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"labeled_primitive_passed": true, "matching_labeled_repetition_divisors": [], "matching_permuted_only_divisors": [], "divisor_tests": [ { "divisor": 2, "time": "12.2510308307397440629321190844221387101487205061166551462532", "relative_cycle_index": 1, "local_time": "0.0", "labeled_error": { "canonical_inf": "2.4642668944159678243556890878716603211968115245595331386864", "position_inf": "1.35600056171830469344425952935411147685715016559475022957498", "velocity_inf": "3.69755417289097919570435424611828702723692517110335034597342", "normalized": "2.0" }, "matching_permutations": [] } ], "minimum_jacobi_radius_estimates": [ 0.8664695907784178, 0.7414615677138143 ], "minima_kind": "adaptive step-endpoint sampled minima; not rigorous lower bounds", "energy_error": "3.27064470136439302336834681973200397722638583941462423576179e-41", "L_error": "1.20540265263696278864877069801103795572789640532955069486188e-41", "steps": 322, "elapsed_seconds": 0.9739749589934945, "completed_at": 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Not direct full-period integration or an interval proof.", "shared_inner_curve_via_half_period_swap": false }, "continuous_angle_audit": { "id": "branch_res1x14_plus_r9of14", "input_sha256": "dc9ace2a67da8e56f7459107c0ae9a1bad53e189ebf28061cbbdebdd315f88c1", "precision_bits": 160, "method": "14D canonical Cartesian state plus continuous MP Jacobi angle quadratures", "period": "24.50206166147948812586423816884427742029744101223331029251", "masses": [ "1.0", "0.4951882724699883524664936151966515665786650202297124075948", "1.0" ], "continuous_windings": [ "4.99999999999999999999999999999999999999927767080323539323", "-9.000000000000000000000000000000000000000095286644882350317" ], "integer_windings": [ 5, -9 ], "integer_errors": [ "7.223291967646067698238715291619520496712951911964580228417e-40", "9.528664488235031742297277965974839837528757266630120840146e-41" ], "integer_winding_passed": true, "winding_gcd": 1, "minimum_jacobi_radius_estimates": [ 0.8664513166168072, 0.7413190634250334 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"periodicity_passed": true, "linear_ellipticity_passed": true, "relative_eigenvalues": [ { "real": "0.996725368207279527280189322342074272400519180167476859476", "imag": "-0.08086124146995920160159342322204105502873855831387230177294", "modulus": "0.9999999999999999999999999999999999992343241125351113347342", "phase_turns": "-0.01288353229844011087680875317311908042877947376324755774329" }, { "real": "0.9967253682072795272801893223420742724005191801674768594758", "imag": "0.08086124146995920160159342322204105502873855831387230177293", "modulus": "0.999999999999999999999999999999999999234324112535111334734", "phase_turns": "0.01288353229844011087680875317311908042877947376324755774329" }, { "real": "0.9999989095337793271031199940062935685260060736030442352722", "imag": "0.00147679763414938315352103186456546963714674183047502322779", "modulus": "1.00000000000000000000000000000000000000404870822736417244", "phase_turns": "0.0002350397288555918989990196843535544005657889985592575879393" }, { "real": "0.9999989095337793271031199940062935685260060736030442352723", "imag": "-0.00147679763414938315352103186456546963714674183047502322779", "modulus": "1.00000000000000000000000000000000000000404870822736417244", "phase_turns": "-0.0002350397288555918989990196843535544005657889985592575879392" } ], "absolute_eigenvalues": [ { "real": "0.9066030138633768550747160661966831014172209487094885217034", "imag": "-0.4219845675541247964847044567097127631024935662407903055776", "modulus": "0.9999999999999999999999999999999999364489013404142407829372", "phase_turns": "-0.06933318077052920277512651336888367558869632234954729269326" }, { "real": "0.9066030138633768550747160661966831014172209487094885216866", "imag": "0.4219845675541247964847044567097127631024935662407903055707", "modulus": "0.999999999999999999999999999999999936448901340414240782919", "phase_turns": "0.06933318077052920277512651336888367558869632234954729269339" }, { "real": "0.9924971777140875151473522387595039326149061548389575412527", "imag": "0.1222675436474086718237126936101962700254338883100441565589", "modulus": "1.000000000000000000000000000000000000336042782871226312513", "phase_turns": "0.01950829749501412761691863380134501524696048688041837979896" }, { "real": "0.9924971777140875151473522387595039326149061548389575412576", "imag": "-0.1222675436474086718237126936101962700254338883100441565594", "modulus": "1.000000000000000000000000000000000000336042782871226312518", "phase_turns": "-0.01950829749501412761691863380134501524696048688041837979896" } ], "relative_map_quality": { "symplectic_defect": "1.02444752261333814791639637483814592515517417276782767714e-33", "reduced_symplectic_defect": "7.839225559352763221190711004180666609156435771587675798127e-36", "flow_neutral_defect": "8.921408833936600090782882785275512952900295567099483421921e-34", "rotation_neutral_defect": "8.281563516142097235222758474257836133167481455438834848395e-35", "energy_covector_defect": "8.921408833936600090779079278337684223088889115149813009985e-34", "angular_covector_defect": "8.281563516142097235211861725585690159592603913518103699645e-35", "stability_indices": [ { "real": "1.999997819067558654206239988012587369713556106355206709926", "imag": "0.0" }, { "real": "1.993450736414559054560378644684148312139494401185835479571", "imag": "0.0" } ], "elliptic": true }, "absolute_reduced_symplectic_defect": "8.619574933678921020879038212218693102319769705531618906727e-34", "full_closure": { "canonical_inf": "3.1719946617386343655613228572926723858146908770827e-36", "position_inf": "1.033153461862474038865715075231602493352253684098e-36", "velocity_inf": "6.233048155434030666345877029745318430644788300918506276448e-36", "normalized": "2.732989206548324711695257019188295055493293342710646133203e-36" }, "conservation": { "max_sampled_energy_error": "6.316722023368507950917496489945503027033868388538946856238e-41", "max_sampled_L_error": "6.328796943998168837195559370045438159125699412739977469274e-41" }, "minimum_clearance": { "value": "0.25844266110893143354545201324189774820218413347691", "time": "10997.51788006725233450951925751126991639599287552471045655", "kind": "minimum over independent MP samples; upper bound on the true minimum", "sample_count": 83 }, "primitive": { "status": "sampled returns only; not an exhaustive primitive-period proof", "tested_sample_count": 72, "earlier_labeled_or_equal_mass_permuted_returns": [], "relative_half_permutation_returns": [] }, "fundamental_family_novelty": "not claimed; known-family mass samples are not new fundamental families", "novelty_dedup_status": "not assessed by this validator", "elapsed_seconds": 429.60762004274875, "completed_at": "2026-09-09T03:40:06.100370+00:00", "formulation": "canonical Cartesian 12+144, fixed arbitrary masses, independent COM pair1,2, four-dimensional H,L quotient", "relative_construction": { "half_time": 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