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 the new Topological Data Analysis (TDA) processor, including configuration parameters, delay embedding options, and usage examples.
  • Reorganized Processors documentation section with updated topic ordering.

[coderabbitai]

📝 Walkthrough

Walkthrough

This PR adds documentation for a new Topological Data Analysis (TDA) metrics processor and reorganizes the Processors section table of contents in SUMMARY.md. The TDA processor documentation describes its aggregation behavior, sliding window mechanics, optional delay embedding, persistent homology computation via Ripser, and output metrics.

Changes

Cohort / File(s)	Summary
Documentation: TDA Processor pipeline/processors/tda.md	New documentation page detailing the TDA processor's functionality, including metrics aggregation, delay embedding options, persistent homology computation, threshold handling strategies, output gauge metrics (Betti numbers), and two YAML configuration examples.
Table of Contents SUMMARY.md	Updated Processors section ordering: repositioned "Filters as processors" and "Conditional processing" entries, and added new "Topological data analysis (TDA)" entry.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Possibly related issues

• Feb 2026 audit - docs: processors: tda plugin doc missing (new) #2497: This PR directly addresses the request to add TDA processor documentation and update the SUMMARY.md table of contents with TDA and reordered Processors entries.

Possibly related PRs

• consolidate YAML / processor info  #2183: Both PRs involve reorganizing the Processors section ordering in SUMMARY.md ("Filters as processors" and "Conditional processing" repositioning).

Suggested reviewers

• cosmo0920
• patrick-stephens

Poem

🐰 A new processor hops into view,
TDA topologies, so mathematically true!
Betti numbers dance, persistent homology flows,
Our docs now complete—watch the knowledge grow! ✨

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 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 a new TDA processor plugin. It is concise, specific, and clearly indicates the primary purpose of the PR.
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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[coderabbitai]

🧹 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

[eschabell]

@patrick-stephens ready for review!