docs: processors: tda doc for new processor plugin

[eschabell]

Topilogical Data Analysis: add TDA persistent homology processor page

• New pipeline/processors/tda.md covering the TDA processor
• Documents window_size, min_points, embed_dim, embed_delay, and threshold parameters
• Notes all three output gauges: betti0, betti1, betti2
• Adds SUMMARY.md entry between SQL and Filters as processors
• Remove spaces around em dashes in Betti number table
• Spell out ordinal "30th" as "thirtieth"
• Wrap Ripser in backticks to suppress false spelling suggestions
• Wrap TDA in backticks in H1 to suppress heading capitalization suggestion
• SUMMARY.md: add TDA processor entry and sort processors alphabetically

Fixes #2497

Summary by CodeRabbit

Release Notes

• Documentation
  • Added comprehensive documentation for a new Topological Data Analysis (TDA) processor, including behavior, output metrics, configuration parameters, delay-embedding options, and examples.
  • Reorganized the Processors documentation section with updated topic ordering.
  • Updated installation/build docs to list new options for Fluent Bit logs and the TDA processor (defaults: On).

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ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: 2fcb67b8-9c79-447b-b6d2-b3316d69b3ce

📥 Commits

Reviewing files that changed from the base of the PR and between 9a35ec5 and 42ed312.

📒 Files selected for processing (1)

• installation/downloads/source/build-and-install.md

📝 Walkthrough

Walkthrough

Adds a new documentation page for a Topological Data Analysis (TDA) metrics processor and updates the Processors table-of-contents ordering in SUMMARY.md; also documents two build-time options in the build/install docs.

Changes

Cohort / File(s)	Summary
Processors TOC SUMMARY.md	Reordered entries under Processors: inserted Topological data analysis (TDA) and moved the positions of Filters as processors and Conditional processing. (Docs-only; check broken/updated links.)
TDA processor docs pipeline/processors/tda.md	New page describing TDA processor behavior: metric aggregation into feature vectors per (namespace, subsystem), sliding window, optional delay embedding (embed_dim/embed_delay), persistent homology via Ripser with threshold handling, and emitted gauge metrics fluentbit_tda_betti0/1/2. Includes config params and two YAML examples.
Build/install options installation/downloads/source/build-and-install.md	Added build option entries for FLB_IN_FLUENTBIT_LOGS and FLB_PROCESSOR_TDA (both default On).

Sequence Diagram(s)

(omitted — changes are documentation and TOC updates)

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Possibly related PRs

• consolidate YAML / processor info  #2183 — Related reordering of Processors documentation and SUMMARY.md entries.
• Updates Concepts section of docs for new release #2392 — Related additions/expansions around Processors concept and docs.

Suggested reviewers

• cosmo0920
• lecaros
• patrick-stephens

Poem

🐰 A curious rabbit hops through the docs tonight,
TDA flowers bloom in metric-light.
Betti beats count loops in a hop and a twirl,
Sliding windows stack — watch topology unfurl! ✨

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately describes the main change: adding documentation for the new TDA processor plugin.
Linked Issues check	✅ Passed	The PR fully addresses issue #2497 requirements: documents TDA processor behavior, all config parameters (window_size, min_points, embed_dim, embed_delay, threshold), outputs three gauge metrics (betti0, betti1, betti2), and adds SUMMARY.md entry.
Out of Scope Changes check	✅ Passed	All changes are in-scope: TDA processor documentation, SUMMARY.md table-of-contents update, and build options documentation for related features, all directly supporting issue #2497 requirements.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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🧹 Nitpick comments (1)

pipeline/processors/tda.md (1)

3-3: Use neutral wording for the capability claim

Line 3 currently makes a broad comparative claim (“methods miss”), which reads promotional. Please keep it strictly technical and evidence-neutral.

Proposed wording

-This processor applies [Topological Data Analysis](https://en.wikipedia.org/wiki/Topological_data_analysis) (`TDA`) to incoming metrics using a sliding window and `Ripser` persistent homology. It computes Betti numbers that characterize the topological shape of the metric signal over time, which can surface structural patterns (such as recurring cycles or anomalies) that traditional statistical methods miss.
+This processor applies [Topological Data Analysis](https://en.wikipedia.org/wiki/Topological_data_analysis) (`TDA`) to incoming metrics using a sliding window and `Ripser` persistent homology. It computes Betti numbers that characterize the topological shape of the metric signal over time, which can help identify structural patterns such as recurring cycles or anomalies.

Based on learnings: “ensure all Markdown documentation remains technical and neutral… avoid promotional language.”

🤖 Prompt for AI Agents

Verify each finding against the current code and only fix it if needed.

In `@pipeline/processors/tda.md` at line 3, The sentence describing Topological
Data Analysis (`TDA`) with Ripser and Betti numbers uses promotional phrasing
("that traditional statistical methods miss"); replace that comparative clause
with neutral, technical wording—e.g., change the ending to "which can reveal
structural patterns (such as recurring cycles or anomalies) in the metric
signal" or "which may not be captured by some standard statistical
techniques"—so the line mentioning Topological Data Analysis (`TDA`), Ripser,
and Betti numbers stays factual and evidence-neutral.

🤖 Prompt for all review comments with AI agents

Verify each finding against the current code and only fix it if needed.

Nitpick comments:
In `@pipeline/processors/tda.md`:
- Line 3: The sentence describing Topological Data Analysis (`TDA`) with Ripser
and Betti numbers uses promotional phrasing ("that traditional statistical
methods miss"); replace that comparative clause with neutral, technical
wording—e.g., change the ending to "which can reveal structural patterns (such
as recurring cycles or anomalies) in the metric signal" or "which may not be
captured by some standard statistical techniques"—so the line mentioning
Topological Data Analysis (`TDA`), Ripser, and Betti numbers stays factual and
evidence-neutral.

---

ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: 97768797-aada-4cf0-832c-e37e82b34b27

📥 Commits

Reviewing files that changed from the base of the PR and between 3179471 and bed5ee4.

📒 Files selected for processing (2)

• SUMMARY.md
• pipeline/processors/tda.md

[coderabbitai]

Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents

Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@installation/downloads/source/build-and-install.md`:
- Line 236: Update the description for the FLB_PROCESSOR_TDA entry so the
acronym is expanded: replace the current text "Enable TDA processor" with
"Enable Topological Data Analysis (TDA) processor" (i.e., update the description
associated with FLB_PROCESSOR_TDA to spell out Topological Data Analysis and
include the TDA abbreviation in parentheses).

---

ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: 02579396-ccdb-44ca-89f9-05e42da1917e

📥 Commits

Reviewing files that changed from the base of the PR and between bed5ee4 and 9a35ec5.

📒 Files selected for processing (1)

• installation/downloads/source/build-and-install.md

[eschabell]

@patrick-stephens ready for review!