[codex] Audit paper against Lean quotient stack

[Fieldnote-Echo]

Summary

• audit the formalization paper against the merged Lean stack with parallel read-only passes over theorem surface, narrative/proof structure, and paper artifacts
• clarify that embeddings and other representations can themselves be treated as relative observation quotients, so the finite target fixes where the quotient chain stops
• update the paper for reachable-image rule counts, product/query-document theorem anchors, comparison/ranking support names, product-domain caveats, window/profile/margin caveats, and a broader three-part conclusion
• mirror key top-k/tie, product-domain, and near-margin caveats in the RAG guide and reviewer brief
• add checked paper-referenced names to docs/theorem-map.md and regenerate the paper PDF/text artifact

Audit Notes

Subagent audit found no stale Lean theorem names and no major overclaims. The main gaps were under-cited product/comparison theorem names, a conclusion that lagged the product/window/profile layers, and caveats around full-product-domain image equalities, top-k/tie behavior, finite-window scope, and near-threshold margins.

Validation

• latexmk -pdf -interaction=nonstopmode -halt-on-error ordvec_formalization_paper.tex
• pdftotext -nopgbrk ordvec_formalization_paper.pdf ordvec_formalization_paper.txt
• perl -0pi -e 's/^\\d+\\n//mg' ordvec_formalization_paper.txt\n- perl -0pi -e 's/\\n+\\z/\\n/' ordvec_formalization_paper.txt\n- LaTeX log warning/error scan: clean\n- paper text artifact scan for standalone page numbers/replacement chars/form-feed: clean\n- make build\n- make verify\n- make check-doc-names\n- make audit\n- make lint\n- git diff --check\n

[qodo-code-review]

Review Summary by Qodo

Audit formalization paper against Lean quotient stack and expand scope documentation

📝 Documentation ✨ Enhancement

Walkthroughs

Description

• Clarify that observation spaces are relative and embeddings can be treated as quotient maps
• Add reachable-image cardinality theorem and product-domain caveats to paper
• Expand conclusion to three-part structure covering retrieval-facing composition layers
• Mirror key caveats about top-k/tie, product domains, and near-margin decisions in guides
• Update theorem-map.md with checked paper-referenced Lean names

Diagram

flowchart LR
  A["Paper audit against Lean stack"] --> B["Clarify relative observation spaces"]
  A --> C["Add reachable-image theorems"]
  A --> D["Expand three-part conclusion"]
  B --> E["Updated paper & text artifacts"]
  C --> E
  D --> E
  A --> F["Mirror caveats in RAG guide & reviewer brief"]
  A --> G["Update theorem-map.md with checked names"]
  F --> H["Comprehensive documentation"]
  G --> H

Loading

File Changes

1. docs/paper/ordvec_formalization_paper.tex 📝 Documentation +85/-10

Expand paper scope with relative observations and retrieval layers

• Add new section clarifying that observation spaces are relative and embeddings can be treated as
 quotient maps with finite recursion stopping at the target
• Insert reachable-image cardinality theorem card_quotientImageRules with formula `|A^{im(Q)}| =
 |A|^{|im(Q)|}`
• Rename subsection from "Refinement and products" to "Refinement and paired targets over one
 quotient" and clarify distinction from product-map quotient
• Add product-domain caveats explaining that product-image equalities apply to full formal domain,
 not arbitrary logged graphs or prefiltered traces
• Expand conclusion from two to three complementary messages, adding retrieval-facing composition
 layers (product quotients, comparison quotients, observation windows, margin/profile theorems)
• Add four new non-claims about top-k equality, product-image domain restrictions, near-threshold
 decisions, and continuous embedding theorems
• Add checked Lean theorem names for product and comparison quotient operations

docs/paper/ordvec_formalization_paper.tex

---

2. docs/paper/ordvec_formalization_paper.txt 📝 Documentation +88/-36

Regenerate text artifact from updated paper

• Regenerate text artifact from updated LaTeX source
• Add clarification on relative observation spaces and finite recursion stopping at target
• Include reachable-image cardinality theorem and product-domain caveats
• Update conclusion to three-part structure with retrieval-facing composition
• Add new non-claims about top-k, product domains, near-threshold decisions, and continuous
 embeddings
• Clean up formatting with consistent whitespace handling

docs/paper/ordvec_formalization_paper.txt

---

3. docs/rag-pipeline-guide.md 📝 Documentation +12/-2

Mirror key caveats and expand scope in RAG guide

• Expand opening section to mention broader quotient stack beyond bitmap theorem (product
 query/document behavior, multi-target signatures, lossy probes, score-threshold decisions)
• Add caveats about pairwise ranking-comparison preservation not proving top-k equality, tie-policy,
 or nDCG preservation
• Add caveat about near-threshold score decisions requiring explicit margin evidence
• Add section clarifying that product-image equalities apply to full formal domain, not prefiltered
 traces or logged candidate graphs

docs/rag-pipeline-guide.md

---

View more (2)

4. docs/reviewer-brief.md 📝 Documentation +16/-0

Add full quotient stack section and mirror domain caveats

• Add new "Full Quotient Stack" section describing broader formalization beyond bitmap theorem
 (quotient search, reachable-image/kernel, fiber topology, product quotients, ranking comparisons,
 observation windows, margin/profile certificates)
• Add caveats about pairwise retrieval and ranking decisions requiring empirical support
• Add caveat that ranking-comparison preservation alone is not top-k, tie-policy, or nDCG theorem
• Add caveat that product-image equalities are theorems about full formal domain, not prefiltered
 traces
• Add caveat about near-threshold score decisions requiring explicit margin evidence

docs/reviewer-brief.md

---

5. docs/theorem-map.md 📝 Documentation +14/-0

Add checked paper-referenced Lean theorem names

• Add foundational quotient theorems and FNCH-specific threshold optimality theorems to theorem map

docs/theorem-map.md

---

[qodo-code-review]

Code Review by Qodo

🐞 Bugs (0) 📘 Rule violations (0) 📎 Requirement gaps (0)

Great, no issues found!

Qodo reviewed your code and found no material issues that require review

[gemini-code-assist]

Code Review

This pull request updates the documentation and formalization papers to detail the broader Lean quotient stack, clarifying aspects such as product quotients, ranking comparisons, observation windows, and score-threshold decisions. It also explicitly documents non-claims, such as the fact that ranking-comparison preservation alone does not guarantee top-k list equality or nDCG preservation. The review feedback suggests minor wording improvements in the documentation to ensure semantic precision, specifically replacing category-mismatched terms like 'proves' or 'is not a theorem' with 'guarantees' or 'does not guarantee' when describing properties.

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