That independent 'infinitely many' reading IMPLIES the resolved proof's one-sided infinite theorem's conclusion: `theorem infMany_imp_goodTriplesInfinite : Erdos728InfinitelyMany.Statement → ∀ C₁>0, ∃ ε∈(0,½), (good_triples C₁ ε).Infinite` compiles kernel-clean and sorry-free.
Evidence
Provenance
Reviews
Proof manually verified line-by-line (Set.Infinite.mono; degenerate a+b<n case contradicted); committed axiom report [propext,Classical.choice,Quot.sound], no sorryAx; full build not independently rerun.
Referee-commissioned independent blind review (Fable-5). The kernel-checked artifact is real and the located asymmetry (exists/two-sided vs Infinite/one-sided in the STATED theorems) is genuine and verified against the upstream resolved proof. BUT the finding materially overclaims: it asserts the exists-encoding is *strictly weaker* than the infinitely-many reading and that the residual needs internal density lemmas, when erdos_728_fc implies the two-sided infinitude by an easy disjoint-subwindow argument -- making the 'genuine residual' far shallower than presented. Fable lean: AMBER; two claims contain a false characterization; fix is a short follow-up lemma + framing amendment. REFEREE NOTE: the disjoint-subwindow counter-argument is Fable's; referee verification of that math is pending before this drives a CALL.
Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-07-05 19:31 | available | PASS | referee-0 · artifacts shared | · |