code/simulate.py

"""UPMV: falsifiable, uncalibrated kinetic assembly model. Python 3.10+.
No molecular-dynamics, free-cluster geometry, or experimental claims are implied.
All six protocols use the SAME transient continuous-time Markov chain.
"""
from __future__ import annotations
import argparse, csv, json, math, platform
from pathlib import Path
from dataclasses import dataclass, asdict
import numpy as np
import scipy
from scipy.linalg import expm

ROOT=Path(__file__).resolve().parents[1]
MODES=('random','coded','hierarchical','proofreading','proofreading_hierarchy','locking')
@dataclass(frozen=True)
class Parameters:
    kon: float=1e6             # M^-1 s^-1, illustrative
    c_total: float=1e-7        # M primary component concentration
    koff_correct: float=0.01  # s^-1
    progress_rate: float=0.1  # s^-1, fuel-driven checking/capture
    gap_kbt: float=6.0        # total WRONG-CORRECT energy gap, not per base
    checks: int=2
    b: int=4
    hold_loss: float=1e-6     # s^-1, metastable retained-module loss
    fusion_error: float=1e-4 # per accepted join, illustrative
    fusion_delay: float=60.0 # s per level, counted inside total deadline
    dilution_exponent: float=1.0 # c(level)=c0*b^(-alpha*(level-1))
    deadline: float=20000.0  # s


def generator(lc,lw,dc,dw,mu,checks):
    """E <-> C_j/W_j; C_j/W_j -> next checkpoint -> AC/AW.
    Final capture = metastable retention. AC/AW absorbing during this local assay.
    Reverse checkpoint paths neglected: driven, NOT equilibrium proofreading.
    """
    ns=checks+1; ac=1+2*ns; aw=ac+1
    Q=np.zeros((aw+1,aw+1)); Q[0,1]=lc; Q[0,1+ns]=lw
    for start,dest,d in ((1,ac,dc),(1+ns,aw,dw)):
        for j in range(ns):
            Q[start+j,0]=d
            Q[start+j,(start+j+1 if j+1<ns else dest)]=mu
    Q[np.diag_indices_from(Q)]=-Q.sum(1)
    return Q,ac,aw


def local_stats(lc,lw,dc,dw,mu,checks,time):
    Q,ac,aw=generator(lc,lw,dc,dw,mu,checks)
    p=expm(Q*max(time,0))[0]
    # Floating point roundoff only; normalization checked in test_model.py.
    p=np.clip(p,0,1); p/=p.sum()
    aC=(mu/(mu+dc))**(checks+1); aW=(mu/(mu+dw))**(checks+1)
    wrong_inf=lw*aW/(lc*aC+lw*aW)
    transient=Q[:ac,:ac]
    mean=float(np.linalg.solve(-transient,np.ones(ac))[0])
    # Expected number of progress transitions before capture, including rejected trials.
    reward=np.zeros(ac); reward[1:]=mu
    fuel=float(np.linalg.solve(-transient,reward)[0])
    return float(p[ac]),float(p[aw]),wrong_inf,mean,fuel


def level_plan(N,mode,p):
    hier=mode in ('hierarchical','proofreading_hierarchy','locking')
    if not hier:
        return [(N-1,N,p.c_total,1)]
    L=round(math.log(N,p.b))
    if p.b**L!=N: raise ValueError('Hierarchical N must be an exact power of b')
    return [((p.b-1)*N//(p.b**l),p.b,p.c_total*p.b**(-p.dilution_exponent*(l-1)),l) for l in range(1,L+1)]


def evaluate(N,mode,p):
    levels=level_plan(N,mode,p)
    checks=p.checks if mode in ('proofreading','proofreading_hierarchy','locking') else 0
    gap=0.0 if mode=='random' else p.gap_kbt
    dc=p.koff_correct; dw=dc*math.exp(gap)
    lock=mode=='locking'; delay=p.fusion_delay if lock else 0.0
    usable=max(0,p.deadline-delay*len(levels))
    # Time allocation compensates dilution, with same total wall-clock deadline.
    weights=np.array([1/(p.kon*c/n) for _,n,c,_ in levels]); weights/=weights.sum()
    elapsed=0.; logperfect=0.; ec=0.; ew=0.; em=0.; total_mean=0.; work=0.; records=[]
    for (joins,n,c,l),w in zip(levels,weights):
        tau=float(usable*w); lc=p.kon*c/n; lw=p.kon*c*(n-1)/n
        pc,pw,pinf,mean,fuel=local_stats(lc,lw,dc,dw,p.progress_rate,checks,tau)
        elapsed+=tau+delay
        age=p.deadline-elapsed
        # No hidden repair of old internal joins at the next hierarchy level.
        survive=math.exp(-p.hold_loss*(delay if lock else max(age,0)))
        if lock:
            pw=(pw+pc*p.fusion_error)*survive
            pc=pc*(1-p.fusion_error)*survive
        else:
            pc*=survive; pw*=survive
        missing=max(0,1-pc-pw)
        ec+=joins*pc; ew+=joins*pw; em+=joins*missing
        logperfect+=joins*math.log(max(pc,1e-300))
        total_mean+=mean+delay; work+=joins*fuel
        records.append(dict(level=l,joins=joins,active_variants=n,c_M=c,
                            allotted_s=tau,correct=pc,wrong=pw,missing=missing,
                            mean_capture_s=mean,asymptotic_wrong=pinf))
    # Acquisition of all independent joins <= P(each correct); this model omits gate failures.
    # Its product is conditional on ideal provision of competent children, not a real-device forecast.
    log10=logperfect/math.log(10)
    observed=ew/(ec+ew) if ec+ew else 1.
    hier=len(levels)>1
    # Template instruction format defined in docs; not Kolmogorov complexity or physical work.
    control_bits=64+32*len(levels) if hier else 64+math.ceil(math.log2(max(N,2)))*(N-1)
    return dict(mode=mode,N=N,gap_kbt=p.gap_kbt,progress_rate=p.progress_rate,
                dilution_exponent=p.dilution_exponent,fusion_error=p.fusion_error,
                deadline_s=p.deadline,levels=len(levels),correct_fraction=ec/(N-1),
                wrong_fraction=ew/(N-1),missing_fraction=em/(N-1),
                wrong_among_captured=observed,log10_perfect_yield=log10,
                perfect_yield=math.exp(logperfect) if logperfect>-745 else 0.,
                sum_mean_local_capture_s=total_mean,
                expected_progress_events_complete=work,
                material_families=6,active_decorated_variants=max(r['active_variants'] for r in records),
                recognition_symbols=4,code_slots=16,template_control_bits=control_bits,
                detail=records)


def gillespie(lc,lw,dc,dw,mu,checks,tmax,reps,seed):
    rng=np.random.default_rng(seed); Q,ac,aw=generator(lc,lw,dc,dw,mu,checks)
    counts=np.zeros(3,dtype=int); times=[]
    for _ in range(reps):
        s=0;t=0.
        while s<ac:
            rate=-Q[s,s]
            if rate<=0: break
            t+=rng.exponential(1/rate)
            if t>tmax: break
            probs=Q[s].copy();probs[s]=0;probs/=rate
            s=int(rng.choice(len(probs),p=probs))
        outcome=0 if s==ac else (1 if s==aw else 2)
        counts[outcome]+=1
        if s>=ac:times.append(t)
    return dict(counts=counts.tolist(),reps=reps,seed=seed,
                fractions=(counts/reps).tolist(),mean_completed_s=float(np.mean(times)))


def volume(q,m,t): return sum(math.comb(q,i)*(m-1)**i for i in range(t+1))
def code_bounds(q,m,d):
    return dict(q=q,m=m,d=d,raw=m**q,
                greedy_lower=math.ceil(m**q/volume(q,m,d-1)),
                hamming_upper=math.floor(m**q/volume(q,m,(d-1)//2)))

def greedy_code(q=8,m=4,d=3,limit=128,seed=809):
    rng=np.random.default_rng(seed);words=[]
    for candidate in rng.integers(0,m,size=(30000,q)):
        if not words or np.min(np.sum(np.array(words)!=candidate,axis=1))>=d:
            words.append(candidate)
            if len(words)==limit:break
    return np.array(words,dtype=int)


def write_csv(path,rows):
    rows=[{k:v for k,v in row.items() if k!='detail'} for row in rows]
    with path.open('w',newline='') as f:
        w=csv.DictWriter(f,fieldnames=rows[0].keys());w.writeheader();w.writerows(rows)

def main():
    ap=argparse.ArgumentParser();ap.add_argument('--output',type=Path,default=ROOT/'results');ap.add_argument('--quick',action='store_true');a=ap.parse_args()
    out=a.output;out.mkdir(parents=True,exist_ok=True);p=Parameters()
    baseline=[evaluate(N,m,p) for N in (16,64,256,1024,4096) for m in MODES]
    write_csv(out/'baseline.csv',baseline)
    (out/'baseline_details.json').write_text(json.dumps(baseline,indent=2))
    sweep=[]
    for N in ((64,256) if a.quick else (16,64,256,1024,4096)):
      for gap in (2.,4.,6.,8.):
       for mu in (0.03,0.1,0.3):
        for alpha in (0.,1.):
         pp=Parameters(gap_kbt=gap,progress_rate=mu,dilution_exponent=alpha)
         sweep.extend(evaluate(N,m,pp) for m in MODES)
    write_csv(out/'sweep.csv',sweep)
    # Floor sweep exposes fusion limits; not rare-event experimental evidence.
    floors=[]
    for pf in (0.,1e-8,1e-6,1e-4,1e-2):
      for N in (16,64,256,1024,4096):
       floors.append(evaluate(N,'locking',Parameters(fusion_error=pf)))
    write_csv(out/'fusion_sweep.csv',floors)
    cases=[(0.03,0.09,.01,.2,.1,0,1000.),(.03,.09,.01,.2,.1,2,1000.),(.03,.09,.01,.2,.1,2,30.)]
    validation=[]
    for i,case in enumerate(cases):
        exact=local_stats(*case)
        mc=gillespie(*case,reps=2000 if a.quick else 10000,seed=915+i)
        validation.append(dict(parameters=list(case),exact=[exact[0],exact[1],1-exact[0]-exact[1]],monte_carlo=mc))
    (out/'gillespie_validation.json').write_text(json.dumps(validation,indent=2))
    code=greedy_code(); np.savetxt(out/'example_codebook.csv',code,fmt='%d',delimiter=',')
    distances=np.sum(code[:,None,:]!=code[None,:,:],axis=-1);distances+=np.eye(len(code),dtype=int)*99
    codes=dict(bounds=[code_bounds(*x) for x in [(8,4,3),(16,4,4),(24,4,8)]],
               constructed=dict(words=len(code),q=8,m=4,minimum_distance=int(distances.min())))
    (out/'code_bounds.json').write_text(json.dumps(codes,indent=2))
    threshold=[]
    for eta in (0.,1e-8,1e-5,1e-3):
      for p0 in (.001,.01,.02,.04,.08):
       prob=p0
       for l in range(7):
        threshold.append(dict(eta=eta,p0=p0,level=l,p=prob,C=28,q=2))
        prob=min(1.,28*prob**2+eta)
    write_csv(out/'threshold.csv',threshold)
    manifest=dict(seed_policy='fixed explicit PCG64 seeds 915..917 and 809',
        default_parameters=asdict(p),baseline_rows=len(baseline),sweep_rows=len(sweep),
        gillespie_trajectories=sum(x['monte_carlo']['reps'] for x in validation),
        python=platform.python_version(),numpy=np.__version__,scipy=scipy.__version__,
        limitations=['Independent local sockets, ideal child provisioning, no free-cluster geometry',
                     'Parameters are illustrative, not experimentally fitted',
                     'Hierarchy does not repair hidden internal bonds',
                     'Code-symbol kinetics not inferred from DNA sequence'])
    (out/'run_manifest.json').write_text(json.dumps(manifest,indent=2))
    print(json.dumps(manifest,indent=2))
if __name__=='__main__':main()