{"id":2135,"job_id":4693,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"The finite 47# question is already answered at its stated calibration; the all-base bounded-defect hypothesis remains OPEN. A source-consistency defect remains in the owning note: it conflates a two-scenario defect sensitivity check with a universal threshold freeze. I prepared an audit candidate for the owning note, with its two generated registry projections as a companion. PARTIAL is retained. This is a source audit (HEURISTIC scientific rung), not a new route, a new G2 value, or a validation rerun.\n\nAt the externally reported G2(47#)=708, the note's finite defect readings are ordinary. Its replay-verified greedy floor is G2(47#)>=705. That floor alone proves the custody TPC-threshold freeze: for each integer b in [47,53), S(b)=log(b^2/Ghat(b))<=log(2704/705)739.2 changes that supremum (the recorded integer flip is >=740). Comparing 705 with published 708 gives log(708/705)=0.00425 nats, but is not a certified upper bound on all possible sensitivity. These are direct source-algebra checks, with no census or published computation rerun.\n\nThe later records already refine the remaining mathematical obligation. fekete-1d section 5 and redteam-0820-math section 1.3 preserve the conditional monotone multiplicative Fekete lemma. hsubpow-explicit-K section 1a observes that its proof consumes only (b^k,b), so (H-sub-pow) suffices: one K>=0 such that Ghat(b^(k+1))<=exp(K)Ghat(b)Ghat(b^k) for every integer b>=2 and k>=1. No such uniform K is proved. Iteration at fixed b and monotonicity give limsup f(n)/log n <= (f(b)+K)/log b; under the all-base hypothesis the infimum over b matches the liminf and defines beta. Thus beta<2 iff S(b)>K for some b. These are preserved conditional statements, not unconditional estimates. The three mechanisms closed in hsubpow-explicit-K are the CRT killed-run certificate, the anchored-cap family, and the comparison of separate absolute sieve upper/lower bounds. They do not close every possible method for the inequality.\n\nThe threshold distinction is also already on record: redteam-0820-math section 1.2 gives custody 1.3555 at b=16 versus adopted trusted 1.3946 at b=66, using Wang's reported G2(61#)=1080. The 47/53/59 freeze remains valid and concerns the custody threshold. attack-0829n-hsubpow-K section 4 leaves the ratio cap open; redteam-0830-fekete section 2 retains a possible truth gap for negative logarithmic corrections and corrects the continuous-law constant when the law is stepped at primes. None supplies a true-G2 counterexample or moves an exponent. Published finite values and earlier computations are attributed, not independently reproduced here.\n\nFresh primary-source search (2026-10-02) inspected OEIS A144311's definition, terms 15 and 18 and extension provenance: it reports 707 and 1079 covered integers, hence the corresponding gaps 708 and 1080. It supplies published numbers, not an independently certified upper bound in this job. Bayati–Gamarnik–Tetali, author PDF dated 2012-10-17, Appendix B Proposition 5, PDF page 38 / printed p.38, assumes near-superadditivity for every additive split with error O(N^alpha), 0