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| #!/usr/bin/env python3 | |
| """Public feedback solver audit against independently known exact models.""" | |
| from fractions import Fraction as F | |
| from pathlib import Path | |
| import json | |
| import subprocess | |
| import sys | |
| import tempfile | |
| from feedback_frontier import analyze | |
| ROOT=Path(__file__).resolve().parent | |
| checks=0 | |
| cases=[] | |
| def check(ok,label): | |
| global checks | |
| if not ok:raise AssertionError(label) | |
| checks+=1 | |
| def matrix(d,terms): | |
| q=[[0 for _ in range(d)] for _ in range(d)] | |
| for i,j,value in terms:q[i-1][j-1]=value | |
| return q | |
| def input_one(q,alpha=None): | |
| data={'generators':[q],'probabilities':['1']} | |
| if alpha is not None:data['alpha']=alpha | |
| return data | |
| def basic(data,name,h,b,beta): | |
| result=analyze(data) | |
| check(result['nilpotent_base_certified'],(name,'base certified')) | |
| check(result['h']==h,(name,'height')) | |
| check(result['b']==b,(name,'spectral order')) | |
| check(result['beta']==beta,(name,'frontier')) | |
| check(result['M']==len(data['generators'][0])**2,(name,'operator dimension')) | |
| check(json.loads(json.dumps(result))==result,(name,'JSON roundtrip')) | |
| cases.append({'name':name,'h':h,'b':b,'beta':beta}) | |
| return result | |
| def zero_matrix(d):return [['0']*d for _ in range(d)] | |
| def main(): | |
| scalar=input_one(matrix(1,[(1,1,{'2':'1'})]),'4') | |
| result=basic(scalar,'scalar feedback',0,'4','4') | |
| check(result['critical']['initial_derivatives']==[[['1']]],'scalar initial value') | |
| check(result['critical']['ode_coefficients']==['-1'],'scalar exponential ODE') | |
| check(result['full_horizon_iff_N_t_beta_bounded'],'scalar all-horizon law') | |
| check(result['alpha_phase']['kind']=='entire_ode','scalar critical phase') | |
| for alpha,kind in [('2','polynomial'),('5','exponential')]: | |
| data=dict(scalar,alpha=alpha);phase=analyze(data)['alpha_phase'] | |
| check(phase['kind']==kind,('scalar alpha phase',alpha)) | |
| if kind=='exponential':check(phase['r']['polynomial_coefficients_descending']==['1','-1'],'exact spectral coefficient polynomial') | |
| cycle=input_one(matrix(3,[(1,2,1),(2,3,1),(3,1,{'1':'1'})]),'2/3') | |
| result=basic(cycle,'fractional three-cycle',2,'2/3','2/3') | |
| check(result['v_k']==[0,0,0,2,2,2,4,4,4],'cycle exact moment orders') | |
| check(result['critical']['ode_coefficients']==['0','0','-3','0','0','3','0','0','-1'],'cycle exact characteristic limit') | |
| E33=zero_matrix(3);E33[2][2]='1' | |
| for k,L in enumerate(result['critical']['initial_derivatives']):check(L==(E33 if k%3==2 else zero_matrix(3)),('cycle leading derivative',k)) | |
| check(result['critical']['first_attaining_word_length']==5,'cycle first higher tie') | |
| check(result['alpha_phase']['gamma']=='4/3','spectral phase normalization') | |
| two_cycle=input_one(matrix(2,[(1,2,1),(2,1,{'1':'1'})]),'1/2') | |
| result=basic(two_cycle,'two-cycle feedback',1,'1','1') | |
| check(result['critical']['ode_coefficients']==['0','-2','0','1'],'two-cycle sinh ODE') | |
| check(result['alpha_phase']['kind']=='polynomial' and result['alpha_phase']['face_indices']==[1],'subcritical Newton face') | |
| protected=input_one(matrix(4,[(1,2,1),(1,3,1),(2,4,{'1':'1'}),(3,4,{'1':'-1'})]),'5') | |
| result=basic(protected,'protected signed cancellation',1,'infinity','infinity') | |
| check(result['all_horizons_baseline_bound'],'protected every horizon') | |
| check(result['critical'] is None,'no finite protected critical scale') | |
| check(result['alpha_phase']['gamma']=='5' and result['alpha_phase']['face_indices']==[1],'protected exact Newton profile') | |
| canceled_cycle=input_one(matrix(4,[(1,2,1),(1,3,1),(2,4,{'1':'1'}),(3,4,{'1':'-1'}),(4,1,{'2':'1'})])) | |
| result=basic(canceled_cycle,'graph feedback canceled exactly',1,'infinity','3') | |
| check(result['v_k'][:4]==[0,0,4,6],'canceled graph transient orders') | |
| check(result['critical']['first_attaining_word_length']==3,'canceled graph first tie') | |
| transient=input_one(matrix(4,[(1,2,1),(1,3,1),(2,4,{'1':'1'}),(3,4,{'1':'-2'}),(4,1,{'3':'1'})]),'8/3') | |
| result=basic(transient,'transient before spectral feedback',1,'8/3','2') | |
| check(result['full_horizon_iff_N_t_beta_bounded'],'transient exact arbitrary horizon law') | |
| check(result['alpha_phase']['kind']=='entire_ode' and result['alpha_phase']['gamma']=='10/3','later spectral ODE normalization') | |
| check(analyze(dict(transient,alpha='2'))['alpha_phase']['kind']=='polynomial','early critical scale is polynomial') | |
| logarithmic=input_one(matrix(3,[(1,2,1),(3,3,{'1':'1'})]),'3') | |
| result=basic(logarithmic,'logarithmic-window counterexample',1,'2','2') | |
| check(not result['full_horizon_iff_N_t_beta_bounded'],'full-horizon iff correctly rejected') | |
| check(result['critical']['first_attaining_word_length'] is None,'no higher critical tie') | |
| check(all(L==zero_matrix(3) for L in result['critical']['all_horizon_test_block']),'finite pure baseline certificate') | |
| check(result['alpha_phase']['kind']=='exponential','superspectral phase selected') | |
| zero=input_one([[0]],'7') | |
| result=basic(zero,'zero family',0,'infinity','infinity') | |
| check(result['alpha_phase']['limit_polynomial_coefficients']=={'0':[['1']]},'zero family identity profile') | |
| rejection=analyze(input_one([[1]])) | |
| check(rejection['status']=='rejected' and not rejection['nilpotent_base_certified'],'nonnilpotent base rejection') | |
| check('beta' not in rejection,'no unsupported frontier after rejection') | |
| invalid=[ | |
| {'generators':[]}, | |
| {'generators':[[[0,1]]]}, | |
| {'generators':[[[{'-1':'1'}]]]}, | |
| {'generators':[[[{'1/2':'1'}]]]}, | |
| {'generators':[[[0]]],'probabilities':['0']}, | |
| {'generators':[[[0]]],'probabilities':['1/2']}, | |
| {'generators':[[[True]]]}, | |
| {'generators':[[[0]]],'alpha':'0'}] | |
| for data in invalid: | |
| try:analyze(data) | |
| except (ValueError,TypeError,KeyError,ZeroDivisionError):check(True,'invalid input rejected') | |
| else:check(False,('invalid input accepted',data)) | |
| # CLI bytes must reproduce the stored exact example and carry rejection exit 2. | |
| completed=subprocess.run([sys.executable,str(ROOT/'feedback_frontier.py'),str(ROOT/'feedback_input.json')],text=True,capture_output=True) | |
| check(completed.returncode==0,'example CLI successful') | |
| check(json.loads(completed.stdout)==json.loads((ROOT/'feedback_output.json').read_text()),'stored example exact CLI reproduction') | |
| with tempfile.TemporaryDirectory() as tmp: | |
| path=Path(tmp)/'input.json';path.write_text(json.dumps(input_one([[1]]))) | |
| completed=subprocess.run([sys.executable,str(ROOT/'feedback_frontier.py'),str(path)],text=True,capture_output=True) | |
| check(completed.returncode==2 and json.loads(completed.stdout)['status']=='rejected','CLI nonnilpotent rejection status') | |
| # JSON decimal tokens retain their literal rational values at the CLI. | |
| path.write_text('{"generators":[[[0]],[[0]],[[0]]],"probabilities":[0.1,0.2,0.7]}') | |
| completed=subprocess.run([sys.executable,str(ROOT/'feedback_frontier.py'),str(path)],text=True,capture_output=True) | |
| check(completed.returncode==0 and json.loads(completed.stdout)['beta']=='infinity','exact decimal probability parsing') | |
| report={'method':'exact rational public API and JSON CLI checks','checks_passed':checks,'failures':0,'cases':cases} | |
| (ROOT/'feedback_api_results.json').write_text(json.dumps(report,indent=2)+'\n') | |
| print(json.dumps(report,indent=2)) | |
| if __name__=='__main__':main() | |