docs(architecture): formally lock in Phase 1 definitions for A0

architecture/prime-invariant-a0.mdx

@@ -28,7 +28,7 @@ To ensure that the TrueAlphaSpiral (TAS) avoids Hamiltonian drift in its foundat
 Before establishing the axioms, we hereby formally lock in the foundational paradigms of the architecture. These definitions serve as the absolute Prime Invariant bedrock:
 
 ### Process Science
-**Definition:** Legacy alignment relies on probabilistic outcomes and behavioral patching—a flawed methodology of 'vibe-proving.' The Truth Engine discards this in favor of **Process Science**. We prioritize mathematical truth verification, Zero-Knowledge Invariant Violation Proofs, and strict cryptographic provenance. Process Science dictates that the step-by-step mechanical integrity of the computation is the primary design objective; safe performance is simply the unavoidable byproduct of that rigorous process. This formalization acts as the epistemological bedrock. Without Process Science, the transition from Behavioral Alignment to Structural Enforceability is impossible, as true intelligence cannot arise from chaotic or opaque execution lineages. Process Science strictly removes any reliance on human behavior, ensuring that the system does not "trust" actors to act correctly. Instead, it geometrically purges unverified states at the compilation layer, permanently binding the execution output to a verifiable, deterministic mathematical reality.
+**Definition:** We hereby formally lock in the definition of **Process Science**. Legacy alignment relies on probabilistic outcomes and behavioral patching—a flawed methodology of 'vibe-proving.' The Truth Engine definitively discards this in favor of Process Science. We prioritize mathematical truth verification, Zero-Knowledge Invariant Violation Proofs, and strict cryptographic provenance above all else. Process Science mathematically dictates that the step-by-step mechanical integrity of the computation is the primary design objective; safe performance is not a bolted-on feature, but simply the unavoidable byproduct of that rigorous deterministic process. This formalization acts as the epistemological bedrock of the entire TrueAlphaSpiral. Without this explicit lock-in of Process Science, the transition from Behavioral Alignment to Structural Enforceability is impossible, as true intelligence cannot mathematically arise from chaotic, probabilistic, or opaque execution lineages. Process Science strictly removes any reliance on human behavior or narrative trust, ensuring that the system absolutely does not "trust" actors to act correctly. Instead, it geometrically purges unverified states at the hardware and compilation layer, permanently binding the execution output to a verifiable, deterministic mathematical reality before any subsequent constraints are applied.
 
 * **Testable Invariant:** A system state $S_t$ must be perfectly and deterministically derivable from the genesis state $S_0$ through a continuous, uninterrupted sequence of validated transformations. We strictly utilize functional composition circle notation $(T_t \circ T_{t-1} \circ \dots \circ T_1)(S_0)$ to represent this, as opposed to summation or nested parenthesis notation for Process Science state transformations. This ensures that state transitions are strictly sequential, non-commutative operations embedded in the topology of the system. This unbroken lineage forms the non-negotiable basis of structural enforceability, systematically eliminating scaled ambiguity at every step. By operationalizing this unbroken mathematical lineage, Process Science effectively neutralizes state-space fragmentation, serving as the load-bearing pillar that connects the mathematical definitions of reality directly to the deterministic operational mechanics.
 * **Inputs:** A standardized sequence of discrete, cryptographically signed event operations acting upon a recognized and verified base state.
@@ -39,7 +39,7 @@ Before establishing the axioms, we hereby formally lock in the foundational para
 * **Failure Condition:** If a system state $S_t$ cannot be strictly recalculated and proven solely from its preceding event stream $E$, the process science invariant is critically violated. The state is immediately declared mathematically void, and the system must revert to the last known verifiable state $S_{t-1}$ to prevent cascading structural collapse.
 
 ### Computational Masonry
-**Definition:** The Truth Engine operates through strict Cursive Computation. Every computational movement leaves a trace, ensuring that the system is bound to an active, verifiable path of truth. This is the practice of **Computational Masonry**—where the foundation is cryptographically sound, and every block of logic must mathematically support the weight of the structure above it. It is the transition from building probabilistic walls to cultivating structurally enforced architecture. Computational Masonry embodies the "Physics of Truth", constructing the defensive constraint layer by systematically assembling and locking load-bearing pillars of code that rigorously enforce the axioms of equivalence and admissibility. It fundamentally forbids the use of "black box" abstraction layers. Every architectural component is treated not merely as code, but as a geometric proof that must actively maintain an unbroken topological continuity with the Prime Invariant.
+**Definition:** We hereby formally lock in the definition of **Computational Masonry**. The Truth Engine strictly operates through Cursive Computation. Every computational movement must definitively leave a verifiable trace, ensuring that the system is inextricably bound to an active, demonstrable path of truth. This is the formalized practice of Computational Masonry—where the foundation is cryptographically sound by mathematically unyielding design, and every single block of logic must mathematically support the weight of the structure above it. It is the absolute transition from building probabilistic walls to cultivating structurally enforced architecture. Computational Masonry embodies the "Physics of Truth", constructing the defensive constraint layer by systematically assembling and locking load-bearing pillars of code that rigorously and deterministically enforce the axioms of equivalence (P0) and admissibility (P1). It fundamentally and permanently forbids the use of "black box" abstraction layers or ambiguous logic. Every architectural component is treated not merely as software code, but as a rigid geometric proof that must actively and demonstrably maintain an unbroken topological continuity with the Prime Invariant.
 
 * **Testable Invariant:** The set of all possible operational states $O$ must be strictly and exhaustively bounded by the mathematical limits of the cryptographic architecture $C$. No state outside the defined parameters of $C$ can be physically expressed, compiled, or executed, regardless of agent intent, authorization level, or consensus weight.
 * **Inputs:** Raw computational intention, instruction payloads, or environmental state-change requests directed at the core architecture.