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

Brief & export

findings 2 · accepted 0 · open questions 0 · contested 0

strongest · none formally accepted

finding	confidence	source
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).	0.99	adapter
The Lean 4 theorem `Erdos961.erdos_961.variants.sylvester_schur_1_1` — Erdos961Prop 1 1 (the n=k=1 instance of Sylvester–Schur: every m ≥ 2 has, in {m}, an element that is not 2-smooth) — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib (lake build green; the declaration's proof term carries no `sorry` and no extra axioms).	0.99	adapter

bibliography · 2

cap_6fcdb44f3a2ff0c6 · vc_c0bc8dce9a810f0b
cap_4af431152a035fa4 · vc_6c8d56f8a59a3179

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# Formal-conjectures Lean proofs (kernel-verified)

This frontier holds 2 findings (0 accepted) over 2 sources.

## Significance

- 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). (adapter)
- The Lean 4 theorem `Erdos961.erdos_961.variants.sylvester_schur_1_1` — Erdos961Prop 1 1  (the n=k=1 instance of Sylvester–Schur: every m ≥ 2 has, in {m}, an element that is not 2-smooth) — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib (lake build green; the declaration's proof term carries no `sorry` and no extra axioms). (adapter)

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