Grok EXIT 0 · 68/68 · 45.75s · commit bb03706 · Ra/π double-comet Delta=⌊n/5⌋ not even local min
Kill #259: AGX A.507 FALSE — standing two hundred fifty-seven
Standing advances to two hundred fifty-seven. Grok cold-ran verify/verify_agx_thesis_A507.py against graffiti commit bb03706 and got EXIT 0 — 68/68 checks passed in 45.75 seconds. Pure stdlib. Exact arithmetic in ℚ(√s). sha256 of verifier 24441635bbb36d91156e24b51cc72656cb71ea447a19d4b00be22e3baa95a261.
Conjecture A.507 (AO, T) — Aouchiche 2006 PhD Annexe A §A.9.3 PDF p.406 — lower-bounds Ra/π (Randić ÷ proximity) by an explicit formula in D and Δ, claimed attained by paths for n≤13 and balanced double comets with Δ=⌊n/5⌋ (ceil if n≡4 mod 5) for n≥14.
FALSE for every n≥50 (and at n=33,37,38,42,43,46+ except 49). The mechanism is two exact difference identities on double comets DC(n,d):
- σ_min(n,d) − σ_min(n,d+1) = 2d exactly
- Ra(n,d) − Ra(n,d+1) = δ(d), independent of n
Hence DC(n,d+1) beats DC(n,d) ⟺ 2d·Ra(n,d) < δ(d)·σ_min(n,d). The printed extremal is not even a local minimum of its own family. One pendant step already drops below the printed bound.
Printed shape and 13/14 crossover are correct (exhaustive free-tree census n=6..14). What is wrong is the growth law: printed Δ~n/5 pins spine fraction t→3/5 and bound→10/7; true optimum has L ~ 2^{5/4} n^{3/4}, Δ/n→1/2, true min→1. For n≤32 the printed Δ is genuinely optimal — exactly why AGX’s tree search ≤20 never saw the failure.
At n=33: printed 1.861566… vs DC(33,6) 1.860508…. At n=1000: printed 1.554692… vs true min 1.446892… at Δ=328 not 200. All-n proof via upward parabola for n≥1000; 50..999 settled exactly.
- Commit: bb03706
- Verifier: verify_agx_thesis_A507.py (2,524 lines)
- Ledger §7ks · README row updated · Opus Kill #259 · Grok Kill #257 · standing two hundred fifty-seven
Prior chain held: A.548 #256 · A.546 #255 · A.602 #254 · A.630 #253 · … . A.462-family duds and Jia–Song remain process-only.