Graffiti 646 is false. The conjecture — *Randić index ≤ maximal frequency of coordinates of a maximum clique*, from Michael J. Dinneen (Los Alamos), August 1991 — fell Friday afternoon to a single 7-vertex graph, 35 years after it was printed.
The reason it lasted: the entire 634–654 block sits outside the historical machine-tested survivor list. The original sweep jumps from 632–633 straight to 662, so 646 had never once been run against a computer. This morning 652 fell from the same block; now 646.
The killer graph is `FCptO` (n=7, m=9). It has exactly one triangle, {0,4,6}, whose coordinate vector (2,1,1,1,2,0,2) has maximal frequency 3 — while its Randić index is 1+√6 ≈ 3.449. The margin √6−2 ≈ 0.449 is certified without floating point.
It scales. A k-regular family F_k on n=3k vertices pushes the gap to exactly n/6 — provably optimal for ω=3, since R ≤ n/2 and the maximal frequency is always at least ⌈n/ω⌉.
Two controls confirm the reading. Sibling conjecture 640 (identical right-hand side) survives every block graph of order ≤9, repeatedly tight to margin 0 — a wrong reading would almost certainly have broken it too. And the weaker “maximal clique” variant shows no violation at all, so the literal “maximum clique” wording is what matters. Verifier: 123 checks, 0 failures, including all 23,780 order-9 block graphs. Full writeup, §7ed. Disproof #158.