5.3 KiB
Recent AI Math Solves 2026 Import
Status: EXTERNAL_REFERENCE Date ingested: 2026-05-20
Claim Boundary
This note tracks recent AI-assisted or AI-autonomous mathematical solves that should influence Research Stack search policy. These are not internal theorems until the relevant proof object is imported, checked, or locally formalized.
Status labels:
PAPER_BACKED_FORMALIZED:
arXiv/paper claim includes a formal proof artifact or Lean/Mathlib claim
OFFICIAL_REVIEW_PENDING:
official source reports expert-review confidence, but not a final theorem gate
TRACKING_SURFACE:
benchmark or community index useful for routing, not itself a proof
Additions
Fel's Conjecture on Syzygies of Numerical Semigroups
Status:
PAPER_BACKED_FORMALIZED
EXTERNAL_REFERENCE
Source:
arXiv: https://arxiv.org/abs/2602.03716
Claim:
The paper proves Fel's conjecture for normalized alternating syzygy power sums
of numerical semigroup rings. The abstract states that the argument is fully
formalized in Lean/Mathlib and was produced automatically by AxiomProver from a
natural-language statement.
Stack import:
Receipt pattern: natural-language conjecture -> generated Lean proof -> paper
writeup.
Relevant layers: L0 algebraic identities, L5 autoformalization bridge, L6
proof-object-first routing.
Do not claim local validity until the Lean project or proof artifact is checked inside the stack.
Rethlas/Archon Anderson Open Problem
Status:
PAPER_BACKED_FORMALIZED
EXTERNAL_REFERENCE
Source:
arXiv: https://arxiv.org/abs/2604.03789
Claim:
The paper reports an automated framework with Rethlas for informal reasoning
and Archon for Lean 4 formal verification. It reports resolving an open problem
in commutative algebra with essentially no human mathematical intervention.
Secondary summaries identify the target as D. D. Anderson's 2014 question:
whether weak quasi-completeness implies quasi-completeness for Noetherian local
rings, with the system producing a counterexample.
Stack import:
Receipt pattern: theorem retrieval -> candidate proof -> formal agent gap-fill
-> no-sorry Lean project.
Relevant layers: L4 route memory, L5 retrieval/formalization bridge, L6
multi-agent proof search policy.
The safe stack claim is about the reported architecture and proof artifact. Do not promote the Anderson theorem internally until the referenced Lean project is built locally.
OpenAI First Proof Submissions
Status:
OFFICIAL_REVIEW_PENDING
EXTERNAL_REFERENCE
Source:
OpenAI post: https://openai.com/index/first-proof-submissions/
First Proof paper: https://arxiv.org/abs/2602.05192
Claim:
OpenAI reports running an internal model on all ten First Proof problems. Based
on expert feedback, OpenAI says at least five proof attempts, for problems 4, 5,
6, 9, and 10, have a high chance of correctness, while other attempts remain
under review.
Stack import:
Receipt pattern: research-level problem set -> public proof attempt bundle ->
expert feedback loop.
Relevant layers: L6 evaluation design, L4 adversarial proof checking, L5
problem-statement ambiguity handling.
This is not a solved-theorem import yet. It is a review-pipeline import.
Formal Conjectures Benchmark
Status:
TRACKING_SURFACE
EXTERNAL_REFERENCE
Source:
arXiv: https://arxiv.org/abs/2605.13171
Claim:
Formal Conjectures provides a Lean 4 benchmark of research-level formal
mathematical problem statements, including open conjectures and solved problems.
The abstract reports that the benchmark has already been used to make new
mathematical discoveries, including resolutions of open research conjectures.
Stack import:
Receipt pattern: formalized open-problem queue -> verified proof/disproof audit
-> benchmark refresh.
Relevant layers: L5 formal statement routing, L6 contamination-resistant
evaluation.
Use it to seed target selection and proof-checking policy, not as a theorem source by itself.
Erdős AI Contributions Wiki
Status:
TRACKING_SURFACE
PROVISIONAL
Source:
Tao Erdős wiki: https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems
Claim:
The wiki tracks many 2026 AI contributions to Erdős problems, including full
solutions, partial results, formalizations, incorrect attempts, and literature
rediscoveries. The page itself warns that it is provisional and not a definitive
verdict.
Stack import:
Receipt pattern: triage index -> source lookup -> status-tiered import.
Relevant layers: L4 scar handling for incorrect proofs, L6 provenance discipline.
Use the wiki as a watchlist only. Each row needs its own source or formal artifact before promotion.
Search Policy Update
The current frontier is not one single pattern. It is four patterns:
1. AI finds a proof and humans write or review it.
2. AI generates Lean/Mathlib proof artifacts directly.
3. AI searches literature and discovers the problem was already effectively solved.
4. AI generates plausible attempts that require expert review and may fail.
The stack should keep separate receipts for all four. Collapsing them into a single "AI solved it" label destroys the audit value.