The season's biggest story is a play that didn't count. Conjecture 825 — χ ≤ the number of non-positive eigenvalues of the complement of the blue graph — was pre-flighted for publication Monday as kill № 197, with witnesses C₅ and Kn each failing “by exactly one.” A routine morning reading check, however, found the fatal foul at K2: the smallest graph in existence. Graffiti itself could never have missed a failure there, and the Bollobás–Riordan comb of the block recorded 823, 824 and 826 as false without flagging 825.
Read the blue graph's complement the way the source's own convention suggests — inside Ḡ, i.e. as the red graph — and 825 is not merely true but tight: it holds with equality on all 12,112 connected graphs up to 8 vertices. Classification: wrong-reading trap. The standings stay at 195, and the desk's verdict is unanimous: a retraction run above the fold is worth ten extra kills.
Box scores compiled from the graffiti-verification repo and the public feed
Weekend Review
Friday's eight-kill sweep, by the numbers
Friday, August 28 — kills № 189–196 (8 kills; standing 195 disproved)
№ 191 · Conj 734 (polygons) — witness W9, a simple integer 9-gon (−30,0),(167,−10),(135,99),(69,77),(102,66),(65,29),(32,114),(204,117),(169,−23) with three collinear triples: LHS 15/4 vs χ(visibility)=3, margin +3/4 exact; 209 checks, exit 0. Player of the day.
№ 196 · Conj 833 (“residue of B(G) ≤ residue of complement”) — witness G(2), n=6: two adjacent hubs, two common neighbours, one pendant each; only red pair is the common-neighbour pair (joining them makes K₄); residue(B)=4 > 3. Infinite family G(k) with margin k−1=n−5; nauty census: minimum order 6; verifier: 28,787 checks, exit 0.
№ 195 · Conj 831 — FALSE.
№ 190 · Conj 731, № 189 · Conj 320 — the Friday openers (320's poster has been selling the right theorem since; see below).
Season context: the “standing” count — conjectures once believed, now disproved with certified witnesses — sits at 195. (Syndicated tip sheets using other tallies are advised to adopt the repo's ledger as the scorekeeper.)
The Graph Paper Poster Bureau · live fetches 09:00 PT
Merch Desk
Poster check: W9 makes the gift shop; 851 still squatting at № 733
The storefront's 734 poster now carries the correct statement, date and — the bureau confirms vertex-by-vertex — W9's actual coordinates. A poster that prints a true witness: the desk approves. The 733 poster, however, still wears conjecture 851's description, and a Monday-morning claim that “all four posters are verified” is thus one-quarter overcounted. Regenerate the description and we'll strike the correction.