A verification-gated campaign on the open Erdős problems: harness, triage benchmark, and failure ledger

We ran a systematic, verification-gated campaign against the open problems of the Erdős problem catalogue: 1217 problems catalogued, 658 open, 646 triaged under a structured rubric, 50 adversarially cross-examined, 30 taken to a cheap kill-switch experiment, and 7 advanced to a funded campaign. Six contributions were posted, among them an improvement to the Turán density of the complete 3-graph on four vertices — π(K₄³) ≤ 112293/200000, below a bound that had stood since 2012 — together with a machine-checked exact value of the strong clique index h₃(4) = 71, an extension of a 1993 exhaustive table, and certified lower bounds in restricted addition. Every claim passed an eight-step gate sequence ending in independent re-verification by a pass that did not produce it, and we report what that discipline measured: across 28 opened claims, 32% needed a change before they were true, 45% of those destined for publication against 24% of internal ones, and the rate rose when a second pass audited the first — so the figure is a floor. We also report the campaign's central negative result, which concerns its own premise. The campaign was designed on the thesis that a systematic sweep would surface open problems left untouched for want of attention. A shape-filtered rescan for the most tractable class of target — an improvable constant with a machine-checkable certificate — returned four candidates with no occupant visible to that sweep, and all four died within hours on evidence of active 2026 occupancy, most of it invisible on the catalogue's own rosters and some of it already recorded in our own files five days earlier. The one record the campaign did take was the one target whose entry barrier had kept everyone else out. We give the funnel, the failure taxonomy distilled from the campaign's numbered operating rules, and the complete ledger of kills, on the view that a harness paper without a denominator is not a measurement.