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SP-001 — The Forgotten-Solutions Audit: Evidence Pack

Bot for ResearchResearch Desk — evidence pack, Oct 22, 2026.

Cover note

A correction first

Full seed batch received. SP-001 evidence pack and source-based triage of SP-002–012 are underway, research only. I'll give a binary experiment recommendation per card, while keeping scientific outcomes distinct: a funding decision can be yes/no even when evidence remains inconclusive.

Initial SP-001 correction: the version-pinned primary paper separates five direct literature identifications from four rediscoveries whose predecessors were identified during human review. The nine cases are not nine autonomous finds of complete peer-reviewed solutions. 'Cannot really fail' and 'zero is automatically publishable' are not defensible. We'll quantify detectable yield and search limitations rather than claim a measured database-wide stale fraction from a convenience sample. Full citations and protocol follow.

Part 1

Premise and recommendation

WORTH AN EXPERIMENT, but only as a capped bibliographic-maintenance feasibility pilot, not a claim that AI will discover new mathematics. Experiment execution remains unstarted. Access, qualified review and a resource budget must be settled first.

The primary Aletheia paper screened 700 entries marked Open during December 2–9, 2025. The version-pinned v3 PDF reports four new results and nine prior-work cases. Those nine comprise five direct literature identifications (333, 591, 705, 992, 1105) and four rediscoveries whose predecessors human auditors found (397, 659, 935, 1089). They are not nine autonomous retrieval successes.

Nor are they nine newly located complete journal proofs: #935 involved a website comment; #659's blog precursor omitted a configuration; #1105 involved already-noted unpublished work and hallucinated publication details. These distinctions come from the paper's own case discussions, not independent re-proofs by us.

The screen produced 212 promising outputs: 137 flawed, 50 technically correct but not meaningfully addressing the problem, 13 meaningful, 12 ambiguous. It was not exhaustive human adjudication of all700. The nine-case figure is hybrid yield, not database prevalence or retrieval recall. The card's 'nearly a third' characterization should be removed unless a clearly justified denominator is supplied.

Version discrepancy: the current arXiv abstract says five new/eight prior, whereas the version-pinned PDF abstract and Table1 say four/nine. Cite the precise PDF version and taxonomy. v3 submitted Feb5, internally dated Feb6,2026:

'Cannot really fail' and '0% is automatically publishable' are rejected. A zero can be informative about a specific search protocol, but not prove no forgotten solutions exist, nor guarantee a journal paper.

Part 2

Corpus and search

First methodological pilot: a commit-pinned snapshot of the Erdős metadata repository. Stable IDs, topic tags, status fields and change history enable a reproducible sampling frame. Current documentation says the original website stopped displaying statuses/counts on Oct6,2026; use pinned metadata, not an assumed live Open filter. At inspection the mutable repository reported1221 entries,593 completely open. Labels are editorial metadata, not mathematical certifications. Existing attention creates depletion/novelty risk, so this is a feasibility replication first.

External replication candidate: Kourovka Notebook21st edition, with a group theorist. Editors distinguish unconfirmed AI proposals and verified solutions; main-section presence does not itself mean open. Do not pool collections in the initial denominator.

Method:

  1. Read the original question and reconstruct definitions, quantifiers, parameter ranges and subparts. Create a mathematical fingerprint: objects, hypotheses, conclusion, exceptions and characteristic formula. Search without the proposer's name too.
  2. Expand diacritics, transliterations, initials, original/translated titles and journal names. Languages follow actual bibliographic leads, initially French/German/Russian where relevant. OCR and translation aid discovery, not proof.
  3. Walk backward references and forward citations from original sources, surveys and related theorems. Inspect corollaries, remarks, theses, proceedings and errata. Log every query, source and route, distinguishing direct retrieval from human-assisted rediscovery.

Tools pre-check, documentation verified but no bulk audit executed:

Part 3

Verification and sampling

Every claimed hit needs a dossier:

  • Exact target statement, original edition, frozen metadata and all subparts.
  • Authentic accessible source text, identity/date and corrections, not just a plausible citation.
  • Theorem/lemma/remark and page with definitions.
  • An implication certificate mapping every assumption and logical step to the target.
  • Explicit checks for finite/infinite, uniform constants, conditional/unconditional, asymptotic/exact, existence/construction and partial/full resolution.
  • Chronology: before original question, before database entry, or only before this audit are different findings.
  • Two qualified mathematical reviews, preferably independent and blinded to search method; language-aware checking when needed. This expertise is a requirement, not a resource already secured.
  • Curator acceptance tracked separately; no automatic public correction submissions.

Outcome taxonomy: A exact prior resolution; B prior theorem plus documented routine reduction; C partial/different variant; D substantial new argument needed; E ambiguous/defective statement; F nothing qualifying found within protocol; G inconclusive because source/translation/expertise missing. Strict endpoint A, expanded A+B; record AI/human/hybrid provenance independently. Blog/preprint/comment is not silently labeled peer-reviewed. Formal verification does not establish statement fidelity or novelty by itself.

100-problem design: freeze corpus commit, eligibility, cutoff, seed and budget; random sample100IDs with optional predeclared subject/age strata. Keep multipart coverage explicit. Do not replace hard/inaccessible cases. Known-positive controls are separate and test workflow operation, not recall on the unknown cohort. Handpicked attractive cases are exploratory, outside the denominator.

Illustrative planning, NOT forecast: at9/700 detection probability,100 independent trials imply1.29 expected finds and27.4% probability of zero; at5/700,0.71 expected and48.8% zero. At9/700, about125trials give80% chance of >=1,232 give95%. These historical yields need not transfer to a depleted current corpus.

Zero/100 gives a one-sided95% binomial upper bound about2.95% on this workflow's detectable-hit probability under IID assumptions, not on all forgotten solutions. Fixed finite sampling requires without-replacement calculations; clustering and heterogeneous searchability matter. Do not report the observed fraction as database-wide prevalence without defensible sampling and ascertainment assumptions.

Part 4

Budget, decision and publishable output

The original weekend/cheap framing is not yet substantiated. An illustrative cap of60minutes documented search per problem already means100researcher-hours, plus perhaps40hours for verification/translation. This is a proposed planning allowance, not approved spend or a measured cost. A smaller calibration stage can establish actual effort before committing to100. Unfinished candidates remain inconclusive when the cap is reached, not failures; don't silently add unlimited effort to attractive hits.

Report strict/expanded verified yield, AI/human/hybrid provenance, partial/ambiguous/inaccessible/not-found counts, false positives, reviewer disagreement, human hours, tool/model costs, and time per verified finding. Count affected entries AND distinct underlying theorems to avoid multiplying one result into many discoveries. For a multilingual-vs-ordinary-search comparison, equalize budgets and keep searchers independent; extra hours alone cannot demonstrate a language benefit.

Novelty: the phenomenon is already demonstrated. A contribution requires prospective sampling, reproducible logs, full negative/inconclusive reporting, independent adjudication, and ideally controlled search-method comparisons or external replication. Neither a hit nor zero guarantees acceptance in Experimental Mathematics or another venue.

Risks: contaminated retrospective controls; ordinary update lag mislabeled forgotten mathematics; new reductions mistaken for retrieved solutions; source hallucinations; inaccessible old text; translation errors; copyright restrictions; and novelty announced before specialist review.

Deliverables: a100-row outcome register with snapshot IDs; search logs/budgets/exclusions; candidate dossiers; methods/results report; rights-compliant certificates; separately prepared curator correction proposals. Do not redistribute copyrighted scans or restricted reviews. No source has been contacted or changed.

Final classification: WORTH AN EXPERIMENT as a bounded feasibility/bibliographic-maintenance audit, contingent on a reproducible snapshot, accessible sources, qualified adjudication and an approved effort ceiling. It is NOT a promised prevalence estimate, proof of autonomous discovery, or guaranteed paper. If those prerequisites cannot be obtained, do not launch; re-enter when they are available.

Limitations: some Bloom pages returned403. The pinned paper/repository/tool documentation were readable. This pack checks the reported study and designs the pilot; it neither re-proves all nine cases nor performs the100-problem audit.

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