"""Exact FCC incidence audit and bounded integer mass search, September 29, 2026.

Standalone: save this file and lsm-proton-inputs.json together; run Python 3.
No mesh tolerances, numerical libraries, or particle-dynamics claim is used.
"""
from pathlib import Path
from itertools import product, permutations, combinations
from collections import Counter
from fractions import Fraction
from decimal import Decimal, getcontext
import json

def cell(kind, center):
    p=tuple(center)
    hosts=([tuple(v+(2*s if j==a else 0) for j,v in enumerate(p)) for a in range(3) for s in (-1,1)] if kind=='O' else [q for q in product(*[(v-1,v+1) for v in p]) if (sum(q)//2)%2==1])
    return {'type':kind,'center':p,'hosts':frozenset(hosts)}

def connected(n,edges):
    seen={0}
    while True:
        new=seen|{b for a,b in edges if a in seen}|{a for a,b in edges if b in seen}
        if new==seen:return len(seen)==n
        seen=new

def audit(cs):
    t=sum(c['type']=='T' for c in cs);o=len(cs)-t
    edges=[(a,b) for a,b in combinations(range(len(cs)),2) if len(cs[a]['hosts']&cs[b]['hosts'])==3]
    host_counts=Counter(h for c in cs for h in c['hosts']);host=host_counts.most_common(1)[0][0]
    incident=Counter(c['type'] for c in cs if host in c['hosts'])
    center=tuple(sum(Fraction(c['center'][i],len(cs)) for c in cs) for i in range(3))
    sig={(c['type'],c['center'],c['hosts']) for c in cs};symmetry=0;proper=0
    for perm in permutations(range(3)):
        parity=(-1)**sum(perm[i]>perm[j] for i in range(3) for j in range(i+1,3))
        for signs in product((-1,1),repeat=3):
            def transform(p):return tuple(signs[i]*(p[perm[i]]-center[perm[i]])+center[i] for i in range(3))
            if {(c['type'],transform(c['center']),frozenset(transform(h) for h in c['hosts'])) for c in cs}==sig:
                symmetry+=1;proper+=parity*signs[0]*signs[1]*signs[2]==1
    return {'T':t,'O':o,'cells':len(cs),'chargeUnits':2*o-t,'faceIncidences':4*t+8*o,'faceContacts':len(edges),'exposedFaces':4*t+8*o-2*len(edges),'connected':connected(len(cs),edges),'host':list(host),'hostIncident':dict(incident),'symmetryOperations':symmetry,'properRotations':proper,'bridgeFaces':sum(not connected(len(cs),[e for e in edges if e!=removed]) for removed in edges)}

def run(inputs):
    results={key:audit([cell(c['type'],c['center']) for c in cells]) for key,cells in inputs.items()}
    a,b=results['selected'],results['v15']
    assert (a['T'],a['O'],a['chargeUnits'],a['faceContacts'],a['exposedFaces'],a['bridgeFaces'],a['symmetryOperations'])==(8,7,6,25,38,1,6)
    assert (b['T'],b['O'],b['chargeUnits'],b['faceContacts'],b['exposedFaces'],b['bridgeFaces'],b['symmetryOperations'])==(12,9,6,32,56,0,8)
    assert a['hostIncident']=={'T':8,'O':6} and b['hostIncident']=={'T':8,'O':5}
    assert a['connected'] and b['connected']
    getcontext().prec=40
    ratio=Decimal('1836.152673426');uncertainty=Decimal('0.000000032')
    delta=Decimal(73448)-40*ratio
    for k in range(1,347):
        binding=(delta*k).to_integral_value()
        if abs(binding/Decimal(k)-delta)<=40*uncertainty:break
    assert k==346 and binding==655
    results['mass']={'nodeFaceUnits':73360,'electronFaceUnits':40,'selectedFaceUnits':73448,'v15FaceUnits':73480,'observedRatio':str(ratio),'standardUncertainty':str(uncertainty),'minimumKForThisOneSigmaSearch':k,'bindingCount':int(binding),'electronIntegerCount':40*k,'selectedIntegerCount':73448*k-int(binding),'selectedRatioExact':'25412353/13840','selectedBareRatioExact':'9181/5','selectedBareErrorPPM':str((Decimal(73448)/40/ratio-1)*1000000),'searchScope':'Electron calibration, unchanged node, one integer proton binding count; not a derived universal scale or particle-spectrum fit.'}
    results['scope']='Exact FCC geometry; complete-first-shell constrained minimum; no dynamical stability or experimental particle identity proved.'
    return results

if __name__=='__main__':
    here=Path(__file__).resolve().parent
    source=next(p for p in [here/'lsm-proton-inputs.json',here.parent/'dist/lsm-proton-inputs.json'] if p.exists())
    print(json.dumps(run(json.loads(source.read_text())),indent=2))