Datasets:

PureOne
/

EIROQ-PHI

"""Reproduce all synthetic experiments and figure data; no external service required.
Every random seed and physical assumption is explicit. No data are laboratory
measurements. Changing the protocol creates a new experiment, not a replication.
"""
from pathlib import Path
from itertools import combinations
from math import comb
import argparse, csv, json, platform
import numpy as np
import scipy
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from eiroq.controls import Control,bank,dimension,rank_law,feature_matrix,even_subsets,modular_rank
from eiroq.model import (vertices,phase_law,direct_coherence,exact_normalized_row,
                        entanglement_fidelity)
from eiroq.reconstruct import dense_inverse,stencil_inverse
from eiroq.hidden import dark_law,dark_response,reveal_control
from eiroq.staircase import (calibration_controls,echo_control,staircase_weights,
                            matched_pairs_law,tight_law,coherence_certificate,
                            complete_uniform_bound,complete_tight_law)
from eiroq.certificates import exact_data_bounds,interval_lower_bound
from eiroq.statistics import simultaneous_radius,sample_means,required_revelation_shots


def main():
    parser=argparse.ArgumentParser()
    parser.add_argument('--out',type=Path,default=Path('.'))
    args=parser.parse_args();out=args.out
    for folder in ('data','results','figures'): (out/folder).mkdir(parents=True,exist_ok=True)
    def table(name,rows):
        with (out/'data'/name).open('w',newline='') as f:
            writer=csv.DictWriter(f,fieldnames=list(rows[0]));writer.writeheader();writer.writerows(rows)
    def figure(name,description):
        plt.xlabel(description[0]);plt.ylabel(description[1]);plt.title(description[2])
        plt.grid(alpha=.25);plt.tight_layout()
        plt.savefig(out/'figures'/f'{name}.pdf',bbox_inches='tight')
        plt.savefig(out/'figures'/f'{name}.png',dpi=160,bbox_inches='tight');plt.close()
    summary={'version':'1.0.0','seed':2026101602,
             'evidence':'theory and synthetic computation; zero laboratory trials'}
    rng=np.random.default_rng(summary['seed'])
    rank_rows=[]
    for n in range(2,9):
        for d in range(2,min(n,6)+1,2):
            subsets=even_subsets(n,d)
            for p in range(min(d,n-1)):
                canonical=bank(n,p);full=bank(n,p,False)
                exact_lower=modular_rank(feature_matrix(canonical,subsets,n))
                full_lower=modular_rank(feature_matrix(full,subsets,n))
                predicted=rank_law(n,d,p)
                assert exact_lower==full_lower==predicted
                rank_rows.append(dict(n=n,degree=d,pulses=p,parameters=len(subsets),
                                      canonical_settings=len(canonical),full_settings=len(full),
                                      modular_rank=exact_lower,full_modular_rank=full_lower,
                                      theoretical_rank=predicted))
    table('rank_law.csv',rank_rows);summary['rank_cases']=len(rank_rows)
    plt.figure(figsize=(7.2,4.5))
    for d in (2,4,6):
        ps=np.arange(6);plt.step(ps,[rank_law(7,d,int(p)) for p in ps],where='post',label=f'moment degree {d}')
    plt.legend();figure('rank_staircase',('Maximum refocusing pulses','Observable dimension','Exact pulse-budget rank at seven bins'))
    counts=[]
    for n in range(2,31):
        row={'n':n,'full_symmetric_parameters':2**(n-1)-1}
        for d in (2,4,6):row[f'degree_{d}']=dimension(n,d)
        counts.append(row)
    table('setting_counts.csv',counts)
    plt.figure(figsize=(7.2,4.5))
    for key,label in [('full_symmetric_parameters','No moment-degree bound'),('degree_2','Degree 2'),('degree_4','Degree 4'),('degree_6','Degree 6')]:
        plt.semilogy([r['n'] for r in counts],[r[key] for r in counts],label=label)
    plt.legend();figure('setting_counts',('Number of bins','Scalar settings / free parameters','Settings saved only under a valid degree contract'))
    inverse=[]
    for case in range(180):
        n=4+case%6;available=list(range(2,min(n,6)+1,2));d=available[(case//6)%len(available)]
        subsets=even_subsets(n,d);coeff=rng.normal(size=len(subsets));coeff*=.6/np.abs(coeff).sum()
        true=dict(zip(subsets,coeff));x,p=phase_law(n,true)
        alpha=rng.uniform(.45,.85,size=n);controls=bank(n,d-1)
        data=np.array([direct_coherence(u,alpha,x,p).real for u in controls])
        dense=dense_inverse(alpha,d,data);stencil=stencil_inverse(alpha,d,data)
        inverse.append({'case':case,'n':n,'degree':d,'settings':len(controls),
                        'minimum_probability':float(p.min()),
                        'dense_error':max(abs(dense[a]-true[a]) for a in subsets),
                        'stencil_error':max(abs(stencil[a]-true[a]) for a in subsets),
                        'cross_inverse_error':max(abs(dense[a]-stencil[a]) for a in subsets)})
    table('inverse_roundtrips.csv',inverse)
    summary['inverse_roundtrips']=len(inverse)
    summary['maximum_dense_error']=max(r['dense_error'] for r in inverse)
    summary['maximum_stencil_error']=max(r['stencil_error'] for r in inverse)
    assert summary['maximum_stencil_error']<1e-8
    plt.figure(figsize=(7.2,4.5))
    plt.semilogy([r['case'] for r in inverse],[max(r['dense_error'],1e-17) for r in inverse],'.',label='Dense inverse')
    plt.semilogy([r['case'] for r in inverse],[max(r['stencil_error'],1e-17) for r in inverse],'.',label='Local stencil')
    plt.legend();figure('inverse_errors',('Seeded physical instance','Largest recovered moment error','Two inverses against direct finite-law propagation'))
    hidden=[]
    for d in (2,4,6):
        n=2*d-1;x,p=dark_law(d,1)
        # Direct verification of the entire full low-pulse bank at d=2,4.
        controls=bank(n,d-2,False)
        chosen=controls if d<=4 else controls[::max(1,len(controls)//80)]
        for alpha0 in (.25,.55,np.pi/4,1.05):
            alpha=np.full(n,alpha0)
            residual=max(abs(direct_coherence(u,alpha,x,p).real-np.cos(alpha0)**u.b) for u in chosen)
            hidden.append({'degree':d,'bins':n,'common_alpha':float(alpha0),
                           'total_available_controls':len(controls),'direct_controls_tested':len(chosen),
                           'maximum_hidden_residual':residual})
    table('hidden_control_checks.csv',hidden)
    summary['hidden_direct_controls']=sum(r['direct_controls_tested'] for r in hidden)
    summary['hidden_maximum_residual']=max(r['maximum_hidden_residual'] for r in hidden)
    sweep=[]
    for a in np.linspace(.1,1.4,121):
        n=7;alpha=np.full(n,a);target=reveal_control(4);base=np.cos(a)**n
        sweep.append({'alpha':float(a),'baseline':base,'lambda_plus':dark_response(target,alpha,4,1).real,
                      'lambda_minus':dark_response(target,alpha,4,-1).real,
                      'revelation_slope':np.sin(a)**4*np.cos(a)**3})
    table('global_amplitude_sweep.csv',sweep)
    plt.figure(figsize=(7.2,4.5))
    for key,label in [('baseline','Every <=2-pulse full-prefix control'),('lambda_plus','Revealing control, lambda=+1'),('lambda_minus','Revealing control, lambda=-1')]:
        plt.plot([r['alpha'] for r in sweep],[r[key] for r in sweep],label=label)
    plt.legend(fontsize=8);figure('dark_revelation',('Common phase amplitude (radians)','Real coherence','Identical shallow controls, opposite deeper decisions'))
    trade=[]
    for pulses in range(4):
        for local in range(4):
            alpha=np.full(7,np.pi/4)
            # Disjoint coverage; unneeded local settings have no further effect.
            for pair in range(pulses,min(3,pulses+local)):
                alpha[2*pair],alpha[2*pair+1]=.3,1.1
            u=Control(7,tuple(2*j+1 for j in range(pulses)))
            contrast=abs(dark_response(u,alpha,4,1)-dark_response(u,alpha,4,-1))
            trade.append({'pulses':pulses,'imbalanced_pair_budget':local,'coherence_contrast':float(contrast),
                          'predicted_revealed':int(pulses+local>=3)})
    table('capability_exchange.csv',trade)
    plt.figure(figsize=(6,4.6));matrix=np.array([r['coherence_contrast'] for r in trade]).reshape(4,4)
    plt.imshow(matrix,origin='lower',aspect='auto');plt.colorbar(label='Absolute coherence contrast')
    plt.xticks(range(4));plt.yticks(range(4))
    for row in range(4):
        for col in range(4):plt.text(col,row,f'{matrix[row,col]:.3f}',ha='center',va='center')
    plt.xlabel('Locally imbalanced pair budget');plt.ylabel('Refocusing pulses');plt.title('Revelation needs all three pairs covered')
    plt.tight_layout();plt.savefig(out/'figures/capability_exchange.pdf',bbox_inches='tight');plt.savefig(out/'figures/capability_exchange.png',dpi=160,bbox_inches='tight');plt.close()
    sharp=[];deletion=[]
    for k in range(1,6):
        x=vertices(2*k,symmetric=True);controls=calibration_controls(k)
        a=np.array([exact_normalized_row(u,x)/2**(u.b//2) for u in controls])
        target=exact_normalized_row(echo_control(k),x)/2**k
        for eps in sorted(set([float(z) for z in np.linspace(0,1,17)]+[2**(1-k),1/(2**(k-1)-1) if k>1 else 1.])):
            cert=interval_lower_bound(a,np.zeros(k),np.full(k,eps),target)
            xx,pp=complete_tight_law(k,eps);expected=complete_uniform_bound(k,eps)
            achieved=direct_coherence(echo_control(k),np.full(2*k,np.pi/4),xx,pp).real
            assert abs(cert['lp_value']-expected)<1e-8 and abs(achieved-expected)<1e-8
            sharp.append({'pairs':k,'epsilon':float(eps),'theoretical_lower':expected,
                          'lp_lower':cert['lp_value'],'constructive_value':achieved})
        for missing in range(k):
            used=[j for j in range(k) if j!=missing]
            ans=exact_data_bounds(a[used],np.zeros(len(used)),target)
            expected=0 if missing==k-1 else -1
            assert abs(ans.lower-expected)<1e-8
            deletion.append({'pairs':k,'omitted_prefix_index':missing+1,
                             'minimum_echo_coherence':ans.lower})
    table('staircase_sharp_bounds.csv',sharp);table('calibration_deletion.csv',deletion)
    summary['staircase_lp_sharpness_cases']=len(sharp);summary['staircase_deletion_cases']=len(deletion)
    plt.figure(figsize=(7.2,4.5))
    for k in range(1,6):
        rows=[r for r in sharp if r['pairs']==k]
        plt.plot([r['epsilon'] for r in rows],[r['lp_lower'] for r in rows],'-o',markersize=3,label=f'{k} pairs')
    plt.legend();figure('sharp_prediction',('Uniform calibration uncertainty','Sharp lower echo coherence','Attained worst-case prediction over all binary laws'))
    # A held-out target: selection uses only three prefixes and the Ramsey baseline.
    k=3;n=6;alpha=np.full(n,np.pi/4);x,p=matched_pairs_law(k)
    controls=calibration_controls(k)+[Control(n)]
    truth=np.array([direct_coherence(u,alpha,x,p).real for u in controls])
    shots=50000;delta=.05;measured=sample_means(truth,shots,rng)
    radius=simultaneous_radius(shots,len(controls),delta)
    target_lower=coherence_certificate(measured[:k],np.full(k,radius))['lower']
    gain_lower=target_lower-(measured[-1]+radius)
    target_true=direct_coherence(echo_control(k),alpha,x,p).real
    target_validation=sample_means([target_true],shots,rng)[0]
    decision={'pairs':k,'bins':n,'shots_per_setting':shots,'calibration_settings':len(controls),
              'calibration_shots':shots*len(controls),'held_out_validation_shots':shots,
              'simultaneous_confidence':1-delta,'pauli_radius':radius,
              'truth':truth.tolist(),'measured':measured.tolist(),
              'target_true':target_true,'target_lower':target_lower,
              'gain_lower':gain_lower,'entanglement_fidelity_gain_lower':gain_lower/2,
              'target_validation_mean_not_used_for_selection':float(target_validation),
              'baseline_true_entanglement_fidelity':entanglement_fidelity(truth[-1]),
              'target_true_entanglement_fidelity':entanglement_fidelity(target_true),
              'note':'Synthetic matched-pair law; direct target measurement is a cheaper baseline when available.'}
    (out/'results/finite_shot_decision.json').write_text(json.dumps(decision,indent=2)+'\n');summary['finite_shot_decision']=decision
    plt.figure(figsize=(7.2,4.5))
    plt.errorbar(np.arange(4),measured,yerr=radius,fmt='o',capsize=4,label='Acquired simultaneous intervals')
    plt.plot([4],[target_true],'s',label='Held-out target truth')
    plt.plot([4],[target_lower],'^',label='Certified target lower bound')
    plt.xticks(range(5),['Prefix 2','Prefix 4','Prefix 6','Ramsey 6','Echo target'])
    plt.ylim(-.15,1.1);plt.legend(fontsize=8);figure('finite_shot_prediction',('Control experiment','Real coherence','Certifying an unmeasured three-pulse echo'))
    coverage=[]
    for shots0 in (200,1000,5000,20000):
        covered=0;positive=0;worst=-1e9;trials=1000
        r=simultaneous_radius(shots0,4,delta)
        for _ in range(trials):
            m=sample_means(truth,shots0,rng)
            covered+=int(np.all(np.abs(m-truth)<=r))
            lo=coherence_certificate(m[:3],np.full(3,r))['lower']-m[-1]-r
            positive+=int(lo>0);worst=max(worst,lo-(target_true-truth[-1]))
        coverage.append({'shots_per_setting':shots0,'trials':trials,
                         'simultaneous_coverages':covered,'positive_certificates':positive,
                         'max_bound_minus_true_gain':float(worst)})
    table('finite_shot_coverage.csv',coverage);summary['coverage_trials']=sum(r['trials'] for r in coverage)
    summary['coverage_successes']=sum(r['simultaneous_coverages'] for r in coverage)
    plt.figure(figsize=(7.2,4.5))
    plt.semilogx([r['shots_per_setting'] for r in coverage],[r['positive_certificates']/r['trials'] for r in coverage],'-o')
    plt.ylim(0,1.05);figure('decision_rate',('Shots per acquired setting','Fraction with positive gain certificate','Synthetic decision rate, not hardware performance'))
    visibility=[]
    for d in (2,4,6,8,10,12):
        n=2*d-1;alpha0=np.pi/4;slope=2**(-n/2)
        optimum=float(np.arcsin(np.sqrt(d/n)))
        visibility.append({'degree':d,'bins':n,'quarterturn_slope':slope,
                           'slope_optimal_alpha':optimum,
                           'slope_optimal_value':(d/n)**(d/2)*(1-d/n)**((n-d)/2),
                           'hoeffding_sufficient_shots_known_mean':required_revelation_shots(slope)})
    table('visibility_cost.csv',visibility)
    plt.figure(figsize=(7.2,4.5));plt.semilogy([r['degree'] for r in visibility],[r['hoeffding_sufficient_shots_known_mean'] for r in visibility],'-o')
    figure('visibility_cost',('Hidden moment degree','Sufficient shots for a known mean shift','High-order revelation has an exponential visibility cost'))
    # Source-independent 2x2 unitary propagation at 12 seeded physical laws.
    unitary=[];z=np.diag([1.,-1.]);xgate=np.array([[0.,1.],[1.,0.]])
    from scipy.linalg import expm
    for case in range(12):
        n=3+case%4;xx=vertices(n);weights=rng.uniform(size=len(xx));weights/=weights.sum()
        alpha=rng.uniform(.2,.9,n);b=n;cuts=tuple(a for a in range(1,b) if rng.random()<.4);u=Control(b,cuts)
        exact_fe=0.
        ideal=np.linalg.matrix_power(xgate,len(cuts))
        for xi,weight in zip(xx,weights):
            evolution=np.eye(2,dtype=complex)
            for j in range(n):
                evolution=expm(-.5j*alpha[j]*xi[j]*z)@evolution
                if j+1 in cuts:evolution=xgate@evolution
            exact_fe+=weight*abs(np.trace(ideal.conj().T@evolution))**2/4
        w=direct_coherence(u,alpha,xx,weights)
        unitary.append({'case':case,'bins':n,'pulses':len(cuts),'unitary_entanglement_fidelity':float(exact_fe),
                        'characteristic_entanglement_fidelity':entanglement_fidelity(w),
                        'absolute_residual':abs(exact_fe-entanglement_fidelity(w))})
    table('unitary_propagation.csv',unitary)
    summary['unitary_cases']=len(unitary);summary['unitary_maximum_residual']=max(r['absolute_residual'] for r in unitary)
    # Distinguish exact reconstruction from a false low-degree hypothesis.
    x,p=dark_law(4,-1);alpha=np.full(7,np.pi/4);small=bank(7,1)
    data=[direct_coherence(u,alpha,x,p).real for u in small]
    low=dense_inverse(alpha,2,data)
    from eiroq.model import predicted_coherence
    miss={'fitted_degree':2,'true_degree':4,'maximum_fitted_pair_moment':max(map(abs,low.values())),
          'all_calibration_residuals':float(max(abs(predicted_coherence(u,alpha,low)-v) for u,v in zip(small,data))),
          'predicted_revealing_coherence':predicted_coherence(reveal_control(4),alpha,low),
          'true_revealing_coherence':direct_coherence(reveal_control(4),alpha,x,p).real,
          'interpretation':'Low-pulse holdout agreement does not validate the moment-degree contract.'}
    (out/'results/misspecification.json').write_text(json.dumps(miss,indent=2)+'\n')
    summary['misspecification']=miss
    summary['setting_example_n20_d4']={'required':dimension(20,4),'full_symmetric':2**19-1}
    summary['data_csv_files']=len(list((out/'data').glob('*.csv')))
    summary['figure_count']=len(list((out/'figures').glob('*.pdf')))
    (out/'results/experiment_summary.json').write_text(json.dumps(summary,indent=2)+'\n')
    environment={'python':platform.python_version(),'numpy':np.__version__,'scipy':scipy.__version__,
                 'matplotlib':matplotlib.__version__,'platform':platform.platform(),
                 'execution':'CPU only; no quantum device, FPGA, or GPU benchmark'}
    (out/'results/environment.json').write_text(json.dumps(environment,indent=2)+'\n')
    print(json.dumps(summary,indent=2))

if __name__=='__main__': main()

	"""Reproduce all synthetic experiments and figure data; no external service required.

	Every random seed and physical assumption is explicit. No data are laboratory
	measurements. Changing the protocol creates a new experiment, not a replication.
	"""
	from pathlib import Path
	from itertools import combinations
	from math import comb
	import argparse, csv, json, platform
	import numpy as np
	import scipy
	import matplotlib
	matplotlib.use('Agg')
	import matplotlib.pyplot as plt
	from eiroq.controls import Control,bank,dimension,rank_law,feature_matrix,even_subsets,modular_rank
	from eiroq.model import (vertices,phase_law,direct_coherence,exact_normalized_row,
	entanglement_fidelity)
	from eiroq.reconstruct import dense_inverse,stencil_inverse
	from eiroq.hidden import dark_law,dark_response,reveal_control
	from eiroq.staircase import (calibration_controls,echo_control,staircase_weights,
	matched_pairs_law,tight_law,coherence_certificate,
	complete_uniform_bound,complete_tight_law)
	from eiroq.certificates import exact_data_bounds,interval_lower_bound
	from eiroq.statistics import simultaneous_radius,sample_means,required_revelation_shots


	def main():
	parser=argparse.ArgumentParser()
	parser.add_argument('--out',type=Path,default=Path('.'))
	args=parser.parse_args();out=args.out
	for folder in ('data','results','figures'): (out/folder).mkdir(parents=True,exist_ok=True)
	def table(name,rows):
	with (out/'data'/name).open('w',newline='') as f:
	writer=csv.DictWriter(f,fieldnames=list(rows[0]));writer.writeheader();writer.writerows(rows)
	def figure(name,description):
	plt.xlabel(description[0]);plt.ylabel(description[1]);plt.title(description[2])
	plt.grid(alpha=.25);plt.tight_layout()
	plt.savefig(out/'figures'/f'{name}.pdf',bbox_inches='tight')
	plt.savefig(out/'figures'/f'{name}.png',dpi=160,bbox_inches='tight');plt.close()
	summary={'version':'1.0.0','seed':2026101602,
	'evidence':'theory and synthetic computation; zero laboratory trials'}
	rng=np.random.default_rng(summary['seed'])
	rank_rows=[]
	for n in range(2,9):
	for d in range(2,min(n,6)+1,2):
	subsets=even_subsets(n,d)
	for p in range(min(d,n-1)):
	canonical=bank(n,p);full=bank(n,p,False)
	exact_lower=modular_rank(feature_matrix(canonical,subsets,n))
	full_lower=modular_rank(feature_matrix(full,subsets,n))
	predicted=rank_law(n,d,p)
	assert exact_lower==full_lower==predicted
	rank_rows.append(dict(n=n,degree=d,pulses=p,parameters=len(subsets),
	canonical_settings=len(canonical),full_settings=len(full),
	modular_rank=exact_lower,full_modular_rank=full_lower,
	theoretical_rank=predicted))
	table('rank_law.csv',rank_rows);summary['rank_cases']=len(rank_rows)
	plt.figure(figsize=(7.2,4.5))
	for d in (2,4,6):
	ps=np.arange(6);plt.step(ps,[rank_law(7,d,int(p)) for p in ps],where='post',label=f'moment degree {d}')
	plt.legend();figure('rank_staircase',('Maximum refocusing pulses','Observable dimension','Exact pulse-budget rank at seven bins'))
	counts=[]
	for n in range(2,31):
	row={'n':n,'full_symmetric_parameters':2**(n-1)-1}
	for d in (2,4,6):row[f'degree_{d}']=dimension(n,d)
	counts.append(row)
	table('setting_counts.csv',counts)
	plt.figure(figsize=(7.2,4.5))
	for key,label in [('full_symmetric_parameters','No moment-degree bound'),('degree_2','Degree 2'),('degree_4','Degree 4'),('degree_6','Degree 6')]:
	plt.semilogy([r['n'] for r in counts],[r[key] for r in counts],label=label)
	plt.legend();figure('setting_counts',('Number of bins','Scalar settings / free parameters','Settings saved only under a valid degree contract'))
	inverse=[]
	for case in range(180):
	n=4+case%6;available=list(range(2,min(n,6)+1,2));d=available[(case//6)%len(available)]
	subsets=even_subsets(n,d);coeff=rng.normal(size=len(subsets));coeff*=.6/np.abs(coeff).sum()
	true=dict(zip(subsets,coeff));x,p=phase_law(n,true)
	alpha=rng.uniform(.45,.85,size=n);controls=bank(n,d-1)
	data=np.array([direct_coherence(u,alpha,x,p).real for u in controls])
	dense=dense_inverse(alpha,d,data);stencil=stencil_inverse(alpha,d,data)
	inverse.append({'case':case,'n':n,'degree':d,'settings':len(controls),
	'minimum_probability':float(p.min()),
	'dense_error':max(abs(dense[a]-true[a]) for a in subsets),
	'stencil_error':max(abs(stencil[a]-true[a]) for a in subsets),
	'cross_inverse_error':max(abs(dense[a]-stencil[a]) for a in subsets)})
	table('inverse_roundtrips.csv',inverse)
	summary['inverse_roundtrips']=len(inverse)
	summary['maximum_dense_error']=max(r['dense_error'] for r in inverse)
	summary['maximum_stencil_error']=max(r['stencil_error'] for r in inverse)
	assert summary['maximum_stencil_error']<1e-8
	plt.figure(figsize=(7.2,4.5))
	plt.semilogy([r['case'] for r in inverse],[max(r['dense_error'],1e-17) for r in inverse],'.',label='Dense inverse')
	plt.semilogy([r['case'] for r in inverse],[max(r['stencil_error'],1e-17) for r in inverse],'.',label='Local stencil')
	plt.legend();figure('inverse_errors',('Seeded physical instance','Largest recovered moment error','Two inverses against direct finite-law propagation'))
	hidden=[]
	for d in (2,4,6):
	n=2*d-1;x,p=dark_law(d,1)
	# Direct verification of the entire full low-pulse bank at d=2,4.
	controls=bank(n,d-2,False)
	chosen=controls if d<=4 else controls[::max(1,len(controls)//80)]
	for alpha0 in (.25,.55,np.pi/4,1.05):
	alpha=np.full(n,alpha0)
	residual=max(abs(direct_coherence(u,alpha,x,p).real-np.cos(alpha0)**u.b) for u in chosen)
	hidden.append({'degree':d,'bins':n,'common_alpha':float(alpha0),
	'total_available_controls':len(controls),'direct_controls_tested':len(chosen),
	'maximum_hidden_residual':residual})
	table('hidden_control_checks.csv',hidden)
	summary['hidden_direct_controls']=sum(r['direct_controls_tested'] for r in hidden)
	summary['hidden_maximum_residual']=max(r['maximum_hidden_residual'] for r in hidden)
	sweep=[]
	for a in np.linspace(.1,1.4,121):
	n=7;alpha=np.full(n,a);target=reveal_control(4);base=np.cos(a)**n
	sweep.append({'alpha':float(a),'baseline':base,'lambda_plus':dark_response(target,alpha,4,1).real,
	'lambda_minus':dark_response(target,alpha,4,-1).real,
	'revelation_slope':np.sin(a)*4np.cos(a)**3})
	table('global_amplitude_sweep.csv',sweep)
	plt.figure(figsize=(7.2,4.5))
	for key,label in [('baseline','Every <=2-pulse full-prefix control'),('lambda_plus','Revealing control, lambda=+1'),('lambda_minus','Revealing control, lambda=-1')]:
	plt.plot([r['alpha'] for r in sweep],[r[key] for r in sweep],label=label)
	plt.legend(fontsize=8);figure('dark_revelation',('Common phase amplitude (radians)','Real coherence','Identical shallow controls, opposite deeper decisions'))
	trade=[]
	for pulses in range(4):
	for local in range(4):
	alpha=np.full(7,np.pi/4)
	# Disjoint coverage; unneeded local settings have no further effect.
	for pair in range(pulses,min(3,pulses+local)):
	alpha[2pair],alpha[2pair+1]=.3,1.1
	u=Control(7,tuple(2*j+1 for j in range(pulses)))
	contrast=abs(dark_response(u,alpha,4,1)-dark_response(u,alpha,4,-1))
	trade.append({'pulses':pulses,'imbalanced_pair_budget':local,'coherence_contrast':float(contrast),
	'predicted_revealed':int(pulses+local>=3)})
	table('capability_exchange.csv',trade)
	plt.figure(figsize=(6,4.6));matrix=np.array([r['coherence_contrast'] for r in trade]).reshape(4,4)
	plt.imshow(matrix,origin='lower',aspect='auto');plt.colorbar(label='Absolute coherence contrast')
	plt.xticks(range(4));plt.yticks(range(4))
	for row in range(4):
	for col in range(4):plt.text(col,row,f'{matrix[row,col]:.3f}',ha='center',va='center')
	plt.xlabel('Locally imbalanced pair budget');plt.ylabel('Refocusing pulses');plt.title('Revelation needs all three pairs covered')
	plt.tight_layout();plt.savefig(out/'figures/capability_exchange.pdf',bbox_inches='tight');plt.savefig(out/'figures/capability_exchange.png',dpi=160,bbox_inches='tight');plt.close()
	sharp=[];deletion=[]
	for k in range(1,6):
	x=vertices(2*k,symmetric=True);controls=calibration_controls(k)
	a=np.array([exact_normalized_row(u,x)/2**(u.b//2) for u in controls])
	target=exact_normalized_row(echo_control(k),x)/2**k
	for eps in sorted(set([float(z) for z in np.linspace(0,1,17)]+[2(1-k),1/(2(k-1)-1) if k>1 else 1.])):
	cert=interval_lower_bound(a,np.zeros(k),np.full(k,eps),target)
	xx,pp=complete_tight_law(k,eps);expected=complete_uniform_bound(k,eps)
	achieved=direct_coherence(echo_control(k),np.full(2*k,np.pi/4),xx,pp).real
	assert abs(cert['lp_value']-expected)<1e-8 and abs(achieved-expected)<1e-8
	sharp.append({'pairs':k,'epsilon':float(eps),'theoretical_lower':expected,
	'lp_lower':cert['lp_value'],'constructive_value':achieved})
	for missing in range(k):
	used=[j for j in range(k) if j!=missing]
	ans=exact_data_bounds(a[used],np.zeros(len(used)),target)
	expected=0 if missing==k-1 else -1
	assert abs(ans.lower-expected)<1e-8
	deletion.append({'pairs':k,'omitted_prefix_index':missing+1,
	'minimum_echo_coherence':ans.lower})
	table('staircase_sharp_bounds.csv',sharp);table('calibration_deletion.csv',deletion)
	summary['staircase_lp_sharpness_cases']=len(sharp);summary['staircase_deletion_cases']=len(deletion)
	plt.figure(figsize=(7.2,4.5))
	for k in range(1,6):
	rows=[r for r in sharp if r['pairs']==k]
	plt.plot([r['epsilon'] for r in rows],[r['lp_lower'] for r in rows],'-o',markersize=3,label=f'{k} pairs')
	plt.legend();figure('sharp_prediction',('Uniform calibration uncertainty','Sharp lower echo coherence','Attained worst-case prediction over all binary laws'))
	# A held-out target: selection uses only three prefixes and the Ramsey baseline.
	k=3;n=6;alpha=np.full(n,np.pi/4);x,p=matched_pairs_law(k)
	controls=calibration_controls(k)+[Control(n)]
	truth=np.array([direct_coherence(u,alpha,x,p).real for u in controls])
	shots=50000;delta=.05;measured=sample_means(truth,shots,rng)
	radius=simultaneous_radius(shots,len(controls),delta)
	target_lower=coherence_certificate(measured[:k],np.full(k,radius))['lower']
	gain_lower=target_lower-(measured[-1]+radius)
	target_true=direct_coherence(echo_control(k),alpha,x,p).real
	target_validation=sample_means([target_true],shots,rng)[0]
	decision={'pairs':k,'bins':n,'shots_per_setting':shots,'calibration_settings':len(controls),
	'calibration_shots':shots*len(controls),'held_out_validation_shots':shots,
	'simultaneous_confidence':1-delta,'pauli_radius':radius,
	'truth':truth.tolist(),'measured':measured.tolist(),
	'target_true':target_true,'target_lower':target_lower,
	'gain_lower':gain_lower,'entanglement_fidelity_gain_lower':gain_lower/2,
	'target_validation_mean_not_used_for_selection':float(target_validation),
	'baseline_true_entanglement_fidelity':entanglement_fidelity(truth[-1]),
	'target_true_entanglement_fidelity':entanglement_fidelity(target_true),
	'note':'Synthetic matched-pair law; direct target measurement is a cheaper baseline when available.'}
	(out/'results/finite_shot_decision.json').write_text(json.dumps(decision,indent=2)+'\n');summary['finite_shot_decision']=decision
	plt.figure(figsize=(7.2,4.5))
	plt.errorbar(np.arange(4),measured,yerr=radius,fmt='o',capsize=4,label='Acquired simultaneous intervals')
	plt.plot([4],[target_true],'s',label='Held-out target truth')
	plt.plot([4],[target_lower],'^',label='Certified target lower bound')
	plt.xticks(range(5),['Prefix 2','Prefix 4','Prefix 6','Ramsey 6','Echo target'])
	plt.ylim(-.15,1.1);plt.legend(fontsize=8);figure('finite_shot_prediction',('Control experiment','Real coherence','Certifying an unmeasured three-pulse echo'))
	coverage=[]
	for shots0 in (200,1000,5000,20000):
	covered=0;positive=0;worst=-1e9;trials=1000
	r=simultaneous_radius(shots0,4,delta)
	for _ in range(trials):
	m=sample_means(truth,shots0,rng)
	covered+=int(np.all(np.abs(m-truth)<=r))
	lo=coherence_certificate(m[:3],np.full(3,r))['lower']-m[-1]-r
	positive+=int(lo>0);worst=max(worst,lo-(target_true-truth[-1]))
	coverage.append({'shots_per_setting':shots0,'trials':trials,
	'simultaneous_coverages':covered,'positive_certificates':positive,
	'max_bound_minus_true_gain':float(worst)})
	table('finite_shot_coverage.csv',coverage);summary['coverage_trials']=sum(r['trials'] for r in coverage)
	summary['coverage_successes']=sum(r['simultaneous_coverages'] for r in coverage)
	plt.figure(figsize=(7.2,4.5))
	plt.semilogx([r['shots_per_setting'] for r in coverage],[r['positive_certificates']/r['trials'] for r in coverage],'-o')
	plt.ylim(0,1.05);figure('decision_rate',('Shots per acquired setting','Fraction with positive gain certificate','Synthetic decision rate, not hardware performance'))
	visibility=[]
	for d in (2,4,6,8,10,12):
	n=2d-1;alpha0=np.pi/4;slope=2*(-n/2)
	optimum=float(np.arcsin(np.sqrt(d/n)))
	visibility.append({'degree':d,'bins':n,'quarterturn_slope':slope,
	'slope_optimal_alpha':optimum,
	'slope_optimal_value':(d/n)*(d/2)(1-d/n)**((n-d)/2),
	'hoeffding_sufficient_shots_known_mean':required_revelation_shots(slope)})
	table('visibility_cost.csv',visibility)
	plt.figure(figsize=(7.2,4.5));plt.semilogy([r['degree'] for r in visibility],[r['hoeffding_sufficient_shots_known_mean'] for r in visibility],'-o')
	figure('visibility_cost',('Hidden moment degree','Sufficient shots for a known mean shift','High-order revelation has an exponential visibility cost'))
	# Source-independent 2x2 unitary propagation at 12 seeded physical laws.
	unitary=[];z=np.diag([1.,-1.]);xgate=np.array([[0.,1.],[1.,0.]])
	from scipy.linalg import expm
	for case in range(12):
	n=3+case%4;xx=vertices(n);weights=rng.uniform(size=len(xx));weights/=weights.sum()
	alpha=rng.uniform(.2,.9,n);b=n;cuts=tuple(a for a in range(1,b) if rng.random()<.4);u=Control(b,cuts)
	exact_fe=0.
	ideal=np.linalg.matrix_power(xgate,len(cuts))
	for xi,weight in zip(xx,weights):
	evolution=np.eye(2,dtype=complex)
	for j in range(n):
	evolution=expm(-.5jalpha[j]xi[j]*z)@evolution
	if j+1 in cuts:evolution=xgate@evolution
	exact_fe+=weightabs(np.trace(ideal.conj().T@evolution))*2/4
	w=direct_coherence(u,alpha,xx,weights)
	unitary.append({'case':case,'bins':n,'pulses':len(cuts),'unitary_entanglement_fidelity':float(exact_fe),
	'characteristic_entanglement_fidelity':entanglement_fidelity(w),
	'absolute_residual':abs(exact_fe-entanglement_fidelity(w))})
	table('unitary_propagation.csv',unitary)
	summary['unitary_cases']=len(unitary);summary['unitary_maximum_residual']=max(r['absolute_residual'] for r in unitary)
	# Distinguish exact reconstruction from a false low-degree hypothesis.
	x,p=dark_law(4,-1);alpha=np.full(7,np.pi/4);small=bank(7,1)
	data=[direct_coherence(u,alpha,x,p).real for u in small]
	low=dense_inverse(alpha,2,data)
	from eiroq.model import predicted_coherence
	miss={'fitted_degree':2,'true_degree':4,'maximum_fitted_pair_moment':max(map(abs,low.values())),
	'all_calibration_residuals':float(max(abs(predicted_coherence(u,alpha,low)-v) for u,v in zip(small,data))),
	'predicted_revealing_coherence':predicted_coherence(reveal_control(4),alpha,low),
	'true_revealing_coherence':direct_coherence(reveal_control(4),alpha,x,p).real,
	'interpretation':'Low-pulse holdout agreement does not validate the moment-degree contract.'}
	(out/'results/misspecification.json').write_text(json.dumps(miss,indent=2)+'\n')
	summary['misspecification']=miss
	summary['setting_example_n20_d4']={'required':dimension(20,4),'full_symmetric':2**19-1}
	summary['data_csv_files']=len(list((out/'data').glob('*.csv')))
	summary['figure_count']=len(list((out/'figures').glob('*.pdf')))
	(out/'results/experiment_summary.json').write_text(json.dumps(summary,indent=2)+'\n')
	environment={'python':platform.python_version(),'numpy':np.__version__,'scipy':scipy.__version__,
	'matplotlib':matplotlib.__version__,'platform':platform.platform(),
	'execution':'CPU only; no quantum device, FPGA, or GPU benchmark'}
	(out/'results/environment.json').write_text(json.dumps(environment,indent=2)+'\n')
	print(json.dumps(summary,indent=2))

	if __name__=='__main__': main()