \State $next\gets s$ +\EndIf +\State \Return $Remote(next, FindSuccessor(key))$ \EndFunction \end{algorithmic} \end{algorithm} @@ -765,18 +842,34 @@ \section{Chord Overlay} \caption{DHT Stabilization} \label{alg:stabilize} \begin{algorithmic}[1] +\Function{BeginStabilize}{$n$} +\State $s\gets head(succ[n])$ +\If{$s=\bot$} + \State \Return $Repair(DiscoverSuccessor(n.did))$ +\ElsIf{$s=n.did$} + \State \Return $Noop$ +\Else + \State \Return $Remote(s, QueryTopology)$ +\EndIf +\EndFunction \Procedure{Stabilize}{$n, topo$} \State $actions\gets []$ -\State $c\gets topo.pred$ \State $s\gets head(succ[n])$ -\If {$c \neq none$ and $c \in (n.did, s)$} -\State $succ[n]\gets insert(succ[n], c)$ -\State $actions\gets actions :: FindSuccessor(c)$ +\If{$s=\bot$} + \State \Return $Repair(DiscoverSuccessor(n.did))$ +\ElsIf{$s=n.did$} + \State \Return $Noop$ \EndIf -\State $succ[n]\gets take(r, merge(succ[n], topo.succ))$ -\If{$head(succ[n]) \neq none$} +\State $c\gets topo.pred$ +\If{$c\neq\bot$ and $c\neq n.did$ and $c\in(n.did,s)_R$} + \State $succ[n]\gets \mathsf{Normalize}_r(n,\langle c\rangle\cdot succ[n])$ +\EndIf +\State $succ[n]\gets \mathsf{Normalize}_r(n,succ[n]\cdot topo.succ)$ \State $h\gets head(succ[n])$ -\State $actions\gets actions :: Notify(h, n.did)$ +\If{$h\neq\bot$ and $h\neq n.did$} + \State $a\gets Remote(h, Notify(n.did))$ + \State $b\gets Remote(h, QuerySuccList)$ + \State $actions\gets actions\cdot[a,b]$ \EndIf \State \Return $Multi(actions)$ \EndProcedure @@ -789,27 +882,40 @@ \section{Chord Overlay} \operatorname{Inv}_{ring}(N,S) \equiv \forall n\in N.\;& p_n=\operatorname{pred}_N(n)\\ - &\land L_n=\operatorname{Succ}^r_N(n). + &\land L_n=\operatorname{Succ}^r_N(n)\\ + &\land \mathsf{head}(L_n)=\operatorname{succ}_N(n). \end{aligned} \] \end{invariant} \begin{invariant}[Lookup owner preservation] \[ +\mathsf{Eval}_S(n,k)\Downarrow o +\] +be the fair closure of Algorithm~\ref{alg:lookup}, where +\(Remote(m,FindSuccessor(k))\) resumes the same lookup at node \(m\). Then +\[ \begin{aligned} -&\mathsf{Steady}(N)\land\operatorname{Inv}_{ring}(N,S)\\ +&(\mathsf{Steady}(N,r)\lor |N|=1) +\land\operatorname{Inv}_{ring}(N,S)\\ &\Rightarrow - \operatorname{Lookup}(S,k)\Downarrow - \operatorname{owner}_N(k). +\forall n\in N.\forall k\in R.\; +\mathsf{Eval}_S(n,k)\Downarrow \operatorname{owner}_N(k). \end{aligned} \] -\[ - \Downarrow - = - \mathsf{Reach}_{A_D}(\ref{alg:lookup},\ref{alg:stabilize}). -\] \end{invariant} +\begin{proof}[Proof obligation] +If Algorithm~\ref{alg:lookup} returns \(Found(s)\) by the interval test, then +\(s=head(L_n)=\operatorname{succ}_N(n)\) and no live node lies in \((n,s)_R\); +therefore \(\operatorname{owner}_N(k)=s\). If it forwards, the chosen target is +either the closest preceding finger/list entry or the first successor; in both +cases it lies in \((n,k)_R\), so \(\delta_{next}(k)<\delta_n(k)\). Finiteness of +\(N\) gives termination. The branches \(key=n.did\) and \(s=n.did\) discharge +the singleton and exact-owner edge cases. Repair branches are outside the +steady-ring premise. +\end{proof} + \section{DID and Resource Algebra} \begin{definition}[DID namespace] @@ -820,9 +926,10 @@ \section{DID and Resource Algebra} \] \[ \begin{array}{rcl} -D(k)&=&H_D(k),\\ -\operatorname{owner}_N(D(k))&\in&N,\\ -\operatorname{Session}&\subseteq&X_D\times K\times Time. +D_K(k)&=&H_D(\operatorname{did}(k)),\\ +\operatorname{owner}_N(D_K(k))&\in&N,\\ +\operatorname{Session}&\subseteq&X_D\times K\times + \mathsf{Time}\times\mathsf{Ctx}\times\mathsf{Cap}. \end{array} \] \end{definition} @@ -889,11 +996,11 @@ \section{DID and Resource Algebra} \begin{invariant}[Placement] \[ \begin{array}{rcl} -K_{\nu,x}&=&\operatorname{replicaKeys}(H_\nu(x)),\\[2pt] -P_{\nu,x}&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(H_\nu(x))),\\[2pt] +P_{\nu,x}&=&\operatorname{set}(\operatorname{RepKey}^{\rho}(H_\nu(x))),\\ +K^{impl}_{\nu,x}&\subseteq&R,\\ \operatorname{Inv}_{place} &\equiv& -\forall \nu,x.\;K_{\nu,x}\subseteq P_{\nu,x}. +\forall \nu,x.\;K^{impl}_{\nu,x}\subseteq P_{\nu,x}. \end{array} \] \end{invariant} @@ -905,11 +1012,14 @@ \section{DID and Resource Algebra} L_{\nu,x}&=&|O_{\nu,x}|,\\ \mathsf{FullRed}_{\nu,x}&\Leftrightarrow&L_{\nu,x}=\min(\rho,|N|),\\ \mathsf{Collapse}_{\nu,x}&\Leftrightarrow&L_{\nu,x}<\min(\rho,|N|),\\ -\mathsf{LiveClaim}_{\nu,x}(\rho)&\Rightarrow&\mathsf{FullRed}_{\nu,x},\\ +\mathsf{LiveClaim}_{\nu,x}(\rho)&\Rightarrow& + \operatorname{Inv}_{place}\land\mathsf{FullRed}_{\nu,x},\\ \mathsf{Report}_{Rings}&\ni& |\{(\nu,x):\mathsf{Collapse}_{\nu,x}\}|. \end{array} \] +When \(|N|<\rho\), fewer than \(\rho\) distinct live owners is not collapse; +collapse means fewer owners than the live topology can realize. \end{obligation} \begin{definition}[Mailbox] @@ -925,8 +1035,8 @@ \section{DID and Resource Algebra} \[ \begin{array}{rcl} h&=&(\nu,\rho,Intro,Relay,\\ -&&Cap,K,exp,rank),\\ -VID(h)&=&H_H(h),\\ +&&\mathsf{Cap},K,exp,rank),\\ +\operatorname{vid}(h)&=&H_H(h),\\ \mathsf{Lookup}(h)&=&P^N_H(h),\\ \mathsf{Valid}(h,\sigma)&=&\operatorname{Auth}_H(h,\sigma). \end{array} @@ -992,13 +1102,14 @@ \section{Cryptographic Carriers and Traffic} \] \[ \begin{aligned} + sid&=(d,s,e,ctx,cap),\qquad d\in X_D,\quad s\in K,\\ m_f&=sid\Vert seq\Vert last\Vert cipher,\\ - \operatorname{FrameValid}_{\Delta}(f) + \operatorname{FrameValid}(f) \Leftrightarrow\;&V(pk_s,\sigma_s,m_f)=\top\\ &\land\; - \operatorname{Session}(D(pk_s),sid,e)\\ - &\land\; - \operatorname{SeqOK}_{\Delta}(seq,last). + \operatorname{Session}(d,s,e,ctx,cap)\\ + &\land\;pk_s=s\\ + &\land\;\mathsf{FrameCtx}(f)=\mathsf{BoundCtx}(sid). \end{aligned} \] \end{definition} @@ -1019,13 +1130,17 @@ \section{Cryptographic Carriers and Traffic} &&{}\land seq-next\leq w\\ &&{}\land(final=\bot\lor seq\leq final)\\ &&{}\land(last\Rightarrow\mathsf{NoFuture}_{\Delta}(seq)),\\ -\operatorname{SeqOK}_{\Delta}(seq,last)&\Leftrightarrow& - \mathsf{Dup}_{\Delta}(seq)\\ -&&{}\lor\mathsf{New}_{\Delta}(seq,last),\\ -\mathsf{Dup}_{\Delta}(seq)&\Rightarrow&\mathsf{emit}=\epsilon. +\operatorname{Accept}_{\Delta}(f)&\Leftrightarrow& + \operatorname{FrameValid}(f) + \land\mathsf{New}_{\Delta}(seq,last),\\ +\operatorname{DropDup}_{\Delta}(f)&\Leftrightarrow& + \operatorname{FrameValid}(f) + \land\mathsf{Dup}_{\Delta}(seq) + \land\mathsf{emit}=\epsilon. \end{array} \] -Here \(w\) is receiver policy, not a signed wire field. +Here \(w\) is receiver policy, not a signed wire field. A duplicate frame may +be valid, but it is not accepted as new input. \end{definition} \begin{definition}[Secret sharing placement] @@ -1112,7 +1227,7 @@ \section{Ordering, Ranking, and Security} \end{aligned} \] \[ - \chi:Domain_a\times Domain_b\to Order. + \chi:\mathsf{Domain}\times\mathsf{Domain}\to\mathsf{Order}. \] \end{definition} @@ -1148,39 +1263,50 @@ \section{Ordering, Ranking, and Security} \begin{table}[htbp] \centering -\footnotesize -\setlength{\tabcolsep}{2pt} -\begin{tabular}{p{1.05cm}|p{2.0cm}|p{2.45cm}} +\scriptsize +\setlength{\tabcolsep}{1.5pt} +\begin{tabular}{@{}>{\raggedright\arraybackslash}p{1.05cm} +>{\raggedright\arraybackslash}p{2.35cm} +>{\raggedright\arraybackslash}p{2.95cm}@{}} \hline -Attack & Predicate & Required boundary \\ \hline -Sybil & many DIDs, one actor & admission and ranking policy \\ -Replay & stale valid $\sigma$ & TTL, nonce cache, stream/final \\ -MITM & wrong key for DID & DID proof and signed envelope \\ -DoS & unbounded resource use & quotas and chunk bounds \\ +Attack & Predicate & Boundary claimed here \\ \hline +Sybil & one actor controls many DIDs & not solved by overlay; admission, ranking, quota \\ +Eclipse & biased neighbor or successor view & not claimed under Byzantine routing; requires secure-routing policy \\ +Replay & stale valid signature or frame & typed session, expiry, nonce/sequence set \\ +MITM & wrong key for DID or session & DID proof, signed envelope, context binding \\ +DoS & unbounded storage, relay, or chunks & quotas, TTL, chunk bounds, backpressure \\ +Privacy & route or relay observation & relay policy only; no anonymity theorem \\ \hline \end{tabular} -\caption{Security predicates and required controls} +\caption{Threat predicates and claim boundaries} \label{security-table} \end{table} \[ \begin{array}{rcl} \mathsf{Base}&\not\vdash& - \mathsf{SybilResist}\land\mathsf{Anon}\land\mathsf{DoSResist},\\ + \mathsf{SybilResist}\land\mathsf{EclipseResist} + \land\mathsf{Anon}\land\mathsf{DoSResist},\\ \mathsf{SecClaim}&\Rightarrow& - \mathsf{Adm}\land\mathsf{Rank} + \mathsf{SelfCertID}\land\mathsf{TypedSession} + \land\mathsf{ReplayReject}\\ +&&{}\land\mathsf{Adm}\land\mathsf{Rank} \land\mathsf{Relay}\land\mathsf{Quota}. \end{array} \] -\begin{obligation}[Replay rejection] +\begin{obligation}[Replay and session-confusion rejection] \[ \begin{array}{rcl} -\operatorname{accept}(s,\eta,t) -&\Rightarrow& - \eta\notin Seen_s\land t Date: Tue, 7 Jul 2026 04:53:24 +0800 Subject: [PATCH 08/19] Address paper review blockers --- papers/cites.bib | 2 +- papers/rings.pdf | Bin 150829 -> 156049 bytes papers/rings.tex | 411 ++++++++++++++++++++++++++++++++--------------- 3 files changed, 281 insertions(+), 132 deletions(-) diff --git a/papers/cites.bib b/papers/cites.bib index 8fbbd5814..bd0bb086d 100644 --- a/papers/cites.bib +++ b/papers/cites.bib @@ -124,7 +124,7 @@ @misc{Libp2p author = {{Protocol Labs}}, title = {{libp2p}: A Modular Network Stack}, year = {2026}, - note = {\url{https://libp2p.io/}} + note = {\url{https://libp2p.io/}, accessed 2026-07-07} } @inproceedings{TorNetwork, diff --git a/papers/rings.pdf b/papers/rings.pdf index 53190d4b6959468b6b8aefe1a43cdb400813886d..81afc48d97c80f08264ecf2b32980b47135d8e5f 100644 GIT binary patch delta 144244 zcmV(@K-RylnhBA^39#%D0WpygB!4zGIWRsx3UhRFWnpa!c-qxnTXP%7m44q}!F>ZO zi%H+R$D-x3C422nL_3mpUA0zH1rkFFGDR{VC|mjUd-^)vgVQquigvP<*am@~zMejp z?_B2S???2A!2jrxX7GPrq$dWy}mdSMmI#6BS9K1>3`Ad^-m{+ zsI#Ykef?iYU%&S4#ZlX|iYeQE$#_G!I?|1RUVU>(2w|KMVc;J|2tOl)o+gTL?tixU+(|13bEg94 zYz~>bZ?w6=&rZXH`c{*({%U)3%=F@yyKZ~B+HF2`uaAvbY**KJx3D*Q;eOrjkktT* zH>{(r@1JA06gUEnm-H~9kk6xSl+Nk)Zy40=BkOO8`)Bq#=ObNW`bq2wV$4LCzF zpa22DA7Ma|4}X|0a@h+NZ8p+p$5T2SuygoeL{Q_RDyG*~1@r3I92HKidc}-i*tSnW zy4Vgc!h^>D*J^ND#Ye4PXNO@I@f&vL+qz$@K6n;?vEOnSl!jiDE=W*auwXE(kIM_SE z;$&xtZw5Q4TXnGbR%f~R=Br*pTNKAhUy~3R+oN)_m}xr-2jOl%M8U3DU7*{){Lt_Z z34h{yPssa0Cd9Y|^0Z3^1C$C6>YTp9O))9O;4+(`2@nP91$GL+y5k`{cX#~>uzIBz 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zy5!MP$Y-}M4q8TU(_&ge??QIcdS^N0+m?C4@29#{Kz5yGIf(002|4^=mh(e@U8*1# z6XtyKHgtIaIDTkX1NBGds^_OJHGub@Sz5p9QVX>GHcQB%OC1mnYu5u2%Uq5A(WL?C zt<`P>2D0bo0qn#7-(J8v*M11Z-fK4jV;SvcV0=@%g|^Xl8lWNin0C@G`h@n-J~}`L z=`giujE(`x4f7T=4&y9OAhl{|O#Ag2CVqMZO<1+*uDl`q=Uc3)~g2i_iQ z&jIg(+B3kX?EAj3JNql7?EiCv`Syc|$TihtPJs$#Ze(+Ga%Ev{3T19&Z(?c+b97;H Wba--QW(qMeI50Od3MC~)Peuxg(vN`v diff --git a/papers/rings.tex b/papers/rings.tex index 8e56248d3..bec648a1a 100644 --- a/papers/rings.tex +++ b/papers/rings.tex @@ -1286,11 +1286,17 @@ \section{Verification Evidence and Evaluation Scope} \] \end{definition} -\begin{definition}[Reliability baseline] +\begin{definition}[Chord performance baseline] \[ \begin{array}{rcl} -failrate&=&\dfrac{|F|}{|Q|},\\[8pt] -timeoutMean&=&\dfrac{1}{|Q|}\sum_{q\in Q}to(q). +\operatorname{fail}(Q,F)&=&\dfrac{|F|}{|Q|},\\[8pt] +\operatorname{timeout}(Q)&=&\dfrac{1}{|Q|}\sum_{q\in Q}to(q),\\[8pt] +\eta&=&(|N|,\mathsf{churn},\mathsf{stabilize},\mathsf{loss}),\\[4pt] +B_C(\eta)&=& + (\mathbb{E}[h_C], + \operatorname{timeout}(Q_C), + \operatorname{fail}(Q_C,F_C)),\\[4pt] +\mathbb{E}[h_C]&\in&O(\log |N|). \end{array} \] \end{definition} @@ -1300,25 +1306,33 @@ \section{Verification Evidence and Evaluation Scope} \begin{aligned} \mathsf{Report}_{Rings} = (&N,\rho,r,\mathsf{transport},\mathsf{runtime},\\ - &\mathsf{scheduler},T_{total},timeoutMean,failrate). + &\mathsf{scheduler},\vec{T}_R, + \operatorname{timeout}(Q_R), + \operatorname{fail}(Q_R,F_R)). \end{aligned} \] \[ - \mathsf{Baseline}_{Chord} + B_C(\eta) \not\equiv - \mathsf{Measurement}_{Rings}. + \mathsf{Report}_{Rings}. \] \end{obligation} \[ \begin{array}{rcl} -\vec{T}&=&(T_{conn},T_{hop},T_{crypto},T_{app},T_{witness}),\\ -\mathsf{PerfClaim}_{R}&\Rightarrow&\mathsf{Measure}_{build}(\vec{T}),\\ -\mathsf{Baseline}_{C}&=&\mathsf{hop/churn}. +\vec{T}_R&=&(T_{conn},h_R T_{hop},T_{crypto},\\ +&&T_{app},T_{witness}),\\ +\mathsf{Overhead}_{R/C} + &=&(T_{conn},T_{crypto},T_{app},\\ +&&T_{witness},\mathsf{runtime}),\\ +\mathsf{PerfClaim}_{R} + &\Rightarrow& + \mathsf{Measure}_{build}(\mathsf{Report}_{Rings})\\ +&&{}\wedge\mathsf{Cite}(B_C). \end{array} \] -Chord remains the overlay baseline~\cite{Chord}; Rings performance requires -Rings-specific measurements. +Chord supplies the lookup/churn baseline~\cite{Chord}; Rings performance +requires Rings-specific measurements. \section{Related Work} From 726b29240cdac6f552214fcc9d3bebcea8ef35d6 Mon Sep 17 00:00:00 2001 From: "Ryan.K" <662346+RyanKung@users.noreply.github.com> Date: Sun, 5 Jul 2026 21:01:34 +0800 Subject: [PATCH 05/19] Add benchmark data to Rings paper --- papers/rings.pdf | Bin 119467 -> 131569 bytes papers/rings.tex | 128 +++++++++++++++++++++++++++++++++++++++-------- 2 files changed, 108 insertions(+), 20 deletions(-) diff --git a/papers/rings.pdf b/papers/rings.pdf index 829c957f6e8d60120637338de200ed9005493e37..0ba1c55d159dc6e0d125f20588089f904dd58fd1 100644 GIT binary patch delta 93158 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