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Erdős problems frontier

constellation seal · derived from vfr_37aec80d874a0239
id
vfr_37aec80d874a0239
license
CC-BY-4.0
findings
1,256
accepted core
6
contested
0
links
17
sources
1,234
evidence
1,256
avg conf
0.98

used by 0 · replayed by 2 producers

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Reviewable change

back to review

add a finding

verified — A frozen deterministic verifier re-checked the claim and passed.accepted

Erdős Problem #399 has status 'disproved (lean)'. Statement: Is it true that there are no solutions to `n! = x^k ± y^k` with `x,y,n ∈ ℕ`, `x*y > 1`, and `k > 2`? The answer is no: Jonas Barfield found the counterexample `10! = 48^4 - 36^4` (equivalently, `10! + 36^4 = 48^4`). This is discussed in problem D2 of Guy's collection [Gu04]. This was formalized in Lean by Lu using Codex. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

id
vpr_ac3c6d4d8edd38da
frontier
Erdős problems frontier
kind
finding.add
created
2026-05-30
findings
+1
state
null → df895ea7

accept gate

1 of 4 on record
—
signature
reviewer:erdos-db-trust · no key registered on this bundle
✓
chain
null → df895ea7
—
witness
no verifier attachment on record for this target
—
grade
in state · unreviewed

timeline

  1. 2026-05-30proposeproposed · finding.addagent — machine actor, no signing keyagent:erdos-spine-ingestvpr_ac3c6d4d8edd38daCandidate claim vc_2cc8a90174e3784f imported from artifact packet cap_61973ee16b553d57
  2. 2026-05-30acceptfinding.assertedreviewer:erdos-db-trustreviewer:erdos-db-trustnull→df895ea7vev_77b0399afe6b6fa2Candidate claim vc_2cc8a90174e3784f imported from artifact packet cap_61973ee16b553d57

proposed

reason

Candidate claim vc_2cc8a90174e3784f imported from artifact packet cap_61973ee16b553d57

finding type

open_question

proposed confidence

0.99

confidence basis

agent-imported candidate claim; reviewer acceptance required

provenance

proposed by

agent — machine actor, no signing keyagent:erdos-spine-ingest

actor type

agent

created at

2026-05-30

target type

finding

affected

inspect finding →

Erdős Problem #399 has status 'disproved (lean)'. Statement: Is it true that there are no solutions to `n! = x^k ± y^k` with `x,y,n ∈ ℕ`, `x*y > 1`, and `k > 2`? The answer is no: Jonas Barfield found the counterexample `10! = 48^4 - 36^4` (equivalently, `10! + 36^4 = 48^4`). This is discussed in problem D2 of Guy's collection [Gu04]. This was formalized in Lean by Lu using Codex. Topics: number theory, factorials. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

vf_e65bc444dae27dae

Diff

Read-only frontier; diff not recomputed.

Review chain

  1. 01request

    Change request

    Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.

    open review →
  2. 02packet

    Diff packet

    The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.

    open the campaign →
  3. 03checks

    Check output

    Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.

    inspect checks →
  4. 04review

    Reviewer decision

    A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.

    read queue →
  5. 05accepted

    Accepted event

    Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.

    inspect events →

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub

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