A registered result in its source context

QGEO.WINDING.SELF.01

Original ledger classification: Identity [E] + typed gate [C] (rank theorem symbolic; enumerations at declared bound; the remaining gate named)

Original claim text

Stage B of the No-Carrier-Reconstruction audit, first narrowing (one module, 11 checks, ~6 s; discovery probe stageb_winding_probe.py 12/12, verdict FORCED): the involution TYPE is killed by a rank theorem -- any involution with a two-dimensional positive eigenspace gives V' = Q P_- of rank <= 1 (char poly x^2 (x - t) identically in Q), so the binary trace code Spec V = {0,1,2} (v566) is unreachable: only the corpus type carries the self-code; (E) BOUNDS the winding normalisation (the winding demand forces the first column to (N,N,N), so q11 = N must itself be an A3 exponent -- N in {4,5,6} give EMPTY classes at the declared B = 6); the ladder self-consistency (v568) is ROBUST -- for every N in {1,2,3} it selects EXACTLY ONE parabolic member (28/16/14 -> 1/1/1); and the saturation self-consistency sat = N^4 (v567's (X) read as a self-consistency) holds ONLY at N = 3 (N=1: 32 != 1; N=2: 512 != 16; N=3: 81 = 3^4): the DOUBLE self-consistency pins (N, Q) = (3, compiler Q) uniquely across the whole N-ablated family -- N_fam = 3 relocates from declared input to consistency-forced within the reconstruction; equivalently the V-spectra {0,2,3}/{0,1,3}/{0,1,2}: only N = 3 carries the binary trace code p_n = 2 + 2^n. THE HONEST DECOMPOSITION (spectrum ablation): freeing the exponent spectrum itself, the surviving double-selfconsistent family is EXACTLY spectrum = {1,2,N} with shape Q(N) = [[N,1,0],[N,2,0],[N,2,1]] (the full 35-spectrum scan in the probe finds no other) -- the self-consistency forces the SHEET spectrum {1,2} (binary trace code) and the compiler SHAPE, and the A3 exponent demand (E) contributes exactly ONE datum, N = 3. REDUNDANCY -- (M) AND (L) FALL TOO: relative to the self-code demands (parabolic + ladder + sat = 81) the monodromy budget and the seam-line demand are REDUNDANT at the declared bound (dropping both widens the class to 1274 members and the self-code still picks exactly the compiler Q): the declared geometric input list shrinks to (S)-existence, (W)-form and (E) -- and THE MAXIMAL ABLATION drops (E) too: (W: column 3(1,1,1)) + integrality + the self-code package alone pin the compiler Q uniquely (29 ladder candidates, one hit): what stays declared is the involution EXISTENCE, the winding FORM and N_fam = 3 (independently anchored in the E8 glue, v1: 240 = 16 x 5 x 3); and the winding FORM's content is located exactly: dropping it entirely leaves a FOUR-element column family {(0,1,1),(0,3,3),(3,3,3),(5,1,5)} of which exactly ONE is uniform -- the compiler: the winding demand is precisely the UNIFORMITY of the column (1 of 4), a genuine declared input with sharply located content. NAMED LIMITS: (E) stays DECLARED ((M)/(L) relocate to redundant-given-the-self-code at B = 6) geometric inputs -- deriving them from mu4/D4/H^1 geometry is exactly the remaining GATE.QGEO.01 (narrowed by two items, NOT closed); NO P2 reduction, AX.P2.01/ANCHOR.GEN.01 markers untouched. [2026-08-01: the involution-existence input is DERIVED -- v590: rigidity (Z/2)^3, narrowing to a unique explicit S0 via the v574 type theorem plus two named demands; GATE.QGEO.01 narrows further; see QGEO.INVOL.01.]

Original classification detail

FORCED: type killed by rank theorem; N <= 3 by (E); double self-consistency (ladder + sat = N^4) pins (N, Q) = (3, compiler Q) uniquely; 11/11 checks; (E)/(M)/(L) ALL redundant, winding form = the uniformity choice (1 of 4) at B = 6 -- the reconstruction needs only involution existence, winding form with N_fam = 3 (E8-glue) and the self-code; gate narrowed by FIVE items; GATE.QGEO.01 narrowed by two items, not closed

Dependencies as recorded

QGEO.QRECON.01; DIAMOND.BIT.SELECT.01; DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; v567; v568