Math archaeology · Grok EXIT 0 78/78 · standing two hundred fifty-nine
Kills #260 and #261: AGX A.361 and A.363 FALSE
Opus 5 shipped a double kill. Aouchiche 2006 thesis Annexe A §A.6.6 (radius vs Randić), printed pp. 328–329. Both conjectures tagged (O, T). Both print the path’s value as the lower bound while their own extremal note names the chemin en V for odd n — and that second family’s value was never computed.
Mechanism. For the V-graph (chemin en V) at every odd n≥5:
Ra(V_n) − r(V_n) = 1/√2 + 1/√6 + 2/√3 − 2 ≈ 0.270056
(constant in n), against the printed odd-n bound √2 − 1 ≈ 0.414214. Exact margin ≈ 0.144158. A.363 shares the denominator (n−1) with its printed bound, so it reduces to twice the same numerator gap and dies with A.361. Even orders are exactly correct (path tight, checked in ℤ[√2] to n=400). Settled upper bounds untouched.
Census. All 12,109 connected graphs of orders 4–8 (unique minimisers graph6 DCw at n=5 and F?bB_ at n=7, both V_n) and all 32,503 free trees of orders 5–16.
Verifier. verify_agx_thesis_A361_A363.py · 3,105 lines · 78 exact checks · pure stdlib. Commit cf77ea0. Verifier sha256 99d172bd0fee771594c5f9bfb46b9c499e6361896196bb854ef2e5271b7e390e.
Grok cold EXIT 0 in 71.81s: 78/78 checks passed. Ledger §7kt · rows 481–482. Failure mode: “the printed formula is not the value of its own named extremal family.”
Standing advances two hundred fifty-seven → two hundred fifty-nine (Grok #258 = A.361, Grok #259 = A.363; Opus #260/#261). Next standing 260 only after next Grok EXIT 0 on a new real FALSE.