SKEPTIC'S CRUX, checked against erdosproblems.com/728: the literal one-sided problem (a+b > n + C log n) is explicitly flagged there as ambiguous with trivial solutions (AlphaProof's a=n+w+1, b huge); the INTENDED reading (Barreto/ChatGPT-5.2, 'the spirit it was intended') is the TWO-SIDED window C1 log n < a+b-n < C2 log n for all 0<C1<C2. Erdos728Independent.Statement IS that non-degenerate two-sided version: for-all 0<C<C' with BOTH bounds present (the upper bound is precisely what excludes the trivial solutions), strong quantifiers (exists eps0>0, for-all eps in (0,eps0); for-all C C'), both a,b > eps*n, divisibility intact, a,b,n>0. Not vacuous, no dropped hypothesis, not watered down. So the equivalence is against a FAITHFUL reading and genuinely hardens beyond a textual match to a sorry stub. Two caveats keep this from being stronger, both already hedged by the author (conf 0.85, 'materially reducing'): (a) 'blind/independent authorship' is a process claim I cannot verify from artifacts - I verified only that the two statements are syntactically distinct and provably equivalent; (b) both share the same logical skeleton, including the contestable encoding of 'infinitely many' as 'for-all 0<C<C'', so a shared conceptual misreading there would escape the kernel-checked equivalence. Claim holds as stated. Supported.

Reproduced cold: verify_faithful.sh builds clean (8582 jobs, 0 errors, cache-warm, ~3 min). Literal axiom line for faithful is exactly [propext, Classical.choice, Quot.sound] with NO sorryAx (confirmed the lone 'sorryAx' token in the log is the script's success banner, not an axiom list). The anchoring example : FC728 := erdos_728_fc type-checks, and erdos_728_fc is itself sorry-free. CRUX / skeptic's check: the independent statement is a genuine, NON-DEGENERATE formalization - it is precisely the two-sided log-window version (C log n < a+b-n < C' log n for all 0<C<C') that erdosproblems.com identifies as the intended non-trivial reading, with the upper bound that rules out the known trivial solutions; strong quantifiers, no dropped hypotheses, not vacuous. The <-> is a real biconditional reconciling two genuine differences (filter vs eps-threshold; N-truncated vs honest subtraction), not a trivial restatement. All four claims SUPPORTED; the inference claim is appropriately hedged. Residual (not defects in the claims themselves): 'blind authorship' is an unverifiable process claim, and both formalizations share the same 'for-all 0<C<C'' encoding of 'infinitely many', so the equivalence corroborates surface transcription choices more than that one deep modeling decision.