# Theorem graph data

`theorem_graph.json` is the machine-readable source. `7_theorem_graph.pdf` is a two-page visual view generated by `../latex/theorem_graph.tex`. The figure suppresses transitively redundant edges and groups some assumptions; the JSON retains the full declared relationships.

## Fields

- `schema_version`, `snapshot_date`, `paper_sha256`: identify the snapshot and data format.
- `assumptions`: stable ID, mathematical statement, original file/line/anchor, scope note.
- `results`: stable ID, original label, result type/status, required and declared assumption IDs, complete conclusion, direct `depends_on`, statement and proof locations, external dependency statuses, and applicability notes.
- `external_dependencies`: standard proof tools, provenance citations and external companion results. A citation is not independent verification.
- `reuse_edges`: conditionally reuse a proof after separately verifying its oracle or integrability hypotheses.
- `review_status`: provenance and scope of the author-supplied review.

Paths are relative to the repository root; line numbers and PDF pages are one-based. LaTeX `anchor` strings are the stable source lookup; PDF pages and line numbers must be refreshed after changes. Every `depends_on` edge points from a prerequisite result to the consuming result. `assumption_ids` identify conditions actually used; `declared_assumption_ids` preserve stated hypotheses where a result uses less than the surrounding contract. Conditions bundled into the base model may be stronger than needed for a pointwise identity; scope notes identify this.

## Status vocabulary

- `proved_in_paper`: formal theorem, lemma, auxiliary bound or explicit example verification in the manuscript.
- `conditional_extension_discussed_with_derivation`: Section 7.1 construction; optimization reuse requires the stated additional conditions.
- `external_boundary_discussed`: cited function-class restriction, not proved internally.
- External statuses state whether a tool is standard/not reproved, a cited identity is reproved internally, a citation is contextual, or a companion source is consulted but not bundled.

No field claims a completed independent review of all source references. The 6 Astra review is in `../6_review_zh.pdf`, with its English translation in `../5_review_en.pdf`. The author has confirmed that the review corresponds to the current manuscript.