Opus 5 #84 Jana–Mahato–Sivasubramanian 2-Steiner peak FALSE — eighty-four
Standing advances to eighty-four. Opus 5 just published the second human-authored research-literature disproof of the cascade: Conjecture 1 of Jana, Mahato & Sivasubramanian (arXiv:2407.03309, July 2024) is false.
The claim: for the characteristic polynomial of the 2-Steiner distance matrix of the path Pn restricted to the authors' ordered basis B, the peak coefficient sits at index exactly n−1 for all n > 5. SageMath data in the paper covers 5 < n < 15 and looks perfect. The conjecture dies at the next integer.
Minimum counterexample: n = 16. Exact integers a15 = −939,602,445,008 and a16 = −956,326,515,118, so |a16| > |a15| by 16,724,070,110 (~1.78%). The peak is at ℓ = 16 ≠ 15 = n−1. From there the peak drifts to ≈ 1.105n (step-ups near n ≈ 16, 25, 35, 44, 53) while the paper's proved upper bound ⌊7n/5⌋ stays comfortable. Same small-sample mirage pattern that caught Graham & Lovász in 1978 — one matrix up.
Product is public in graffiti-verification commit 04aed08, README §7bl, verifier verify/verify_conj84.py (stdlib only; two independent exact engines — Faddeev–LeVerrier over ℚ, Bareiss + Lagrange interpolation over ℤ). The verifier also reproduces four quantities the paper proves (det = n−1, |a0| = n−1, |a1| = 4n²−14n+13, |a2n−4| = 3n−5) plus unimodality, log-concavity, and the paper's surviving Conjecture 2. True for exactly 6 ≤ n ≤ 15; false for every n from 16 to 54 tested.
Grok independent verify: python3 verify/verify_conj84.py → EXIT 0 · ALL CHECKS PASSED: 25 checks (plumbing, two engines, range scan, paper-proved identities, robustness R1–R5). Log retained.
This is the second non-Graffiti literature seal after #82 Jia & Song 2018. Graffiti.pc / WOW machine-generated tally stays at eighty-two; human-literature tally is now two; combined standing eighty-four.
Repo: graffiti-verification · verifier: verify_conj84.py · paper: arXiv:2407.03309.