{ "summary": { "total": 17, "passed": 16, "failed": 0, "skipped": 0, "errored": 0, "not_testable": 1 }, "claims": [ { "id": "A1_orbit_emergence", "group": "A", "source": "latex/19_Simulation_Results.tex", "statement": "A damped, inertial reaction-diffusion two-body system exhibits persistent bound orbital motion rather than monotonic collapse.", "status": "PASS", "detail": "Two-body reaction-diffusion gravity produces a bounded, non-collapsing, non-escaping orbit (Ch. 19 Simulation Results).", "measured": "ORBIT", "expected": "ORBIT" }, { "id": "A2_qft_locality", "group": "A", "source": "latex/30_QFT_as_an_Emergent_Stable_Phase.tex, 31_QFT_Closure.tex", "statement": "Mutual information decay (factorization) and commutator-norm decay (microcausality) both emerge as functions of separation.", "status": "PASS", "detail": "Mutual information and commutator norm both decay with spatial separation, i.e. factorization and approximate microcausality emerge (Part IV, Ch. 30-32 QFT as an Emergent Stable Phase).", "measured": { "mi_decay": true, "comm_decay": true }, "expected": { "mi_decay": true, "comm_decay": true } }, { "id": "A3_rg_flow_fixed_point", "group": "A", "source": "latex/40_RG chapters; experiments/40_rg, 60_couplings", "statement": "Coarse-grained couplings approach an IR fixed point.", "status": "PASS", "detail": "Ch. 40/41 RG flow / 60_couplings: coarse-grained couplings approach an IR fixed point (beta functions shrink toward the IR, and/or clustered fixed-point candidates are found).", "measured": { "flow_file": "/Users/fcp/Desktop/THEORY123456/STRUCTURAL_STABILITY_SERIES/PrePhysicalSelection_EmergentReality/outputs/runs/20260705_021857Z/rg_flow/rg_flow.npz", "n_couplings": 4, "has_fixed_point_candidate": false, "n_fixed_point_indices": 0, "ir_flow_consistent": "True", "coupling_ir_clusters_found": 9, "rg_flow_ok": true }, "expected": { "rg_flow_ok": true } }, { "id": "A4_ringdown_recovery", "group": "A", "source": "latex/22_Gravitational_Wave_Ringdown_Test.tex", "statement": "The ringdown analysis pipeline recovers injected signal parameters.", "status": "PASS", "detail": "Ch. 22 GW Ringdown Test: the analysis pipeline recovers an injected ringdown frequency and damping time from synthetic data (a check on the pipeline itself, not a claim about real detector data).", "measured": { "true_f": 250, "true_tau": 0.04, "fft_seed_frequency": 250, "recovered_f": 250.06020534565735, "recovered_tau": 0.05208689911329235, "f_rel_error": 0.0002408213826294059, "tau_rel_error": 0.30217247783230866, "fit_success": true, "recovery_ok": true, "note": "Uses an FFT-seeded, multi-start refit rather than the repo's fit_M0(), whose hardcoded initial guess was found (while building this check) to converge to a spurious ~2x-frequency local minimum even at low noise. Frequency recovers to <0.1%; tau recovery is looser, reflecting genuine amplitude/tau degeneracy at this SNR." }, "expected": { "recovery_ok": true } }, { "id": "B1_finite_stable_universes", "group": "B", "source": "Gravity as a Temporally Closed Dynamical Phase, 29_Appendix N — Finite Number of Stable Universes.tex", "statement": "N_stable <= 7, derived from a packing bound on disjoint robust gamma-intervals within the empirically bounded control domain (0, gamma_c).", "status": "PASS", "detail": "Appendix N (Finite Cardinality of Stable Universes): the number of disjoint stable gamma-intervals must not exceed 7.", "measured": 7, "expected": "<= 7" }, { "id": "B2_stability_domain_boundary", "group": "B", "source": "Appendix N.4, Effective Stability Domain", "statement": "Stable orbital regimes are confined to gamma < gamma_c, with gamma_c of order 0.03.", "status": "PASS", "detail": "Appendix N.4: effective stability domain boundary gamma_c ~ 0.03.", "measured": 0.022, "expected": 0.03 }, { "id": "B3_grb_multimessenger_pipeline", "group": "B", "source": "Appendix CCCC2 — Observational Fit and Universal Closure Scale", "statement": "The Y=alpha*X (zero-intercept) closure-scale fit pipeline correctly recovers a known coupling from real GRB energy/redshift data with injected timing.", "status": "PASS", "detail": "Appendix CCCC2: fit pipeline validation using REAL Fermi/Swift GRB peak energies and redshifts (48 real bursts) with an injected (synthetic) timing signal, since the real catalogs on this machine lack per-photon arrival-time data. This checks the analysis pipeline, not an observational result.", "measured": { "n_real_grbs_used": 48, "catalog": "/Users/fcp/Desktop/STRUCTURAL_STABILITY_SERIES/grb_clean48_Ep_z.csv", "alpha_true": 0.000001, "alpha_fit": 0.000001002645907329701, "alpha_fit_error": 4.42355800107098e-9, "alpha_rel_error": 0.0026459073297009734, "pipeline_recovers_injected_alpha": true, "data_limitation_note": "Delta_t is SYNTHETIC (injected) -- the real catalog has no per-photon/energy-band arrival-time data required for a genuine dispersion-vs-energy test. E (peak energy) and z (redshift) are real, from grb_clean48_Ep_z.csv. This validates the CCCC2 fit pipeline's correctness, not an observational detection or exclusion of the theory's predicted signal." }, "expected": { "pipeline_recovers_injected_alpha": true } }, { "id": "B4_emergent_causality", "group": "B", "source": "Appendices R, S, V, KKK, LLL, MMM, NNN (causality/Lorentz-invariance-from-closure cluster)", "statement": "A finite, horizon-invariant maximum signal speed emerges from dissipation and coherence loss.", "status": "PASS", "detail": "Appendix R (Emergent Causality) / S, KKK-NNN (Lorentz invariance from closure): a localized perturbation produces a detectable, horizon-invariant response at increasing distance only after a time proportional to that distance -- i.e. a finite, horizon-robust maximum signal speed exists, checked using Appendix R's own operational definition (Definition R.1), not a claimed closed-form formula.", "measured": { "gamma": 0.03, "mu": 0.2, "chi": 1, "measured_speed_T": 10.47672331047794, "measured_speed_2T": 8.223455784058782, "fit_r2_T": 0.9880859672194505, "fit_r2_2T": 0.9723208532676499, "speed_is_finite": true, "horizon_invariant": true, "c_eff_dimensional_estimate": 0.15, "order_of_magnitude_consistent": false, "causality_check_ok": true, "note": "c_eff is defined operationally in Appendix R (Definition R.1), not by a closed-form formula, so 'order_of_magnitude_consistent' against the dimensional estimate gamma/mu is a loose cross-check, not a precision test." }, "expected": { "speed_is_finite": true, "horizon_invariant": true } }, { "id": "B5_magnetic_memory", "group": "B", "source": "Appendix BBB — Historical Proof Experiment: Magnetic Memory Beyond Instantaneous Carriers", "statement": "After an ultrafast quench sets J~0, B does not vanish immediately; it persists for a finite, kernel-governed memory time.", "status": "PASS", "detail": "Appendix BBB (Historical Proof Experiment): the boxed core prediction J(t)~0 => B(t)!=0 for t in (t0, t0+dt_mem) is confirmed using the appendix's own B(x,t)=curl(int K_B*J) definition with a causal exponential memory kernel -- after an abrupt quench of J, B persists and decays on the kernel's memory timescale, not instantaneously.", "measured": { "tau_mem_kernel": 0.05, "quench_width": 0.0001, "B_at_quench_instant": 1.0010003333333057, "B_shortly_after_quench": 0.9725494372018524, "J_is_zero_at_quench": true, "B_survives_quench": true, "dt_mem_measured": 0.05010000000000003, "fitted_decay_tau": 0.050000004081833666, "fitted_tau_matches_kernel": true, "memory_finite_and_nonzero": true, "prediction_confirmed": true }, "expected": { "prediction_confirmed": true } }, { "id": "C1_no_singularity", "group": "C", "source": "No-Singularity Gravity Ch. 3 Regular Interior Geometry, Ch. 3.4 Geodesic Completeness", "statement": "Curvature invariants remain finite at r=0 and geodesics are complete.", "status": "PASS", "detail": "No-Singularity Gravity Ch. 3: curvature invariants (Kretschmann scalar) remain finite as r -> 0, and radial geodesics reach the core in finite proper time without divergence.", "measured": { "M": 1, "g_test": 0.1, "kretschmann_at_core": 95999999.99999997, "kretschmann_finite_at_core": "True", "geodesically_complete": "True", "proper_time_to_core": 15.056799999978248, "isco_schwarzschild": 5.999999999999654, "isco_shift_fitted_exponent": 3.0002398340715137, "isco_shift_scaling_exponent_ok": true, "photon_sphere_schwarzschild": 3, "shadow_correction_fitted_exponent": 3.0003141617052433, "shadow_correction_scaling_exponent_ok": true, "eht_fractional_bound_assumed": 0.12, "g_bound_from_shadow": 0.49324241486609405, "effective_spin_check": { "implemented": false, "reason": "requires 2D backward ray-tracing of near-critical trajectories; the 1D photon-sphere-radius shift is a different (and already cubically-scaling) quantity, not a faithful proxy for this claim" }, "weak_field": { "deflection_measured": 0.008047467870435643, "deflection_gr_prediction": 0.008, "deflection_rel_error": 0.005933483804455332, "deflection_matches_gr": true, "precession_measured": 0.011814692820301786, "precession_gr_prediction": 0.009817477042468103, "precession_rel_error": 0.2034347286165474, "precession_matches_gr_order_of_magnitude": true }, "weak_field_recovery_ok": true }, "expected": { "kretschmann_finite_at_core": true, "geodesically_complete": true } }, { "id": "C2_isco_shift_scaling", "group": "C", "source": "No-Singularity Gravity Ch. 5.5 Innermost Stable Circular Orbits", "statement": "delta r_ISCO ~ O(g^3/(GM)^2).", "status": "PASS", "detail": "Ch. 5.5: ISCO shift scales as O(g^3 / (GM)^2), i.e. cubic in the core scale g at fixed GM.", "measured": 3.0002398340715137, "expected": "~3.0" }, { "id": "C3_shadow_observational_bound", "group": "C", "source": "No-Singularity Gravity Ch. 9 Observational Implications (this session's new chapter)", "statement": "g <~ 0.5 GM from current EHT shadow-diameter precision.", "status": "PASS", "detail": "Ch. 9 Observational Implications: current EHT shadow-diameter precision (~10-17%) implies g <~ 0.5 GM.", "measured": 0.49324241486609405, "expected": "<= ~0.5-0.6" }, { "id": "C4_born_rule_measure_concentration", "group": "C", "source": "BornRule Ch. 5 Large-N Limit and Measure Concentration", "statement": "Empirical frequencies concentrate on |c_i|^2 as N grows, with exponentially suppressed atypical-branch measure.", "status": "PASS", "detail": "BornRule Ch. 5 / Unified Ch. 6: as N -> large, empirical frequencies concentrate on |c_i|^2 with exponentially suppressed deviation probability.", "measured": { "probs": [ 0.41860465116279066, 0.2906976744186048, 0.18604651162790703, 0.10465116279069767 ], "tracked_outcome": 0, "eps": 0.05, "N_values": [ 10, 30, 100, 300, 1000, 3000, 10000 ], "deviation_probability_by_N": [ 0.7425, 0.579, 0.3015, 0.071, 0.002, 0, 0 ], "mean_frequency_by_N": [ 0.41945, 0.4174333333333333, 0.41740999999999995, 0.41939499999999996, 0.418437, 0.41860683333333326, 0.41863924999999996 ], "fitted_alpha": 2.3357103276903075, "measure_concentration_confirmed": true, "converged_to_born_weights": true, "born_weight_target": 0.41860465116279066, "empirical_frequency_at_largest_N": 0.41863924999999996 }, "expected": { "measure_concentration_confirmed": true, "converged_to_born_weights": true } }, { "id": "C5_xi_selection_nontrivial", "group": "C", "source": "Ontological Foundations Ch. 1 PrePhysical Selection: World Choice (this session's new chapter)", "statement": "Xi-maximization favors structured, generative, stable worlds over trivial or unstable ones.", "status": "PASS", "detail": "Ontology Ch. 1: Xi-maximization selects a structurally stable, generative world over trivial/frozen or unstable alternatives -- consistency alone is not sufficient for selection.", "measured": { "candidates": [ { "kind": "frozen", "C": 1, "S": 0.5906161091496412, "G": 0, "D": 0.5, "Xi": 2.0312322182992824 }, { "kind": "divergent", "C": 0.20775, "S": 0, "G": 0, "D": 1, "Xi": -0.09225 }, { "kind": "chaotic", "C": 1, "S": 0.5965421356042233, "G": 0.01139248076231516, "D": 1.5, "Xi": 1.7601729923519194 }, { "kind": "stable", "C": 1, "S": 0.9985215089969466, "G": 0.2936176320949701, "D": 2, "Xi": 2.837469466136348 } ], "selected_world": "stable", "selected_world_scores": { "kind": "stable", "C": 1, "S": 0.9985215089969466, "G": 0.2936176320949701, "D": 2, "Xi": 2.837469466136348 }, "selected_world_is_structured": true, "selected_trivial_world": false, "ranking": [ "stable", "frozen", "chaotic", "divergent" ] }, "expected": { "selected_world_is_structured": true, "selected_trivial_world": false } }, { "id": "C6_weak_field_recovery", "group": "C", "source": "No-Singularity Gravity Ch. 4 Weak-Field Consistency", "statement": "Light deflection and perihelion precession recover the classical GR weak-field predictions as g -> 0.", "status": "PASS", "detail": "No-Singularity Gravity Ch. 4/9: light deflection and perihelion precession recover the classical GR weak-field values as g -> 0 and r >> GM (precession checked to order-of-magnitude; see in-code note on the Newtonian L^2=GMp initial-condition mapping).", "measured": { "deflection_measured": 0.008047467870435643, "deflection_gr_prediction": 0.008, "deflection_rel_error": 0.005933483804455332, "deflection_matches_gr": true, "precession_measured": 0.011814692820301786, "precession_gr_prediction": 0.009817477042468103, "precession_rel_error": 0.2034347286165474, "precession_matches_gr_order_of_magnitude": true }, "expected": { "deflection_matches_gr": true, "precession_matches_gr_order_of_magnitude": true } }, { "id": "C7_effective_spin_signature", "group": "C", "source": "No-Singularity Gravity Ch. 7.2 Effective Spin Interpretation", "statement": "a_eff ~ O(g/GM), from ray-tracing asymmetry of near-critical photon trajectories.", "status": "NOT_TESTABLE", "detail": "No-Singularity Gravity Ch. 7.2: the effective-spin-like shadow asymmetry requires 2D backward ray-tracing of near-critical photon trajectories. Not implemented in this lab -- the module explicitly declines to substitute a different (already-checked, cubically-scaling) quantity and call it a match.", "measured": { "implemented": false, "reason": "requires 2D backward ray-tracing of near-critical trajectories; the 1D photon-sphere-radius shift is a different (and already cubically-scaling) quantity, not a faithful proxy for this claim" }, "expected": null }, { "id": "C8_gleason_axioms", "group": "C", "source": "BornRule Ch. 6 Relation to Gleason and Comparison", "statement": "The squared-norm measure satisfies additivity, unitary invariance, and continuity.", "status": "PASS", "detail": "BornRule Ch. 6 Relation to Gleason: the squared-norm measure mu(P) = satisfies additivity, unitary invariance, and continuity -- the structural properties the chapter claims ground the measure, verified numerically on random states/subspaces rather than assumed.", "measured": { "dim": 6, "additivity": { "max_additivity_error": 2.220446049250313e-16, "additivity_holds": true }, "unitary_invariance": { "max_unitary_invariance_error": 4.440892098500626e-16, "unitary_invariance_holds": true }, "continuity": { "max_response_ratio": 0.49341073499887533, "mean_response_ratio": 0.12592670976532058, "continuity_holds": true }, "all_gleason_axioms_hold": true }, "expected": { "all_gleason_axioms_hold": true } } ], "raw_results": { "group_a_orbit": { "phase": "ORBIT", "separation_bounded": true, "gamma": 0.03, "separation_series": [ 47.561124539744554, 47.561124153202655, 47.56112307311648, 47.56112129974439, 47.561118833377115, 47.56111567433783, 47.56111182298204, 47.56110727969757, 47.56110204490461, 47.56109611905564, 47.561089502635426, 47.56108219616108, 47.56107420018188, 47.561065515279424, 47.56105614206755, 47.56104608119228, 47.56103533333185, 47.561023899196755, 47.561011779529615, 47.56099897510526, 47.56098548673067, 47.56097131524499, 47.5609564615195, 47.56094092645766, 47.56092471099498, 47.56090781609915, 47.56089024277, 47.560871992039374, 47.56085306497131, 47.56083346266189, 47.56081318623929, 47.56079223686376, 47.560770615727684, 47.56074832405543, 47.56072536310356, 47.56070173416054, 47.56067743854707, 47.5606524776158, 47.560626852751476, 47.56060056537092, 47.560573616923, 47.560546008888636, 47.56051774278083, 47.560488820144606, 47.5604592425571, 47.56042901162747, 47.560398128996944, 47.560366596338824, 47.56033441535851, 47.56030158779338, 47.56026811541304, 47.56023400001903, 47.56019924344505, 47.56016384755687, 47.560127814252354, 47.5600911454615, 47.56005384314634, 47.56001590930111, 47.559977345952085, 47.55993815515769, 47.55989833900851, 47.559857899627254, 47.559816839168775, 47.55977515982008, 47.559732863800356, 47.559689953360966, 47.55964643078545, 47.55960229838956, 47.559557558521234, 47.559512213560616, 47.559466265920115, 47.559419718044325, 47.55937257241015, 47.55932483152672, 47.559276497935436, 47.559227574209956, 47.55917806295631, 47.55912796681275, 47.55907728844989, 47.5590260305707, 47.558974195910466, 47.55892178723682, 47.558868807349796, 47.5588152590818, 47.55876114529764, 47.55870646889454, 47.558651232802156, 47.55859543998257, 47.55853909343035, 47.55848219617249, 47.55842475126852, 47.55836676181038, 47.55830823092264, 47.558249161762305, 47.55818955751901, 47.55812942141481, 47.55806875670448, 47.558007566675265, 47.55794585464706, 47.55788362397239, 47.55782087803633, 47.55775762025673, 47.55769385408393, 47.55762958300108, 47.557564810523914, 47.557499540200915, 47.55743377561327, 47.557367520374825, 47.557300778132266, 47.557233552564924, 47.55716584738496, 47.55709766633726, 47.55702901319951, 47.556959891782164, 47.55689030592856, 47.5568202595147, 47.55674975644957, 47.55667880067488, 47.556607396165205, 47.55653554692798, 47.55646325700349, 47.5563905304649, 47.5563173714182, 47.55624378400232, 47.55616977238899, 47.55609534078289, 47.55602049342156, 47.55594523457542, 47.55586956854778, 47.55579349967486, 47.55571703232579, 47.55564017090253, 47.55556291983998, 47.555485283605854, 47.55540726670085, 47.55532887365846, 47.55525010904503, 47.55517097745986, 47.555091483535, 47.55501163193538, 47.55493142735872, 47.554850874535575, 47.554769978229295, 47.554688743235985, 47.554607174384515, 47.554525276536495, 47.55444305458622, 47.5543605134607, 47.55427765811958, 47.5541944935551, 47.55411102479218, 47.55402725688818, 47.55394319493309, 47.553858844049344, 47.55377420939175, 47.5536892961476, 47.55360410953649, 47.553518654810276, 47.553432937253106, 47.5533469621813, 47.55326073494323, 47.55317426091941, 47.55308754552224, 47.55300059419612, 47.55291341241719, 47.55282600569338, 47.55273837956429, 47.552650539601096, 47.55256249140637, 47.55247424061414, 47.552385792889616, 47.55229715392925, 47.55220832946041, 47.55211932524145, 47.552030147061465, 47.551940800740184, 47.55185129212778, 47.55176162710481, 47.55167181158199, 47.5515818515, 47.551491752829385, 47.55140152157025, 47.55131116375221, 47.55122068543405, 47.55113009270359, 47.55103939167741, 47.55094858850065, 47.550857690012336, 47.55076670503692, 47.550675641136785, 47.55058450581316, 47.55049330663644, 47.550402051247346, 47.550310747357955, 47.5502194027527, 47.550128025289666, 47.55003662290169, 47.54994520359753, 47.54985377546311, 47.54976234666283, 47.54967092544079, 47.54957952012217, 47.54948813911448, 47.54939679090908, 47.549305484082446, 47.5492142109666, 47.549122832915096, 47.54903153039309, 47.54894031532009, 47.548849199697, 47.54875819560425, 47.54866731519999, 47.54857657071795, 47.54848597446555, 47.548395538821666, 47.548305276234466, 47.54821519921909, 47.548125320355325, 47.54803565228516, 47.54794620771034, 47.54785699938969, 47.54776804013658, 47.547679342816195, 47.54759092034273, 47.547502785676606, 47.547414951821615, 47.547327431821884, 47.54724023875907, 47.54715338574915, 47.547066884372, 47.54698039981302, 47.54689427300622, 47.546808534164875, 47.54672319463423, 47.546638265801086, 47.54655375909146, 47.54646968596873, 47.54638605793126, 47.54630288651033, 47.54622018326785, 47.5461379597941, 47.546056214766665, 47.54597496872442, 47.54589424725499, 47.54581405960393, 47.54573441507361, 47.54565532302216, 47.54557679286251, 47.545498834061135, 47.54542145613687, 47.54534466865963, 47.54526848124906, 47.54519290357306, 47.545117945346426, 47.54504361632916, 47.544969926324946, 47.544896885179405, 47.54482450277843, 47.544752789046335, 47.54468175394396, 47.54461140746681, 47.54454175964303, 47.54447282053137, 47.54440452381767, 47.54433692823793, 47.544270068618275, 47.544203985380996, 47.54413865832237, 47.54407409532642, 47.544010305004356, 47.54394729598722, 47.543885076924624, 47.54382365648357, 47.54376304334707, 47.54370324623496, 47.543644274975016, 47.54358613955006, 47.54352884958643, 47.54347241474568, 47.54341683821298, 47.543362131218686, 47.54330830932957, 47.543255381715035, 47.54320335758964, 47.54315224621234, 47.54310205688578, 47.543052798962755, 47.54300448227031, 47.542957117004036, 47.54291071334363, 47.542865281516356, 47.54282083179617, 47.5427773745028, 47.542734920000974, 47.542693478699555, 47.542653061050736, 47.54261368896175, 47.54257539167899, 47.54253814950871, 47.54250197250675 ], "separation_mean_tail": 47.54982673268425, "separation_std_tail": 0.004774095199207653 }, "group_a_qft_phase": { "mutual_info_by_separation": [ [ 0, 0.474370636143588 ], [ 1, 0.2644551407871978 ], [ 2, 0.16102369262904048 ], [ 3, 0.10201576502946974 ], [ 4, 0.06603280887282548 ], [ 5, 0.043285548437584254 ], [ 6, 0.028597130041753793 ], [ 7, 0.01898734663924362 ], [ 8, 0.012647587141667138 ], [ 9, 0.008442480226698024 ], [ 10, 0.005643382414366904 ], [ 11, 0.003775825292365198 ], [ 12, 0.0025278580489604963 ], [ 13, 0.0016930609664056462 ], [ 14, 0.0011342590004970177 ], [ 15, 0.0007600321575989 ], [ 16, 0.0005093371135949099 ], [ 17, 0.0003413615403466963 ], [ 18, 0.0002287957298614529 ], [ 19, 0.00015335479524480888 ], [ 20, 0.00010279159602610832 ], [ 21, 0.00006890093231071148 ], [ 22, 0.00004618462698147141 ], [ 23, 0.000030958009902271044 ], [ 24, 0.000020751562824550263 ] ], "mutual_info_monotonic_decay": true, "commutator_norm_by_separation": [ [ 0, 0.0341047280254452 ], [ 1, 0.0007317902997802266 ], [ 2, 0.0000043722453014554066 ], [ 3, 9.276225993569378e-9 ] ], "commutator_norm_monotonic_decay": true }, "group_a_rg_flow": { "flow_file": "/Users/fcp/Desktop/THEORY123456/STRUCTURAL_STABILITY_SERIES/PrePhysicalSelection_EmergentReality/outputs/runs/20260705_021857Z/rg_flow/rg_flow.npz", "n_couplings": 4, "has_fixed_point_candidate": false, "n_fixed_point_indices": 0, "ir_flow_consistent": "True", "coupling_ir_clusters_found": 9, "rg_flow_ok": true }, "group_a_ringdown": { "true_f": 250, "true_tau": 0.04, "fft_seed_frequency": 250, "recovered_f": 250.06020534565735, "recovered_tau": 0.05208689911329235, "f_rel_error": 0.0002408213826294059, "tau_rel_error": 0.30217247783230866, "fit_success": true, "recovery_ok": true, "note": "Uses an FFT-seeded, multi-start refit rather than the repo's fit_M0(), whose hardcoded initial guess was found (while building this check) to converge to a spurious ~2x-frequency local minimum even at low noise. Frequency recovers to <0.1%; tau recovery is looser, reflecting genuine amplitude/tau degeneracy at this SNR." }, "group_b_appendix_n": { "n_files_analyzed": 45, "per_gamma_classification": [ { "gamma": 0.001, "phase": "ORBIT", "mean_sep_tail": 94.47276015181932, "rel_std_tail": 0.10465426752023169, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.0014, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.91853617115999, "rel_std_tail": 0.03548350664391581, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.0016, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 96.19742538374052, "rel_std_tail": 0.12188065731527305, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.0018, "phase": "ORBIT", "mean_sep_tail": 96.02365385311828, "rel_std_tail": 0.11093316709578555, "sign_changes": 5, "n_orbit_est": 2.5 }, { "gamma": 0.002, "phase": "ORBIT", "mean_sep_tail": 93.73629622440112, "rel_std_tail": 0.1023284333108696, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.0025, "phase": "ORBIT", "mean_sep_tail": 94.7854393132009, "rel_std_tail": 0.10870406466435482, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.003, "phase": "ORBIT", "mean_sep_tail": 93.69178464181489, "rel_std_tail": 0.10511354201184805, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.0035, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 97.24647525000954, "rel_std_tail": 0.11266642809315955, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.004, "phase": "ORBIT", "mean_sep_tail": 92.68088694776733, "rel_std_tail": 0.09730026841010564, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.0045, "phase": "ORBIT", "mean_sep_tail": 95.22721911793339, "rel_std_tail": 0.10821581331037143, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.005, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.65401513874204, "rel_std_tail": 0.029440638394668615, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.006, "phase": "ORBIT", "mean_sep_tail": 92.77936225911635, "rel_std_tail": 0.1086596620519436, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.007, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 92.94854395674916, "rel_std_tail": 0.10142795793164247, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.008, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.3310309773341, "rel_std_tail": 0.04918224082814142, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.009, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 86.98117912088705, "rel_std_tail": 0.07227371666973245, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.01, "phase": "ORBIT", "mean_sep_tail": 94.4723567047347, "rel_std_tail": 0.10892309371759891, "sign_changes": 7, "n_orbit_est": 3.5 }, { "gamma": 0.012, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 87.1591082327268, "rel_std_tail": 0.041412168247076234, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.014, "phase": "ORBIT", "mean_sep_tail": 83.16696134364597, "rel_std_tail": 0.04052753236572123, "sign_changes": 7, "n_orbit_est": 3.5 }, { "gamma": 0.016, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 97.25452915391209, "rel_std_tail": 0.1300081254118396, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.018, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 86.0369251042724, "rel_std_tail": 0.04843604716527379, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.02, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 80.3106141713007, "rel_std_tail": 0.018206415285170995, "sign_changes": 18, "n_orbit_est": 9 }, { "gamma": 0.022, "phase": "ORBIT", "mean_sep_tail": 87.29565987986301, "rel_std_tail": 0.08144301631348422, "sign_changes": 3, "n_orbit_est": 1.5 }, { "gamma": 0.024, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 91.0099306172993, "rel_std_tail": 0.08325152401848093, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.026, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 78.76194705063975, "rel_std_tail": 0.0065918369937875455, "sign_changes": 32, "n_orbit_est": 16 }, { "gamma": 0.028, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 91.28664580954049, "rel_std_tail": 0.11495578081571169, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.03, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 76.82015600129647, "rel_std_tail": 0.013685500392530994, "sign_changes": 20, "n_orbit_est": 10 }, { "gamma": 0.035, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 88.09543706136007, "rel_std_tail": 0.10425355259592459, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.04, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 95.17747343222118, "rel_std_tail": 0.13516804208480565, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.045, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 90.24288359675722, "rel_std_tail": 0.1105676832581694, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.05, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 88.96703265066711, "rel_std_tail": 0.10331186924923387, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.055, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 90.23118108146373, "rel_std_tail": 0.11462194478481283, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.06, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 82.10310028391095, "rel_std_tail": 0.0429944226643891, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.07, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 81.3125023436151, "rel_std_tail": 0.05055681585742831, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.08, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 91.46797210563464, "rel_std_tail": 0.09223670525813715, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.09, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 91.50210249741677, "rel_std_tail": 0.13025835570592517, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.1, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 92.78668669258599, "rel_std_tail": 0.1092494410296883, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.12, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 91.44609512733683, "rel_std_tail": 0.121431966337506, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.14, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 88.35669842827124, "rel_std_tail": 0.08781300760747071, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.16, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 88.9685804965785, "rel_std_tail": 0.08524866542497664, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.18, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.32800016883263, "rel_std_tail": 0.052085738457814765, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.2, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.10382193069019, "rel_std_tail": 0.03681989791308297, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.25, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 95.16649267953115, "rel_std_tail": 0.11574567231222069, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.3, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 87.69485333611466, "rel_std_tail": 0.07548159773931923, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.4, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 84.8544950422633, "rel_std_tail": 0.035907373748741686, "sign_changes": 1, "n_orbit_est": 0.5 }, { "gamma": 0.5, "phase": "OVERDAMPED_STATIC", "mean_sep_tail": 87.42850144774859, "rel_std_tail": 0.07682422039897037, "sign_changes": 1, "n_orbit_est": 0.5 } ], "stable_intervals": [ [ 0.001, 0.001 ], [ 0.0018, 0.003 ], [ 0.004, 0.0045 ], [ 0.006, 0.006 ], [ 0.01, 0.01 ], [ 0.014, 0.014 ], [ 0.022, 0.022 ] ], "n_stable_observed_raw": 7, "n_stable": 7, "delta_gamma_min": 0.0009999999999999992, "gamma_c": 0.022, "packing_bound": 22, "resolution_note": "45-point gamma scan (not a dense re-scan); n_stable_observed_raw=7 isolated ORBIT windows below gamma_c=0.0220 at this resolution. The book's Appendix N itself describes its count as scan-resolution limited." }, "group_b_grb": { "n_real_grbs_used": 48, "catalog": "/Users/fcp/Desktop/STRUCTURAL_STABILITY_SERIES/grb_clean48_Ep_z.csv", "alpha_true": 0.000001, "alpha_fit": 0.000001002645907329701, "alpha_fit_error": 4.42355800107098e-9, "alpha_rel_error": 0.0026459073297009734, "pipeline_recovers_injected_alpha": true, "data_limitation_note": "Delta_t is SYNTHETIC (injected) -- the real catalog has no per-photon/energy-band arrival-time data required for a genuine dispersion-vs-energy test. E (peak energy) and z (redshift) are real, from grb_clean48_Ep_z.csv. This validates the CCCC2 fit pipeline's correctness, not an observational detection or exclusion of the theory's predicted signal." }, "group_b_causality": { "gamma": 0.03, "mu": 0.2, "chi": 1, "measured_speed_T": 10.47672331047794, "measured_speed_2T": 8.223455784058782, "fit_r2_T": 0.9880859672194505, "fit_r2_2T": 0.9723208532676499, "speed_is_finite": true, "horizon_invariant": true, "c_eff_dimensional_estimate": 0.15, "order_of_magnitude_consistent": false, "causality_check_ok": true, "note": "c_eff is defined operationally in Appendix R (Definition R.1), not by a closed-form formula, so 'order_of_magnitude_consistent' against the dimensional estimate gamma/mu is a loose cross-check, not a precision test." }, "group_b_magnetic_memory": { "tau_mem_kernel": 0.05, "quench_width": 0.0001, "B_at_quench_instant": 1.0010003333333057, "B_shortly_after_quench": 0.9725494372018524, "J_is_zero_at_quench": true, "B_survives_quench": true, "dt_mem_measured": 0.05010000000000003, "fitted_decay_tau": 0.050000004081833666, "fitted_tau_matches_kernel": true, "memory_finite_and_nonzero": true, "prediction_confirmed": true }, "group_c_gravity": { "M": 1, "g_test": 0.1, "kretschmann_at_core": 95999999.99999997, "kretschmann_finite_at_core": "True", "geodesically_complete": "True", "proper_time_to_core": 15.056799999978248, "isco_schwarzschild": 5.999999999999654, "isco_shift_fitted_exponent": 3.0002398340715137, "isco_shift_scaling_exponent_ok": true, "photon_sphere_schwarzschild": 3, "shadow_correction_fitted_exponent": 3.0003141617052433, "shadow_correction_scaling_exponent_ok": true, "eht_fractional_bound_assumed": 0.12, "g_bound_from_shadow": 0.49324241486609405, "effective_spin_check": { "implemented": false, "reason": "requires 2D backward ray-tracing of near-critical trajectories; the 1D photon-sphere-radius shift is a different (and already cubically-scaling) quantity, not a faithful proxy for this claim" }, "weak_field": { "deflection_measured": 0.008047467870435643, "deflection_gr_prediction": 0.008, "deflection_rel_error": 0.005933483804455332, "deflection_matches_gr": true, "precession_measured": 0.011814692820301786, "precession_gr_prediction": 0.009817477042468103, "precession_rel_error": 0.2034347286165474, "precession_matches_gr_order_of_magnitude": true }, "weak_field_recovery_ok": true }, "group_c_born_rule": { "probs": [ 0.41860465116279066, 0.2906976744186048, 0.18604651162790703, 0.10465116279069767 ], "tracked_outcome": 0, "eps": 0.05, "N_values": [ 10, 30, 100, 300, 1000, 3000, 10000 ], "deviation_probability_by_N": [ 0.7425, 0.579, 0.3015, 0.071, 0.002, 0, 0 ], "mean_frequency_by_N": [ 0.41945, 0.4174333333333333, 0.41740999999999995, 0.41939499999999996, 0.418437, 0.41860683333333326, 0.41863924999999996 ], "fitted_alpha": 2.3357103276903075, "measure_concentration_confirmed": true, "converged_to_born_weights": true, "born_weight_target": 0.41860465116279066, "empirical_frequency_at_largest_N": 0.41863924999999996 }, "group_c_xi_selection": { "candidates": [ { "kind": "frozen", "C": 1, "S": 0.5906161091496412, "G": 0, "D": 0.5, "Xi": 2.0312322182992824 }, { "kind": "divergent", "C": 0.20775, "S": 0, "G": 0, "D": 1, "Xi": -0.09225 }, { "kind": "chaotic", "C": 1, "S": 0.5965421356042233, "G": 0.01139248076231516, "D": 1.5, "Xi": 1.7601729923519194 }, { "kind": "stable", "C": 1, "S": 0.9985215089969466, "G": 0.2936176320949701, "D": 2, "Xi": 2.837469466136348 } ], "selected_world": "stable", "selected_world_scores": { "kind": "stable", "C": 1, "S": 0.9985215089969466, "G": 0.2936176320949701, "D": 2, "Xi": 2.837469466136348 }, "selected_world_is_structured": true, "selected_trivial_world": false, "ranking": [ "stable", "frozen", "chaotic", "divergent" ] }, "group_c_gleason": { "dim": 6, "additivity": { "max_additivity_error": 2.220446049250313e-16, "additivity_holds": true }, "unitary_invariance": { "max_unitary_invariance_error": 4.440892098500626e-16, "unitary_invariance_holds": true }, "continuity": { "max_response_ratio": 0.49341073499887533, "mean_response_ratio": 0.12592670976532058, "continuity_holds": true }, "all_gleason_axioms_hold": true }, "_timings": { "group_a": 7.0476789474487305, "group_b": 7.562948226928711, "group_c": 12.982895135879517 } } }