frontiers / frontier

Formal-conjectures Lean proofs (kernel-verified)

id: vfr_97d7d25957384f80
license: CC-BY-4.0
findings: 2
accepted core: 0
contested: 0
links: 0
sources: 2
evidence: 2
avg conf: 0.99

used by 0 · replayed by 0 · first seat open

e4/4 · finding.asserted · reviewer:will · 2026-06-03 · null→5d1d

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cap_6fcdb44f3a2ff0c6 · vc_c0bc8dce9a810f0b

id: vs_43a760d77de5ac98
frontier: Formal-conjectures Lean proofs (kernel-verified)
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

1 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

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locator

title:cap_6fcdb44f3a2ff0c6 · vc_c0bc8dce9a810f0b

imported

2026-06-03T12:00:00+00:00

extraction mode

artifact_to_state_import

authors

Canopus Lean proof-search adapter

caveats

source requires human review before being treated as evidence

Bound findings

The Lean 4 theorem `Erdos1054.f_undefined_at_2` — f 2 = 0 — for the Erdős-1054 function f(n) = least m such that n is a sum of the k smallest divisors of m (some k ≥ 1), f is UNDEFINED at n=2 (junk value 0). Proof: any such sum is 1 + R where the i=0 term is the least divisor 1 and every other term is 0 or a strictly larger divisor (≥ 2), so the sum is never 2. — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib v4.27.0 (lake build green; `#print axioms` = [propext, Classical.choice, Quot.sound] only — NO sorryAx).
theoretical · vf_b8e3badb634a19a0

Evidence atoms

vea_ce9c4151b3cfec97computational · supports
{"artifact_id":"va_f78d5e0808a9ac34","artifact_packet_id":"cap_6fcdb44f3a2ff0c6","candidate_claim_id":"vc_c0bc8dce9a810f0b"}

Review, event, and evaluation records

events

vev_8e115d71ace1e871finding.asserted
Candidate claim vc_c0bc8dce9a810f0b imported from artifact packet cap_6fcdb44f3a2ff0c6
reviewer:will · 2026-06-03

reviewable changes

vpr_46734a4a9d2acfe0finding.add
Candidate claim vc_c0bc8dce9a810f0b imported from artifact packet cap_6fcdb44f3a2ff0c6
applied · agent:canopus-lean-2026-06-03 · 2026-06-03

evaluations

No evaluation rows are attached.