{"schema_version":"1.0","revision":"20261022-r4","title":"Photon statistics: detection, practical morphology, and red-channel upper limits","status":"EXECUTED_CONDITIONAL_STATISTICAL_PROTOTYPES_NOT_MISSION_VALIDATION","assembled_utc":"2026-10-22T08:25:08.926108+00:00","question_tags":["A2","C8","C9","E16","E17","G21","G22"],"software":{"python":"3.12.14","numpy":"2.3.5","scipy":"1.18.1","random_generator":"NumPy default_rng PCG64","no_new_installation":true},"summary":{"signal_scenarios":81,"signal_trials_each":1000,"independent_signal_trials":81000,"noise_only_trials":9000,"practical_runtime_after_imports_s":172.1852927999571,"old_oracle_result_CSVs_byte_identical":5,"same_generator_oracle_balanced_pairs":54,"independent_profile_objective_comparisons":243,"exact_count_deterministic_controls":63,"interpretation":"Detecting the3ms pulse does not ensure enough early photons to classify its rise.","mission_useful_rate":"NOT_COMPUTABLE_FROM_AVAILABLE_INPUTS"},"practical_morphology":{"schema_version":"1.0","status":"EXECUTED_CONDITIONAL_IDEAL_POISSON_PRACTICAL_MORPHOLOGY_PROTOTYPE","start_utc":"2026-10-22T08:12:39.510267+00:00","finished_utc":"2026-10-22T08:15:31.695664+00:00","runtime_s":172.1852927999571,"seed_base":20261022081001,"scenario_count":81,"trials_each_scenario":1000,"total_signal_trials":81000,"parameters":{"receiver_rises_10_90_us":[30,80,200],"plateau_equivalent_PE_in_3ms":[100,1000,10000],"background_cps":[50.0,10000.0,1000000.0],"sample_rate_khz":[10,50,100],"pulse_end_after_onset_ms":3.0,"prewindow_ms":10.0,"prewindow_position_ms":[-10.5,-0.5],"candidate_gate_ms":[-0.2,3.2],"morphology_early_window_ms":[-0.2,0.6],"late_plateau_window_ms":[1.0,2.5],"true_onset_distribution_us":[-100,100],"onset_grid_us":[-150,150,5],"alpha_per_predefined_gate":2.866515718791933e-07,"acceptance_profile_loglikelihood_margin":2.9444389791664403,"deadtime_diagnostic_ns":17.0},"algorithm":{"label_definition":"Linear receiver-input expected PE-rate morphology after any assumed transport, not intrinsic discharge history or cloud depth.","waveform":"A linear0-to100% ramp lasting rise_10_90/0.8, then unit plateau, with total pulse ending3ms after onset.","amplitude":"Peak rate A=N_plateau_equivalent/3ms. 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Not simultaneous over all scenarios, not uncertainty in the true event 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Model mismatch, real source variation, cloud-kernel variation and actual detector response are absent.","Unknown onset is restricted to an already available200us coarse bracket; identifying that bracket in a blind stream is outside scope.","The fixed3.4ms detection gate covers each simulated pulse; constructing such gates blindly and overlapping-window search trials remain operational inputs.","The nonnegative nuisance fit can favor flexible fast templates; reported Monte Carlo confusion counts, not the score margin, quantify performance under this generator.","Only linear independent photon registration is simulated. Peak rate times17ns flags an assumed counter's possible occupancy; it is not a deadtime correction or restoration of Poisson statistics.","Per-gate false alarm alpha is not a mission false-trigger rate. A specified finite test count permits a Bonferroni familywise upper bound; actual streaming trials are unknown.","PE counts include an unspecified end-to-end photon-detection efficiency. Aperture photons require a separately verified spectral/angular efficiency.","No molecular source yield, source brightness distribution, population completeness or optical duty/exposure model is supplied. Useful mission event rate is NOT COMPUTABLE.","A real morphology classifier requires end-to-end hardware waveforms and separately labeled optical/radio control populations.","Fitted-grid errors and Monte Carlo intervals do not cover systematic model uncertainty. Samples are10/20/100us integrations; sampling rate is not analog bandwidth."]},"oracle_reference":{"status":"EXECUTED_IDEAL_POISSON_KNOWN_HYPOTHESES_TOY_NOT_FLIGHT_PERFORMANCE","actual_research_start_utc":"2026-10-22T08:19:43.741453+00:00","calculation_finished_utc":"2026-10-22T08:19:46.701932+00:00","parameters":{"pulse_end_s":0.003,"rise_10_90_s":[3e-05,8e-05,0.0002],"N_plateau_equivalent_PE":[100,300,1000,3000,10000],"background_cps":[50.0,10000.0,1000000.0,100000000.0],"hardware_bin_s":[2e-05,0.0001],"onset_phases_fraction":[0.0,0.25,0.5,0.75],"fixed_scale":"Peak amplitude A=N_plateau_equivalent/3ms is fixed across competing rise hypotheses. Actual integrated source PE differs because ramp areas differ."},"counts":{"rise_comparison_rows":320,"detection_rows":480,"source_count_rows":15,"Monte_Carlo_rows":72,"Monte_Carlo_samples_each_hypothesis_per_row":20000,"single_bin_exact_distribution_controls":5,"coarse_bin_information_monotonicity_checks":160},"MC_familywise_bound":{"confidence_at_least":0.99,"halfwidth":0.010940168809006156,"method":"Hoeffding for40000 bounded independent error scores per scenario, followed by a union bound over all72 scenarios. No Gaussian count or confidence approximation."},"proofs":["For one Poisson bin, sum_k sqrt(P_mu(k)P_nu(k))=exp[-(mu+nu)/2+sqrt(mu*nu)]=exp[-(sqrt(mu)-sqrt(nu))^2/2]. Independence multiplies affinities, so log affinity sums over bins.","Equal-prior optimal error Pe=(1-TV)/2. Since min(p,q)<=sqrt(p*q), 1-TV<=BC; hence Pe<=BC/2.","Cauchy-Schwarz applied to |p-q|=|sqrt(p)-sqrt(q)|*(sqrt(p)+sqrt(q)) gives TV<=sqrt(1-BC^2); hence Pe>=(1-sqrt(1-BC^2))/2.","Bounds concern fixed simple hypotheses with known parameters. They are not Gaussian approximations, significance thresholds, or measured classification errors. Very small displayed numeric bounds can underflow; natural-log bounds are retained."],"waveform_reference_plane":"The templates specify expected PE rate at the hypothetical linear receiver input, after any assumed atmospheric transport. They are not asserted intrinsic NBE emission histories or cloud-depth labels.","high_background_registration_limit":"The1e8cps background is only an ideal Poisson-registration scenario; it is not a realizable17ns nonparalyzable counter operating point. Count-loss response is studied separately.","limitations":["Known pulse start, rise templates, peak amplitude, background and pulse end. No nuisance fitting or training/generalization error.","Poisson PE arrivals, independent hardware-bin counts and ideal linear photon registration. No deadtime, saturation, gain fluctuations, excess noise, afterpulsing, analog filtering or threshold crossings.","End-to-end photon detection efficiency is absorbed into PE amplitude. Aperture/source brightness distribution and cloud depth are not specified.","Background is known and constant. Actual source and total counts are separate; early source-only counts are not directly labeled in the detected mixture.","The exponential optical decay after plateau is not modeled; pulse stops at3ms identically under each hypothesis. This arbitrary shared cutoff adds no artificial inter-hypothesis timing signal.","Binning, unobserved timing/nuisance parameters, or additional hypothesis-independent stochastic processing cannot add information relative to an oracle retaining the known waveform and photon times. Correlated physical variation could encode other information, so no universal real-population misclassification claim is made.","Binary equal-prior fast-versus-slow error does not establish a three-class classifier, cloud-top/depth inference, event-rate completeness or actual instrument performance.","All paired means include full hardware bins straddling onset/termination. Expected source counts in physical0–30/200us windows are analytic integrals, not a claim that a coarse sampled detector can recover partial-bin photon times."],"all_checks_passed":true,"original_study_start_utc":"2026-10-22T00:48:38Z","revision_rerun_note":"Numerical algorithm and seeded results match the original; copied script START metadata now records this execution. See rerun_verification.json."},"oracle_current_generator":{"status":"EXECUTED_KNOWN_NUISANCE_ORACLE_ON_SAME_SEEDED_GENERATOR","start_utc":"2026-10-22T08:19:50.028528+00:00","finished_utc":"2026-10-22T08:19:59.688317+00:00","runtime_s":9.658936799969524,"truth_rows":[{"N_plateau_equivalent_3ms_PE":100,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":30,"fast_comparator_us":30,"scenario_seed":20261022081001,"trials":1000,"wrong_oracle":219,"oracle_error":0.219,"individual_95pct_Wilson_interval":[0.19446904537483753,0.24568159289404448],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":80,"fast_comparator_us":80,"scenario_seed":20261022081002,"trials":1000,"wrong_oracle":307,"oracle_error":0.307,"individual_95pct_Wilson_interval":[0.27919575142340997,0.3362813773520143],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":30,"scenario_seed":20261022081003,"trials":1000,"wrong_oracle":130,"oracle_error":0.13,"individual_95pct_Wilson_interval":[0.11056377462484193,0.1522680266544689],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":80,"scenario_seed":20261022081003,"trials":1000,"wrong_oracle":212,"oracle_error":0.212,"individual_95pct_Wilson_interval":[0.1877940523073313,0.2384101605803485],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":10000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":30,"fast_comparator_us":30,"scenario_seed":20261022081004,"trials":1000,"wrong_oracle":275,"oracle_error":0.275,"individual_95pct_Wilson_interval":[0.24822587402252644,0.30349616729597334],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":10000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":80,"fast_comparator_us":80,"scenario_seed":20261022081005,"trials":1000,"wrong_oracle":371,"oracle_error":0.371,"individual_95pct_Wilson_interval":[0.341606326344111,0.40138097734516226],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":10000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":30,"scenario_seed":20261022081006,"trials":1000,"wrong_oracle":195,"oracle_error":0.195,"individual_95pct_Wilson_interval":[0.17163009389189862,0.22070422878429005],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":10000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":80,"scenario_seed":20261022081006,"trials":1000,"wrong_oracle":261,"oracle_error":0.261,"individual_95pct_Wilson_interval":[0.23473118426217232,0.289098006293923],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":1000000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":30,"fast_comparator_us":30,"scenario_seed":20261022081007,"trials":1000,"wrong_oracle":468,"oracle_error":0.468,"individual_95pct_Wilson_interval":[0.43725522419222734,0.4989896883508483],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":1000000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":80,"fast_comparator_us":80,"scenario_seed":20261022081008,"trials":1000,"wrong_oracle":474,"oracle_error":0.474,"individual_95pct_Wilson_interval":[0.4432107820528304,0.5049882093884185],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":1000000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":30,"scenario_seed":20261022081009,"trials":1000,"wrong_oracle":495,"oracle_error":0.495,"individual_95pct_Wilson_interval":[0.4640902748007247,0.525947992784131],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":100,"background_cps":1000000.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":200,"fast_comparator_us":80,"scenario_seed":20261022081009,"trials":1000,"wrong_oracle":498,"oracle_error":0.498,"individual_95pct_Wilson_interval":[0.46707750038234924,0.5289378066515931],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":1000,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":30,"fast_comparator_us":30,"scenario_seed":20261022081010,"trials":1000,"wrong_oracle":1,"oracle_error":0.001,"individual_95pct_Wilson_interval":[0.00017654637062607809,0.0056425585979579355],"ties":0,"known_nuisance_only":true},{"N_plateau_equivalent_3ms_PE":1000,"background_cps":50.0,"sample_rate_khz":10,"truth_receiver_rise_10_90_us":80,"fast_comparator_us":80,"scenario_seed":20261022081011,"trials":1000,"wrong_oracle":32,"oracle_error":0.032,"individual_95pct_Wilson_interval":[0.022757107858710962,0.04482473808376865],"ties":0,"known_nuisance_only":true},{"N_plateau_equivale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is a conditional synthetic receiver-morphology study, not a flight sensitivity/completeness validation.","The classes mean30/80/200us10-to90% rises at a hypothetical linear receiver input after transport; they do not label source depth.","Source brightness, cloud transfer, line spectrum, detector PDE and source occurrence population are outside this count-level calculation.","The practical code has an external coarse onset bracket and a specified event gate. Blind stream triggering and a mission false-alarm rate are unvalidated.","A fixed ln19 profile-score margin is not calibrated95% confidence. Always show accepted fraction, rejected fraction and the error interval together.","The3-class fast-subtype distinction is harder than the grouped fast-vs-slow test; these are separate decisions.","Only exact model-matched templates and constant backgrounds are generated. Real independently labeled optical/radio controls are still needed.","Post-counting electronic filtering, detector excess noise, afterpulses, saturation and deadtime are not simulated.17ns occupancy is an illustrative hardware flag, not Poisson restoration.","Known-background red limits are invalid if a noisy finite baseline is silently substituted. The provided alternative uses a conservative Bonferroni construction.","Red limits constrain expected registered counts in a specified window, not thermal-source absence. Selection, red-window timing, throughput and population ratios remain physical inputs.","A useful mission event rate is NOT COMPUTABLE without an absolute received-fluence distribution, completeness and exposure definition.","No empirical wide-FOV event rate is inferred from the conditional geometric/population proxy; source geography and coverage remain unknown."],"source_refs":[{"id":"DERIVATION","title":"Own derivations, exact controls and independent audit","url":null,"locator":"README.md; count_inference/README.md; count_inference/morphology_profile_independent_review.json","role":"Mathematical basis, not a new experimental source."},{"id":"SCIPY_POISSON","title":"SciPy official Poisson distribution API","url":"https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html","locator":"Methods sf/logsf; Notes PMF","checked":"2026-10-22","role":"Numerical implementation documentation; web manual1.18.0, installed library1.18.1."},{"id":"SCIPY_BINOM","title":"SciPy official binomial distribution API","url":"https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html","locator":"Methods sf; Notes binomial PMF","checked":"2026-10-22","role":"On/off conditional test implementation."},{"id":"SCIPY_CHI2","title":"SciPy official chi-square distribution API","url":"https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html","locator":"Methods ppf/isf","checked":"2026-10-22","role":"Poisson interval inversion."},{"id":"NUMPY_POISSON","title":"NumPy official Generator.poisson API","url":"https://numpy.org/doc/stable/reference/random/generated/numpy.random.Generator.poisson.html","locator":"Generator.poisson; Notes PMF","checked":"2026-10-22","role":"Synthetic exact Poisson variate generator; current web manual differs from installed2.3.5."},{"id":"MMIA_HERITAGE","title":"The Modular Multispectral Imaging Array (MMIA) of the ASIM payload","url":"https://link.springer.com/article/10.1007/s11214-019-0593-y","locator":"Earlier primary heritage audit in research/detectors_optics/mmia_optical_heritage/optical_heritage_review.json","role":"Instrument context only. This prototype is not a reanalysis of its proprietary event waveforms."}],"files":{"practical_scenarios_csv":"practical_morphology_scenarios.csv","compact_alias_csv":"statistics_scenarios.csv","practical_full_json":"practical_morphology_results.json","current_oracle_json":"oracle_current_generator_results.json","count_inference_json":"count_inference/count_inference_results.json","synthetic_per_trial_arrays":"synthetic_trial_summaries/case_000.npz through case_080.npz","scripts":["practical_morphology.py","oracle_same_generator.py","oracle_reference/calculate_ideal_poisson_rise.py","count_inference/count_inference.py","count_inference/review_morphology_profile.py","assemble_statistics.py"]}}