{ "updated_utc": "2026-09-09T08:57:42.929220+00:00", "catalogue_version": "0.2.0", "catalogue_sha256": "1595020915fcb61f1a8fd141eb8bfae87d99503f95f7a665491e7a75a9d59ba0", "numerical_results": 45, "unmatched_primitive_classes_with_Euler_exclusion": 42, "linearly_elliptic_unmatched_classes": 0, "global_priority_claim": false, "scope": "This inventory separates numerical periodicity, known-class exclusions and candidate family novelty. Unique primitive classes are not automatically separate visual motifs. Repeated parameter samples are grouped by primitive class. Unlisted literature and collision-mediated ancestry remain possible.", "orbits": [ { "id": "r4_full_mass_23_000497", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAbaBab", "primitive_root": "AAbaBab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ 0, 1 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 9.30138817151722, "masses": [ "1.0", "0.91744456478490511735367136580940388014740917081887", "1.0" ], "period": "20.76236112486948486691105902881576525201160429033", "energy": "-1.054574302394417927705114779113123575586544193226785646595", "angular_momentum": "9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-1.686857355016659854598879965573224638527583011803114932095", "3.298872532627227121980771242513529194156144600069780110375e-42", "1.497327209472495288425651615487244689299534854078885067905", "1.225994503262722712198077124251352919415563009235953092645e-41", "0.3131426449815699556492995909052281681257018773474850679049", "-1.454669246737277287801922875748647080584323843133096933476e-41", "-6.095878900000000000000000000000000000000051850565611561469e-41", "0.2994182556831499098515880405146620570822910212002471477463", "4.737100239999999999999999999999999999999985485084692678586e-41", "0.5056952516715216893041640281538530891771740006853057045073", "1.358778660000000000000000000000000000000066365480918882883e-41", "-0.8051135073546715991557520686685151462594650218855528522536" ], "G": "1", "normalized_full_period_closure": "3.560604449144996398731214910758116695055722332069097068986e-39", "closest_distance_numerically_refined": 0.010765150567650601, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 3.8025835369381866e-08, "visual_priority_score": 52.42527705585814, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000219_independent160.json", "sha256": "4157e5ec666167824fd1017c5ec499d6ce18d8421c4a46ab6a10b1658da34bc4" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000219_topology192.json", "sha256": "87cf6dd3df294d8ef6575da95b2b102173b6c25a323370f27af969f268604a67" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000219_trajectory_audit.json", "sha256": "041ad8192b40e657145f2df58898d3c5fb129486db3816efdd5a20cc07657365" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000245", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAABabbbaB", "primitive_root": "AAAABabbbaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ -2, 1 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 1054.5315566472743, "masses": [ "1.0", "0.922976885779562133390962034442538962397804", "1.0" ], "period": "6.1143398636939206611552805267005336053392", "energy": "-2.114555629834641417807667898962992168792247490180593067447", "angular_momentum": "0.0", "initial_cartesian_canonical_state": [ "-1.15608196508048162933243729108797323899618832897298484616", "-1.658389169557585473254305254773751218430746533365535275016e-38", "0.3382142445499112155369959830829893418130816710270151538397", "1.477261083044241452674569474522624878156925346663603242719e-37", "0.8439180349195173305649957950932000266197116710270151538397", "-1.197638916955758547325430525477375121843074653336426095581e-37", "-2.090000000000000000000000000000000000000000000019189271385e-39", "-0.2491838816775404699761819695025634742146947165336523452305", "-8.921999999999999999999999999999999999999999999997715097706e-38", "0.985493430830004818474617395012514931927545", "9.130999999999999999999999999999999999999999999999634024844e-38", "-0.7363095491524643484984354255099514577128502834663476547695" ], "G": "1", "normalized_full_period_closure": "7.730908816646092097035430713521369687126274586969002315553e-36", "closest_distance_numerically_refined": 0.059950325637666835, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 5.214739751124853e-11, "visual_priority_score": 70.44391733075827, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000246_independent160.json", "sha256": "77c5cf681360ccdb1748738b7c0b0d4cce6cedd1a5eb3a6b90544e62f26fc322" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000246_topology192.json", "sha256": "b0143e9fc4041e11734d1a129df622e82d4c4c49c03982240dd18e4687b35856" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000246_trajectory_audit.json", "sha256": "45633cdf93f2d122fbae1325e7d2fb6533b0a265e3df4118828eaad5fec93ab7" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000300", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAABabbaBABabbaB", "primitive_root": "AAAAABabbaBABabbaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 185692.3969253983, "masses": [ "1.0", "0.948124683057427364800599599909689901870576161", "1.0" ], "period": "28.3809319093890172653315976709754118949574846", "energy": "-1.212948214279183177709019719489507394914928658930733436691", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-1.593879725962032009102878057207950607175245911535993279371", "-1.563333543559772404260560421265975909512849099912578844048e-43", "1.252746050333678943250588688132995560518910402964006720629", "5.753216645644022759573943957873402409021012999651481480665e-42", "0.406120274037968712374616178889693819952189331464006720629", "-5.298433354355977240426056042126597590695445276390066151382e-42", "-9.696140000000000000000000000000000001741154491378375725529e-42", "0.2852358010075907110857162307660965513129536963101516620087", "1.157030000000000000000000000000000000073780566211744316828e-41", "0.6738178992272103718866720183898724386008837836", "-1.874159999999999999999999999999999998996651170739067442749e-42", "-0.9590537002348010829723882491559689899138374799101516620087" ], "G": "1", "normalized_full_period_closure": "1.304986415849664822786268302689939651727486944655170739067e-36", "closest_distance_numerically_refined": 0.04442946361799289, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 3.838365270070199e-08, "visual_priority_score": 65.40376654919017, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000300_independent160.json", "sha256": "bd438f080ce0dd820f9c0f85265433db2ca8455826f603ed036dab56b3b5216a" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000300_topology192.json", "sha256": "7bf27ec4579519f36fde01f820bfba9b3b672492626f64b59126a626eef6ad43" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000300_trajectory_audit.json", "sha256": "93f8142ff0246ec1c2da68801616a2035889a2d4fea0edc1a49a1e43c2c4125e" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000416", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABaBAbbABaB", "primitive_root": "AABaBAbbABaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 357244.6874451407, "masses": [ "1.0", "0.97952147651056424027243554217796421579449619672", "1.0" ], "period": "22.7515241313273128362238518669909870515385405978", "energy": "-1.188532997296062118587684116483499594902002815240960503249", "angular_momentum": "1.86690458335834251214321921613403727217707565061635013993e-60", "initial_cartesian_canonical_state": [ "-1.914579018187398848632943577610556773966082001624576462958", "2.074637362445648484548268097136707670109241362207616266326e-41", "1.867399623425909343048465960423223297955466725955423537042", "4.394852362445648484548268097136707670109080374369044809033e-41", "0.08542098181398048226843823160764037995160014881542353704159", "-6.379489637554351515451731902863292329890473023235923387224e-41", "-1.536511179999999999999999999999999999999816398073100104404e-40", "0.1881149426492687606864604041225944760657862303472877662497", "1.625418299999999999999999999999999999999870493305729658365e-40", "0.2111304122918497997061904179477172607563862851654244675006", "-8.890712000000000000000000000000000000005409523262955396115e-42", "-0.3992453549411185603926508220703117368221725155127122337503" ], "G": "1", "normalized_full_period_closure": "3.632388900519535783686799466941867133997608563032232629554e-37", "closest_distance_numerically_refined": 0.02585985988851267, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 4.900332806201391e-09, "visual_priority_score": 61.42373212081069, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000416_independent160.json", "sha256": "a1bbd5993ce10c4502e4ecd7f54014d45bf24e6b18bdd7d1a541117f6304fab2" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000416_topology192.json", "sha256": "3bbc6d203983eb151de7049ca3fac99723ac7d2ee6d45f128e67cf2b48ea658e" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000416_trajectory_audit.json", "sha256": "1c2c47ca52192f99d8f6b62be8775e969546df6d199a47780bf7773c9cc75ec9" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000428", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABaaBAAbaBBab", "primitive_root": "AABaaBAAbaBBab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": false, "euler_family_obstruction": { "homology": [ 0, 2 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 3468.2444802466557, "masses": [ "1.0", "0.93095894615795251289495788429570251502142", "1.0" ], "period": "37.68996945033667083733210008483666744614", "energy": "-1.242282395706841064963191137580302935446263665990324743249", "angular_momentum": "-1.24460305557222834142881281075602484811805043374423342662e-60", "initial_cartesian_canonical_state": [ "-1.824288850334512016967562264571516780822270311618934052971", "-1.312217181458246563526785207576630786495664173566006499511e-38", "1.770838238863987316315423067934847268082229688381065947029", "-3.862217181458246563526785207576630786495664173568345663342e-38", "0.1757111496654897978541389350710033401937296883810659470289", "4.90778281854175343647321479242336921350433582643177602421e-38", "5.334999999999999999999999999999999999999999999997084245338e-38", "0.1606902773404629389046801208327030983862435293709667249425", "-1.063000000000000000000000000000000000000000000000038961302e-37", "0.2014764571783493751796532895409431401583129412580665501149", "5.295000000000000000000000000000000000000000000003305367681e-38", "-0.3621667345188123140843334103736462385445564706290332750575" ], "G": "1", "normalized_full_period_closure": "4.832398620461812139021176167072988160718083062980294869334e-34", "closest_distance_numerically_refined": 0.08803510918700265, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 1.7495855597626786e-09, "visual_priority_score": 70.89202111176321, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000524_independent160.json", "sha256": "c92cc3dea3e6fc4b6764c33abc4c0e71575905eb7701e6976f3017798e5f2514" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000524_topology192.json", "sha256": "3d1f347d019bd52b844fcda7518602dd5c87a3bda0a55b7e16198b8831cbe4a9" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000524_trajectory_audit.json", "sha256": "3b3767efadcbdf65011fdfb5fa3c8235c689d99ce9f37e5ef71995034ff73991" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000567", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAABaBAbaBabAbaBabABaB", "primitive_root": "AAABaBAbaBabAbaBabABaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 115039.8673363028, "masses": [ "1.0", "1.007817884032847685282047139733047292662751092825745677078", "1.0" ], "period": "40.05579975739553214146661398217415130088120209882725022992", "energy": "-1.222491840512742901210788312943791212485398193123150200359", "angular_momentum": "1.493523666686674009714575372907229817741660520493080111944e-59", "initial_cartesian_canonical_state": [ "-1.60828515992070288190392180545709343295981200454672556619", "0.0", "1.207133093305728871016336304684636946587509355584338294604", "0.0", "0.3917148400792971180960781945429065670401879954532744338098", "0.0", "0.0", "0.3037438294417521726161533123746519039461990327662352478268", "0.0", "0.7450013002282061926001089996945049685606436526115512415746", "0.0", "-1.048745129669958365216262312069156872506842685377786489401" ], "G": "1", "normalized_full_period_closure": "2.23564961507808866655305620572200600000547212412664441044e-36", "closest_distance_numerically_refined": 0.05910949506210037, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 4.253612784221872e-08, "visual_priority_score": 65.28429391745571, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000567_independent160.json", "sha256": "fd4c75c3bcb0951ba9f8392bca6b48ed6a1f93d06708d486e5b5060ad4577dd4" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000567_topology192.json", "sha256": "d79ecbc9e837a1065779cc5974d6c90e9504a1d8e012ea39b9c3d4e8595a142e" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000567_trajectory_audit.json", "sha256": "99df427a73d76b755caf9c0a8eb4a77feaa6735779d2a9734afe91d6dafe9b83" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000568", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABaBAbaBabAbaBabABaB", "primitive_root": "AABaBAbaBabAbaBabABaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ 1, -2 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 128389.40227274332, "masses": [ "1.0", "0.9635892181263042081880885164319054236977511871131639441828", "1.0" ], "period": "35.55944923787725769693176988888026379554416814994934756929", "energy": "-1.247295388921699944998145566408315071781232213274196379145", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-1.55925756150315651037563017414816157047956556991103549511", "0.0", "1.160780031537984288640422320258248623523302966632757821399", "0.0", "0.4407424384968434896243698258518384295204344300889645048895", "0.0", "0.0", "0.2849789213203642384279759723822978273079896617211691380154", "0.0", "0.7915667850527948571211782351622013885506872367579069791751", "0.0", "-1.076545706373159095549154207544499215858676898479076117191" ], "G": "1", "normalized_full_period_closure": "3.871607032218104042172485538828341351239369241278667056e-36", "closest_distance_numerically_refined": 0.03479270780377053, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 1.8965521797476015e-07, "visual_priority_score": 56.79759827943816, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000568_independent160.json", "sha256": "2048fd747922bd3663c013c7847830a0f8e7350fe4a80f5edc7089a53a7aaaf9" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_31_000568_topology192.json", "sha256": "a032183d0f3797a4e0ce114bedc9d942bec274f048ceedfe06540e154687b042" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_31_000568_trajectory_audit.json", "sha256": "1da0e7200cc179e99400351f2a68b55366dd47365bb569f54df191b9ac1b50c8" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_31_000645", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABaaBAAbaBab", "primitive_root": "AABaaBAAbaBab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ 0, -1 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 56.77236719621385, "masses": [ "1.12", "0.9614210110320869370316528196917998554128133184594500767996", "0.88" ], "period": "43.59916523505811202335840877075496628395623309125536490776", "energy": "-0.7348908428529739670282984887901879881915797808218421977223", "angular_momentum": "9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-0.9497874975008812332639828080129383362734847663567326837909", "0.0", "0.1451757278030864899533838149927996542682287626471213999658", "0.0", "1.050212502499118766736017191987061663726515233643267316209", "0.0", "0.0", "-0.6625940688680657358519935944472638625149456059968334639423", "0.0", "1.464236785495497896913823547904608553052442128711050409628", "0.0", "-0.8016427166274321610618299534573446905374965227142169456855" ], "G": "1", "normalized_full_period_closure": "2.122637037391705224193164018119782056124209338260445722035e-39", "closest_distance_numerically_refined": 0.08515651775854723, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 7.48707373876556e-09, "visual_priority_score": 66.0207103755171, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_32_000357_independent160.json", "sha256": "00364368d1ef9d7573c6e0c7506e9fcc9661010fb3a2e8221ea4ffa9842f2f97" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_32_000357_topology192.json", "sha256": "8f43d99b4b7a9cf1b8e9e8b7d8d819cb9c8f6259b6c4dc7d247d1e7f6ed00ec0" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_32_000357_trajectory_audit.json", "sha256": "32383562149bbd332cbafdad85ba8584b3bebd5289172da99762dab9b97d6fec" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_32_000371", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAABabAbaB", "primitive_root": "AAABabAbaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 2812.841432842998, "masses": [ "1.12", "1.013411246750235594861658343185958084295376906951481874894", "0.88" ], "period": "198.4446447082221839644809366796547910311099742785042579756", "energy": "-0.2593779793663149425025864918719376184036001549502798680906", "angular_momentum": "3.982729777831130692572200994419279513977761387981546965185e-59", "initial_cartesian_canonical_state": [ "0.184190056160868766670270895217126549812839286105151198022", "0.0", "-2.100213629113488752389492692559389803387550157551911289344", "0.0", "2.184190056160868766670270895217126549812839286105151198022", "0.0", "0.0", "-1.145261012803573904212910022788320157302753677568562270215", "0.0", "0.5346186293041784571349966571519400736882763684132912503446", "0.0", "0.6106423834993954470779133656363800836144773091552710198709" ], "G": "1", "normalized_full_period_closure": "7.977098189764762714303524588630706750823938146416683462941e-37", "closest_distance_numerically_refined": null, "clearance_note": null, "scipy_mp_trajectory_difference": null, "visual_priority_score": 58.97536273479808, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_32_000522_independent160.json", "sha256": "35e6c6c08f1bbba530337a40bf7236ab5abc4a15fb91d294f1333676831c5480" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_32_000522_topology192.json", "sha256": "754d074360ee5c8d6f5b100728709f9a95c55e83316d22ba5e911bf310566273" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000013", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAAAABaB", "primitive_root": "AAAAAAABaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": false, "euler_family_obstruction": { "homology": [ -2, -2 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 121.96868992043996, "masses": [ "1.25", "1.13350500664732113320301619514936641419179333929958", "0.75" ], "period": "10.450222032675935851019525544377387894725463406343", "energy": "-1.347000368258789147862152204923611889688180028986703484466", "angular_momentum": "-2.987047333373348019429150745814459635483321040986160223889e-59", "initial_cartesian_canonical_state": [ "-0.1363459073926750678586375601381291776647773317806185976174", "-2.11180076693026024496573223182560632403221142810389377645e-41", "-1.082754975070588478363134502655650960105108403901042347617", "1.739171712519739755034267768174393675967788543967074009087e-41", "1.863654092607535007810305971857080398136010133687011402383", "8.911881534697397550342677681743936759677881349201192046188e-42", "-5.349495704287500000000000000000000000000000125073902226677e-41", "-1.161994247881157172429488117404512619138682862193966181741", "-5.9237661348999999999999999999999999999999999216702184999e-41", "0.78875283179668773112378058410807721802572291135948", "1.127326183918750000000000000000000000000000004674412072658e-40", "0.3732414160844694413057075332964354011129599508344861817415" ], "G": "1", "normalized_full_period_closure": "8.652989562664569054698625545324953090912539985491158166098e-40", "closest_distance_numerically_refined": 0.07621301769765915, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 5.0782711369379285e-11, "visual_priority_score": 70.2344694226729, "visual_series": "nested binary turns: A^nBaB", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000031_independent160.json", "sha256": "54758a1cef1ec6d3644d1cc018742816772918ea8039d7fba1679cd345db57c5" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000031_topology192.json", "sha256": "0c68512f03846d1a72b763d9c6a5652f13f828902088b404b795942e38b48aac" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000031_trajectory_audit.json", "sha256": "8bfeb30e56959d759d34e83a3ceb4f8444c0c08619b59dc44c6ec99069dc13d4" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000035", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABabAbaB", "primitive_root": "AABabAbaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 31.38177270999816, "masses": [ "1.25", "1.111898887308061191861535397070999903748792074868786", "0.75" ], "period": "15.1040018036211679359571759523235359355222360617076", "energy": "-1.320476892030010948834890416450584082245167223081692481502", "angular_momentum": "-1.991364888915565346286100497209639756988880693990773482592e-59", "initial_cartesian_canonical_state": [ "-0.3446685262746502439859629338805293508583783689279475011259", "-4.75281419579072704803651237209778652517885332561341451457e-42", "-0.7290797362099073191517328704536004378755751824825887511259", "9.825857043334272951963487627902213474821147235673943611072e-42", "1.655331473725284698692449473198476676013352706242102498874", "-6.645789024790727048036512372097786525178852659997954377083e-42", "3.204078965637500000000000000000000000000000118206679560917e-41", "-2.060020786213109889230570939449956424314614613181784004622", "9.210547200999999999999999999999999999999999051542565486349e-42", "1.72790731534015390973012896266584637735134406684048893", "-4.125133685737500000000000000000000000000000023360936109552e-41", "0.3321134708729559795004419767841100469632705463412950746216" ], "G": "1", "normalized_full_period_closure": "4.041094551016820388375739145883103855864385814014535151245e-39", "closest_distance_numerically_refined": 0.14473667084525715, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 2.4478703786190437e-11, "visual_priority_score": 76.1499299923243, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000035_independent160.json", "sha256": "9de05e920d9cab49810c80aba96778dcaca384b9f2327a1f4c04bdc5d44d5281" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000035_topology192.json", "sha256": "31b48254e4a10d540dd9a9a26546fffbcb566f204ee75e3ebebd9b1e62067e8f" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000035_trajectory_audit.json", "sha256": "6b08b49b96b1fca16d254a871767c4b752017a120e59e8360be511d8ded28b5e" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000055", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAABBAAABBAbABB", "primitive_root": "AAABBAAABBAbABB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 32300.856698124313, "masses": [ "1.25", "1.021646512939969007092839810438978942524881844462568656494", "0.75" ], "period": "43.63782077802118930460996640698675536092200669313852273543", "energy": "-0.834710664900285664944930288544483846640232247613101668217", "angular_momentum": "-1.991364888915565346286100497209639756988880693990773482592e-59", "initial_cartesian_canonical_state": [ "-0.2197999788787253330659583088543013011503826425486242295839", "0.0", "-1.037932424583000018408849631896843161833295031878861569198", "0.0", "1.780200021121274666934041691145698698849617357451375770416", "0.0", "0.0", "-1.444833517347887664593315700285903919587934581720780733212", "0.0", "1.025383685958600698911581425549533084862525687108644792605", "0.0", "0.4194498313892869656817342747363708347254088946121359406068" ], "G": "1", "normalized_full_period_closure": "8.428815885218461400770969316761865014231487134042278361261e-37", "closest_distance_numerically_refined": 0.03451497512242273, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 3.332241527154167e-08, "visual_priority_score": 62.43835376480688, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000055_independent160.json", "sha256": "e7670b9f745431dd3eb2b40b37f4714f58546b6c88eb8650c8aa3f13e764b213" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000055_topology192.json", "sha256": "d080b333f0a62f464ce9147c093674cef7eb5063f7fadd09e0a68ff9869b68c3" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000055_trajectory_audit.json", "sha256": "f12c1cd7017b5eba48e670dd25ddd226143e4175fb8e7953a18f560643eec184" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000100", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAABBAABB", "primitive_root": "AAABBAABB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ -5, -4 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. 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A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ -3, -2 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 262.66056262311065, "masses": [ "1.25", "1.129574472283579741511149907575073334093459055612049655308", "0.75" ], "period": "5.540067187063512131781020217428158221528508657406410500819", "energy": "-2.310880651855311011957460568517074293483697142761474176018", "angular_momentum": "-1.493523666686674009714575372907229817741660520493080111944e-59", "initial_cartesian_canonical_state": [ "-0.6420920732024163704678673251789747540428903012219485871168", "0.0", "-0.1910594289182791266181800143559159051027505159859830413924", "0.0", "1.357907926797583629532132674821025245957109698778051412883", "0.0", "0.0", "-1.239557980660433821630718204947398478400644708742663242033", "0.0", "1.600495938260191551739394141125754522944954911776409793367", "0.0", "-0.360937957599757730108675936178356044544310203033746551334" ], "G": "1", "normalized_full_period_closure": "1.667526942736831091694559332996901914481097918460595233181e-38", "closest_distance_numerically_refined": 0.03797388897474026, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 9.913980747455753e-11, "visual_priority_score": 68.36376000410026, "visual_series": "nested binary turns: A^nBaB", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000161_independent160.json", "sha256": "28d28510dcc62dba48a89739e28eb08a510e5aa2a0a2ccd9091e843a8b3f685a" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000161_topology192.json", "sha256": "f309a3f079621f545d709c53f1682772de1e1e99216239ce593a7d148615a7e7" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000161_trajectory_audit.json", "sha256": "a50154d32e99863622cfe2c71e6938622b82e96b9ea083fa1f5a4822882d1814" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000166", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAABaaB", "primitive_root": "AAAAABaaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ -3, -2 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 92.0710559026068, "masses": [ "1.25", "0.9050030805904860365160845672613829371156712493938534243704", "0.75" ], "period": "12.92401882363090754736311201576722172937879550423345312916", "energy": "-1.37551923079026503944408210448553339389991069833045215961", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-0.279107869475961674669964911952400505106675420765048139806", "0.0", "-1.040642050006716055728375351958891739085554492154385789782", "0.0", "1.720892130524038325330035088047599494893324579234951860194", "0.0", "0.0", "-1.055213861715840905872461668273613320899185116536618622345", "0.0", "0.7642229230079879537298247146497217841564535975137343298049", "0.0", "0.2909909387078529521426369536238915367427315190228842925398" ], "G": "1", "normalized_full_period_closure": "6.134024750298159745445979929845418723038849183740451193533e-40", "closest_distance_numerically_refined": 0.1360059509095123, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 6.597522528295485e-11, "visual_priority_score": 83.8671156898243, "visual_series": "nested binary turns: A^nBaaB", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000166_independent160.json", "sha256": "1566ab2a5afb6f047c5bcc2f939bbc3c3d5e99d0690678bcd441e466c4ceaaa8" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000166_topology192.json", "sha256": "19739211caa0247172ac27c2950d771b97ab014ba0c4e69b59a7964083bd3a64" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000166_trajectory_audit.json", "sha256": "6e895f64dcbe798b716fcbfacc5576d779ab1042457a0216eb1bbbb995c96971" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000283", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAAAAAbabbbab", "primitive_root": "AAAAAAAAbabbbab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 1871.945796624163, "masses": [ "1.25", "0.7092920574925907359899316592128821511593811018371885662573", "0.75" ], "period": "7.462315355150551109598673185888738595327778878903173123726", "energy": "-1.990019542579431758549785147706540405537755230468316617153", "angular_momentum": "4.978412222288913365715251243024099392472201734976933706481e-60", "initial_cartesian_canonical_state": [ "-1.17700440185220854421974475309316373477632378766294068575", "0.0", "1.204029841703589164203593511711616110260424896049575531463", "0.0", "0.8229955981477914557802552469068362652236762123370593142504", "0.0", "0.0", "0.0734261720066536916443615889855888073417617823303644912534", "0.0", "0.3854045837006318585704154813044624593213952250836660165627", "0.0", "-0.4588307557072855502147770702900512666631570074140305078161" ], "G": "1", "normalized_full_period_closure": "1.792351961449686143184335921055132404155072579188933333333e-38", "closest_distance_numerically_refined": 0.01096418581288075, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 2.422875233776267e-08, "visual_priority_score": 58.86753474073692, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000283_independent160.json", "sha256": "dacf8d8d4cd289bb70e5325c1870dbb61690934801ed6397338a01adeb6334ea" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000283_topology192.json", "sha256": "ddcd647d8e44ea83ce834870ca709d6cc172673ce51ed7556981107f7eb05543" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000283_trajectory_audit.json", "sha256": "3d156d37dde70500bf36b2426ff073766db12482d8a923ff3d02e5a353ee164d" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000393", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AABBAABBAABaBAABaB", "primitive_root": "AABBAABBAABaBAABaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 848.5060548330225, "masses": [ "1.25", "1.000145181466190981420804190561647491346473990444670267823", "0.75" ], "period": "70.71253506717448697255694616321154137534943938513590961089", "energy": "-0.683941025728320491135632156595557028643701059422396122466", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-0.08585161059701972329807256415361399556380775332358516020256", "0.0", "-1.328103962725398027581000181395607713287114203297096700449", "0.0", "1.914148389402980276701927435846386004436192246676414839797", "0.0", "0.0", "-1.219038741999831420680840367583162586608660253390448212212", "0.0", "0.7519703031132618541398720503811598665641708776995585435943", "0.0", "0.4670684388865695665409683172020027200444893756908896686174" ], "G": "1", "normalized_full_period_closure": "3.234965695739140033045235662015671053022298099382174598094e-38", "closest_distance_numerically_refined": 0.01963509396286019, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 7.788385048002056e-09, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000393_independent160.json", "sha256": "09767fac6c5b54c160790477b82743987896b32726a577349e3286641bbb012c" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000393_topology192.json", "sha256": "2e9d0ba2d2508e7aeb8071156600de8fd9ca9d26d150032a88d9cc5dfe8cf4fd" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000393_trajectory_audit.json", "sha256": "e6ed887feb552fc1e4cceb2257ee5b4f7669177f0e98c2be5a2fe73d54d0bdb6" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000403", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAAAAAAAAAAAAAAAAAAAABaaaaB", "primitive_root": "AAAAAAAAAAAAAAAAAAAAAAABaaaaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 3189.11945322889, "masses": [ "1.25", "1.066021879434459459289573125929842896917212676641382468397", "0.75" ], "period": "4.995151400477242916822161049637700417199394939922265573474", "energy": "-4.415614917384756567243839141957004829259868500081631973592", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-1.259655231296310387534744607014117204108738363440434151839", "0.0", "0.9561815589876825145059143745019716464466372268841614681085", "0.0", "0.7403447687036896124652553929858827958912616365595658481606", "0.0", "0.0", "0.0568677932201924137078502832675307072647668224502033960855", "0.0", "0.5269518059953275565093475101328608711115941794482854374588", "0.0", "-0.5838195992155199702171977934003915783763610018984888335443" ], "G": "1", "normalized_full_period_closure": "1.468416069897366405743015909448434686467271750544933333333e-36", "closest_distance_numerically_refined": 0.020650801976236963, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 9.762046430661364e-07, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000410_independent160.json", "sha256": "4f1af46be61812d610e019f6bcf35695d1867dea0b9fb7488ebccb1f3b643c9e" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000410_topology192.json", "sha256": "d85573133ef500195ad043d87b9b760da74b281feb461e2438e25a0a6c79b7c3" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000410_trajectory_audit.json", "sha256": "39254264d353479154a00d461c7ae5c4a5f281847d2b3d83ed2e0b92c55a56c6" } }, "visual_reviewed_by_assistant": false }, { "id": "r4_mirror_mass_33_000451", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAAABaaaB", "primitive_root": "AAAAABaaaB", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 538.0521725548066, "masses": [ "1.25", "1.043938944378168784880427726024546460482066146159982961739", "0.75" ], "period": "5.616335344059181143534308279725665804064099323440367904118", "energy": "-2.840932438573693445832590421283079245791815231374884770694", "angular_momentum": "-4.978412222288913365715251243024099392472201734976933706481e-60", "initial_cartesian_canonical_state": [ "-0.6874589914859528458181747041749514414840821746914371812198", "0.0", "-0.1198173683448513247237450894143732343701839414538891248768", "0.0", "1.31254100851404715418182529582504855851591782530856281878", "0.0", "0.0", "-0.5735987847485642193533879074307522727688659990784180630312", "0.0", "0.8009151815852708131968280657833437740500050556019666348975", "0.0", "-0.2273163968367065938434401583525915012811390565235485718663" ], "G": "1", "normalized_full_period_closure": "2.256279038808444779250910468052984627970988522571972433025e-39", "closest_distance_numerically_refined": 0.1046627946230411, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 3.142444637838082e-10, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000451_independent160.json", "sha256": "54dd94291232dceeefe5fdd487a2995fdf12e6083d03899e8e9acd5e9fda32cd" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_mirror_mass_33_000451_topology192.json", "sha256": "610d700712b180fa51a78ff80a4fd21c308d2c7390d1643a5cb47abf910c4858" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_mirror_mass_33_000451_trajectory_audit.json", "sha256": "e1e83d96a103ca6027d35734961747554a0f8ee2b78a8743c242c67c25b41562" } }, "visual_reviewed_by_assistant": false }, { "id": "raw_iso_0_000031", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAABaab", "primitive_root": "AAAABaab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 64.10906051413446, "masses": [ "1.0", "1.076717480740261998942604775921388213914595314907705375366", "1.0" ], "period": "4.794038483880661124056088633865426060101575636786407051959", "energy": "-2.63453748577567813815578833422674409966011891793505766616", "angular_momentum": "-2.48920611114445668285762562151204969623610086748846685324e-60", "initial_cartesian_canonical_state": [ "-0.5", "-0.4082682937253168351781038309261871554036356772050244678481", "0.0", "0.7583573240486915488203633242154080442746742068058695919763", "0.5", "-0.4082682937253168351781038309261871554036356772050244678481", "-0.08647060202269714211056121656320732028501409327068539804025", "-0.201757639008038944707665123516045074100984638841248647862", "0.1729412040453942842211224331264146405700281865413707960805", "0.0", "-0.08647060202269714211056121656320732028501409327068539804025", "0.201757639008038944707665123516045074100984638841248647862" ], "G": "1", "normalized_full_period_closure": "5.0986032794617710074918087411968516070001886497403e-40", "closest_distance_numerically_refined": 0.08906917701582442, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 1.0524980886827962e-10, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_0_000031_independent160.json", "sha256": "3d08942626aa9d0f79d0be414cc404855aed292348fb898947d2180d0e611d42" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/raw_iso_0_000031_topology192.json", "sha256": "1fd9e3c91fdb7a405765841fce6a357ca0660e15144f61f6a98ccc6ea1c66b34" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_0_000031_trajectory_audit.json", "sha256": "f32b0b0922076c1d5ff72d152b319ddd35f8522d20230ebb986d8ff738ffffbf" } }, "visual_reviewed_by_assistant": false }, { "id": "raw_iso_0_000060", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "AAAABBAAbab", "primitive_root": "AAAABBAAbab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 834.0809234236134, "masses": [ "1.0", "0.5627071770422284195983109690648314132261632319172613841753", "1.0" ], "period": "33.14877016667037397304413238743504198736235352104658931304", "energy": "-0.6600944875500707999504630172323829817382187918802231312076", "angular_momentum": "-9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-0.5", "-0.2399914084808456984904600196495445082671438364123001847101", "0.0", "0.8529886174273391855665192836551385146290717717793821599763", "0.5", "-0.2399914084808456984904600196495445082671438364123001847101", "-0.3697990360612501363637261626615365678654661161379926664785", "-0.8083659200300939405274959875698970351569049585813498396214", "0.7395980721225002727274523253230731357309322322759853329571", "0.0", "-0.3697990360612501363637261626615365678654661161379926664785", "0.8083659200300939405274959875698970351569049585813498396214" ], "G": "1", "normalized_full_period_closure": "5.2287048344077581483766524769456435616341974094105e-39", "closest_distance_numerically_refined": 0.2094247165855331, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 1.6575557593156987e-10, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_0_000060_independent160.json", "sha256": "45d81758b69ff5b910a5909efdc46f9141c377f6bb278a343e10ff7873b97327" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/raw_iso_0_000060_topology192.json", "sha256": "6cf74085f6256a821de55b8f207bb67116eac4192bc80ed5950f0fb274a08229" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_0_000060_trajectory_audit.json", "sha256": "15a369f6d45df5deb086df6d6748576f8da37b359f436ae33ea93515a6be5945" } }, "visual_reviewed_by_assistant": false }, { "id": "raw_iso_10_000913", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "ABaBAbABabAbaBAbABaBAbaBab", "primitive_root": "ABaBAbABabAbaBAbABaBAbaBab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. 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H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 1.2912559955346903, "masses": [ "1.0", "1.077141184862737665684896065616727687970449891017565615708", "1.0" ], "period": "27.69046921591973077374477719682722901893583296363336411109", "energy": "-1.825036261794743913931338388851786914177309434053258416804", "angular_momentum": "9.956824444577826731430502486048198784944403469953867412962e-60", "initial_cartesian_canonical_state": [ "-0.5", "-0.3457462375997031212906301830233836651432917593960356878631", "0.0", "0.6419701380998857288122729450630723211587826650953545857787", "0.5", "-0.3457462375997031212906301830233836651432917593960356878631", "-0.4072313074830504739143319590425344883268715077911139857895", "-0.8044580621971269403293301481291328289134175540177044474529", "0.814462614966100947828663918085068976653743015582227971579", "0.0", "-0.4072313074830504739143319590425344883268715077911139857895", "0.8044580621971269403293301481291328289134175540177044474529" ], "G": "1", "normalized_full_period_closure": "8.200079516545963228578319359671642970076109023407634845669e-39", "closest_distance_numerically_refined": 0.007206268517056741, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 1.1267826316441187e-07, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_10_000913_independent160.json", "sha256": "119d7db3c561f71a7c9d059c532daecfba86329fc0781c31d440c0b9306a57f3" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/raw_iso_10_000913_topology192.json", "sha256": "f3d38d565cf3c0c9eab57aa499450fe680afe828ff2af3d5e0be04afcc38f90b" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_10_000913_trajectory_audit.json", "sha256": "71d7f0f6309e9f776e3f5817aace37cb61224c5e3759c334ecf21a3226e108a7" } }, "visual_reviewed_by_assistant": false }, { "id": "raw_iso_1_000292", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": true, "family_status": "topologically_distinct_candidate_relative_to_screened_catalogues", "global_priority_established": false, "canonical_word": "ABaBAbaBAbABabAbaBAbABabABaBAbaBab", "primitive_root": "ABaBAbaBAbABabAbaBAbABabABaBAbaBab", "word_power": 1, "reported_period_is_not_a_repeated_traversal": true, "primitive_period_argument": "An n-fold repeated absolute orbit would have an n-fold shape word. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": true, "euler_family_obstruction": { "homology": [ -1, -1 ], "Euler_half_twist_ancestor_excluded": true, "allowed_lines": [ "a=-b", "a=2b", "b=2a" ], "scope": "Excludes collision-free continuations and integer powers of periodic Euler-half-twist orbits with an exchangeable equal-mass outer pair. It does not exclude all other relative/periodic families.", "proof": "Fullshape loop=gamma*P(gamma)^(-1) because both halfsegment endpoints have the same Euler shape. H=(I-P)h; the three transposition images are the three root lines." }, "catalogue_classification": { "classification": "novel_primitive_topology_candidate", "reason": "Primitive calibrated word absent from indexed classes; needs reliable event extraction, geometric comparison, and broader novelty review.", "expanded_reference_match": null, "word_match_count": 0, "root_match_count": 0, "word_matches": [], "root_matches": [], "qualifies_from_topology_alone": false, "primitive_topology_priority": true, "global_priority_established": false }, "stability": "unstable", "largest_nontrivial_multiplier": 1.577515822998737, "masses": [ "1.0", "1.023100320931024442505449040258552136102164861278706041784", "1.0" ], "period": "33.82994069557669524085828324137346939312839188761208543282", "energy": "-1.831351386134574229677135624252961322379968305200156701171", "angular_momentum": "0.0", "initial_cartesian_canonical_state": [ "-0.5", "-0.3379678665499013765631020200876077469253280637359597947858", "0.0", "0.6606739527602719883615132063453989323626182844327224967333", "0.5", "-0.3379678665499013765631020200876077469253280637359597947858", "-0.3796407943490879584809299862255948305329768640149065782659", "-0.7582503471062651649886057194003676698091511725714710371705", "0.7592815886981759169618599724511896610659537280298131565319", "0.0", "-0.3796407943490879584809299862255948305329768640149065782659", "0.7582503471062651649886057194003676698091511725714710371705" ], "G": "1", "normalized_full_period_closure": "4.1935478628419703765398022771817804346842841695059e-36", "closest_distance_numerically_refined": 0.004735359650750948, "clearance_note": "Minima numerically refined from all sign-bracketed distance-derivative roots on the independent dense trajectory; not an interval-certified lower bound.", "scipy_mp_trajectory_difference": 2.468025463997492e-07, "visual_priority_score": null, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_1_000292_independent160.json", "sha256": "6c6b351299f89276f5ca504d229b2d6404a8746bd93d19228b81c41e0b10c495" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/raw_iso_1_000292_topology192.json", "sha256": "4a76ab93112df8dfa209f27011fd45382f775a55504f3b9f81a3abbcef2ffce6" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_1_000292_trajectory_audit.json", "sha256": "b74068275420411f385ce4ec65a8d00a3bab18293051cece641a0230f39a03d5" } }, "visual_reviewed_by_assistant": false } ] }