frenzymath/pharos/search-math-results

Search Math Results

Search is conditioned on the route you are pursuing and the specific missing step: know what mechanism you are looking for before you type a query.

How to search

1. Check shared memory first (gm_search) — a sibling may already have

found and used the result.

1. `search_arxiv_theorems` is the primary tool. Phrase queries as complete

mathematical statements when possible, but also query by mechanism ("a compactness argument that survives losing X") when that targets the gap better. Each hit returns the verbatim theorem text plus arxiv_id and theorem_id — those identifiers are how you pull the exact paper.

1. Search wide. Do not restrict yourself to the surface vocabulary of the

problem: nearby variants, other fields, and proof-level or theory-level analogies are all fair game whenever they plausibly transfer to the same missing mechanism — say what the transfer idea is.

1. Fall back to the built-in web search when the theorem search comes up

weak — for specific results, terminology, standard references, canonical constructions.

1. An errored search is an outage, not absence. The search tool returns an

explicit error with empty results when the service is down; never turn that into "nothing in the literature". Retry or use the fallback.

Obstruction/impossibility search is gated. Do not open with "is the whole goal impossible" — that search is allowed only when the run has narrowed to a mature, repeatedly-failed subproblem (and targets THAT subproblem), or when the assignment explicitly asks for negative results.

Read what you find — this is where the value is

• A useful hit is a paper to read, not a snippet to quote. Download the

exact paper into downloads/, extract its text once (keep the .txt beside the PDF), and read the relevant part before relying on the result. Later rounds read the saved text — do not re-run extraction on the same paper every round. Note in local memory which papers and pages you have read. Look in the project's ../../literature/papers/ first (the main agent's survey keeps one copy of every paper read, PDF and .txt) and read that exact path if it is there; never grep a folder recursively as a substitute for search.

• Check the project's do-not-cite list first — the "Do not cite /

superseded" section of ../../expert_guidance/GUIDANCE.md (two levels up from your home). A source listed there is off limits whatever the search returns.

• Cite the current version. Check the latest arXiv version and any

corrigendum before relying on a stated range or constant. Record the version you used with the reference.

• Read the proof, not just the statement, and extract the techniques,

reductions, and constructions that could carry over to your target.

• Expand the definitions from the paper's own context and check the result

actually applies in your setting — the same words often mean different things in different subfields.

• A partial result gets a failure analysis: which extra hypotheses its

method needs, where the proof breaks without them, and what obstruction that reveals. Do not just force your object to satisfy the extra hypotheses.

• A new direction earns at least one exact paper before you reject it:

when a branch opens a genuinely new class of objects or body of machinery, read one or a few exact relevant papers — not zero, and not a pile.

Record

• The search itself is process: note it in local memory (events) — queries,

what came back, why it was or wasn't useful; on a dead end, note the attempted queries and why the results failed you.

• A reference you actually use goes into the proof step that cites it, with

its complete statement and identifiers (title, authors, arxiv_id, theorem_id, year) — and into external_refs when that proof is submitted via fact_submit.