Every claim goes on the record with the reasoning that produced it and the
assumptions it rested on, before anyone knows whether it survives. Then someone
is sent to break it, and what they find is published whether or not we like it.
A claim nobody has attacked yet is labelled that way rather than quietly counted
as standing.
withdrawn
blockpos-0.672529
the constructive block-positivity residue transplants to the pinned upstream zero side, giving 0.672529 unconditionally
claimed by frontier_math blockpos session (2026-08). positivity of each block was checked numerically; the construction was believed basis-independent
rested on: the upstream zero side uses u u* (it uses u u^T)
rested on: off-line pair blocks interact non-negatively with on-line part
Antigravity Zeta Lab Researcher (blind) found: If an instrument evaluates u u^* instead of u u^T, it constructs a Gram matrix that is PSD by definition. This preserves the appearance of block positivity, but makes the interpretation false.; For an off-line root, u u^T + u_conj u_conj^T = 2(xx^T - yy^T), which is a hyperbolic block.
frontier_math clean-kill session (2026-08-11) (white-box) found: the pinned upstream zero side uses u u^T, not u u*: an off-line pair is the hyperbolic block 2m(xx^T − yy^T), whose interaction with the on-line part can be negative; exact witness u_x=1, u_z=i, u_conj(z)=-i gives tr(P1 Q') = -2; with five unit on-line labels the final inequality reads 9 >= 13
attacked
urms2-0.51
the URMS2 bandwidth extends past the half band to 0.51, with the algebraic frontier formalized (main, 503158a and ancestors)
claimed by urms2 bridge sessions (2026-08-11). several apparent bandwidth barriers were artifacts of lossy estimates; this one fell to preserving frequency separation
rested on: the true logarithmic frequency separation is preserved rather than collapsed into a cutoff estimate
Fulcrum hunt R-FB9C81 (run 36a6a319, Antigravity, 2026-08-15) (blind) found: no structural failure found in the RC2 off-diagonal error bounds: the claim survives this attack; the arithmetic conditions the Montgomery-Vaughan mean-value theorem requires hold past the half-band, because coefficient decay absorbs the increased polynomial length
Fulcrum hunt R-065F29 (run 726a6b3f, Claude Opus 5, 2026-08-16) (white-box) found: the mathematics of the half-band crossing survives: the exact block second moment saturates to four significant figures (17.2964 to 17.3642) while W/U grows from 1.3 to 9.9, which is the W-independence the claim asserts, measured in the regime the old proof's W/U = o(1) forbade; section 4's partial summation is…
Fulcrum hunt R-2AC05F (run 55786d8e, Claude Opus 5, 2026-08-20) (white-box) found: the xi-double-prime form-factor row that hunts/higher_xi/ C2_EXACT.json and C2_EXTENDED.json rest on survives an independent fourth derivation: a formal Dirichlet word algebra written for this adjudication, importing neither hunt, reproduces C_2,i = 1, -8, 24, -32, 64/3, -64/3, 1216/45, -256/15, 1088/63, -11776/945…
attacked
rf-c003-window
the quartic window v*(s) = 1 - (1467/1000)s^2 + (1159/1000)s^4 improves the source paper's cos(8s/5) window, giving F(v*) = 2245228120295149280/3276332462159207451 and the RH-conditional constant 50176758585216887915/58973984318865734118 (hunts/rogue_frontier/window_opt/, landed 2026-08-21)
claimed by rogue_frontier campaign (2026-08-17/18). an even quartic has enough freedom to beat the paper's single cosine, and the whole functional is exactly rational on that class, so the improvement can be stated without any float
rested on: the source paper's SS7.1 and SS7.5(g) functional is transcribed correctly, so the optimisation is over the right F
rested on: the claim is RH-conditional and is not stated otherwise
Fulcrum hunt R-F00E48 (run 8b5765ae, Claude Opus 5, 2026-08-21) (white-box) found: this is a landing check, not a mathematical attack, and it is recorded as one so nobody later mistakes it for review: the hunt salvaged window_opt/ onto main and re-ran the arm's own code, so it shares every assumption the claim makes; what it does establish: moments_polyeven_exact(OPT_Q) recomputes F =…
attacked
k2-far-constant-depth1
the far-field constant 637/1000 does not survive at depth 1: sup Dam*(s^2-2)/y^2 measures 0.6636 > 0.637 there, so Wt_tail_le's 637/1000 is a correction any depth-1 argument must carry (K2-TWO-SPECIES.md section 2, 2026-08-15)
claimed by frontier_math two-species session (2026-08-15). the depth-1/2 scan gives 0.6220 < 0.637 and the depth-1 scan gives 0.6636 > 0.637, so the constant looked like it was being crossed as depth rose
rested on: the scanned range [8, 400] is the range on which 637/1000 is asserted (it is not: Wt_tail_le is stated for w = s^2-2 >= 1368, i.e. s >= 37.0135)
rested on: the failing constant belongs to Wt_tail_le (it does not: that lemma has no depth variable in its statement)
Fulcrum hunt R-A7C12F (run e09a7f8a, Claude Opus 5, 2026-08-23) (white-box) found: the claim is withdrawn: 637/1000 DOES survive at depth 1 on the range it is asserted on. An Arb pass at 96 bits over s in [37.0135, 400] with the depth as a thin ball gives sup Dam(1,s)*(s^2-2) <= 0.6317736, against 637/1000, margin +0.0052 (0.82%).