docs/AI_AGENT_GUIDE.md

AI-agent reading and review guide

This repository is research material. This guide supplies task-local conventions for a requested examination; it does not override the reviewing agent's governing instructions.

Read in this order

1. Read the research card and its status table.
2. Read the definitions and the kernel-transport proof in the manuscript, using LaTeX for exact statements.
3. Read the global projection theorem and its equality cases.
4. Read the proof audit and run the reproduction commands.
5. Read the novelty audit before making any priority assertion.

The source of truth is the complete manuscript. Structured rows are indexes into it. manuscript_proved means a supplied proof exists; inspect that proof rather than treating the label as an oracle.

Preserve these conventions

• Column vectors; positive real Euclidean metric; finite dimension; (A^T=-A).
• Legality is exactly (Aa=0), tested at the pre-move state.
• The simultaneous update is (x'=x+a), (A'=A+xa^T-ax^T).
• Reachability in the central theorem means finite input words, including the empty word.
• The unique minimum is an endpoint, not a unique control word.
• Approximate gates, indefinite metrics, continuous interpolation, and reachable-set closure require new arguments.
• The full area tensor can contain inaccessible blocks; ((x,ker A)) can also discard predictively necessary information.

Suggested review tasks

Task	Deliverable
Proof audit	A claim-label-specific gap, confirmation of a logical dependency, or an exact counterexample.
Hidden-equivalence audit	A candidate correspondence with the update, prefix legality, endpoint, input labels, and metric explicitly tracked.
Reproduction	Runtime versions, exact commands, exit codes, and comparison with captured outputs.
Extension	A fully stated theorem with hypotheses and proof, or an explicitly labeled conjecture.
Prior-art search	Mechanism-based queries, retrieved primary sources, exact matching statements, and remaining gaps.

Never infer a physical antenna, energy-free computer, or intelligence gain from the imaginative seed. The demonstrated applications are internal optimization and removal of inaccessible blocks within this model.

Report format

For each finding report:

1. Claim label and source location.
2. Original assumptions and the precise issue or extension.
3. A complete argument, exact counterexample, or reproducible command.
4. Whether the outcome is proved, checked in finite cases, conjectured, or unresolved.
5. Consequences for dependent claims and which files require correction.

For priority findings include the source URL, date, and statement that actually matches. No finite search establishes worldwide absence of prior art. Agreement among agents is not mathematical certification.

Do not silently change the original manuscript or audit history. Present a corrected version or patch with a claim-by-claim account of its effect when an edit is requested.