[ { "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. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": false, "euler_family_obstruction": { "homology": [ -2, 0 ], "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": 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": true, "display_label": "Long-lobed flower", "viewer_period_at_E_minus_one": 20.50019959707492 }, { "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": true, "display_label": "Interlaced petals", "viewer_period_at_E_minus_one": 22.918608036386335 }, { "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. 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": 1452.8520876583605, "masses": [ "1.12", "1.03041983040403268150363867034104357851536114588186879707", "0.88" ], "period": "17.70814651286225357713100003827665567138157112508488004097", "energy": "-0.9999999999999995102869904153995288640993735464764931054701", "angular_momentum": "-4.978412222288913365715251243024099392472201734976933706481e-60", "initial_cartesian_canonical_state": [ "-1.341192355685327521669758775269684703611802154213956901635", "-0.4047543544049244551916687186132037540398252644994894887603", "0.8812045333279899847835568803662491916523577182604086512805", "0.7856105685509180300649034707121675002521997621646315710247", "0.6751418324823575219932775403212132386306128132331836727999", "-0.4047543544049287019295105877955347577884487214948524004785", "-0.6509909844781345077731094228524799790709253888519288703537", "0.1270053119596937612845020580821094951161060140910650951406", "-0.1753856320185989308903376069306651089348050778897665126517", "0.2296012235290020238830142733642911531640591470533068530127", "0.8263766164967334386634470297831450880057304667416953830055", "-0.3566065354886957851675163314464006482801651611443719481533" ], "G": "1", "normalized_full_period_closure": "3.293960947705362429154332480740008138624666098620154166004e-39", "closest_distance_numerically_refined": 0.12178260447430243, "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": 8.369527293439205e-12, "visual_priority_score": 78.84457301350963, "visual_series": "mixed structure", "proof_files": { "independent_cartesian": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_full_mass_23_000497_independent160.json", "sha256": "fd0534016ab6f94f0db159e821ff45473854c5a31a97ebfcae6befcc7f7b68e7" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/r4_full_mass_23_000497_topology192_v2.json", "sha256": "cedfdd9640472f08cd0bd4f02f096fa55ecebe0ca615cee882ba2ec7c672d61a" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/r4_full_mass_23_000497_trajectory_audit.json", "sha256": "189a3a152ff7a43e93038cb01407414f92af23bc1aa0e6cd100cc0ab34937127" } }, "visual_reviewed_by_assistant": true, "display_label": "Asymmetric loops", "viewer_period_at_E_minus_one": 17.708146512862243 }, { "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. A non-power word rules this out, conditional on the numerical topology.", "homology_primitive": false, "euler_family_obstruction": { "homology": [ -5, 0 ], "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": 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": true, "display_label": "Woven loops", "viewer_period_at_E_minus_one": 17.77774119329394 }, { "id": "r4_mirror_mass_33_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": "AAABaB", "primitive_root": "AAABaB", "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": 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": true, "display_label": "Nested crossings", "viewer_period_at_E_minus_one": 16.33717983079132 }, { "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. 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": 1.2912559955346903, "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": true, "display_label": "Weak-instability lattice", "viewer_period_at_E_minus_one": 68.27120397936616 }, { "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": true, "display_label": "Near-equal-mass weave", "viewer_period_at_E_minus_one": 83.84144576994139 }, { "id": "raw_iso_10_001128", "numerical_periodicity_and_L0_passed": true, "candidate_for_new_primitive_family": false, "family_status": "isolated_unequal_mass_family_candidate", "global_priority_established": false, "canonical_word": "AABAbbaabaBB", "primitive_root": "AABAbbaabaBB", "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": false, "euler_family_obstruction": { "homology": [ 0, 0 ], "Euler_half_twist_ancestor_excluded": false, "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": "linearly elliptic", "largest_nontrivial_multiplier": 1.0, "masses": [ "1.0", "0.6123560888279948351624851400415065255699671717924355130568", "1.0" ], "period": "9.075588356851627090403838322715111897213853619462408121146", "energy": "-1.517078436942168075614583685899089597571564212615789541492", "angular_momentum": "0.0", "initial_cartesian_canonical_state": [ "-0.5", "-0.1438135030266039872812752137539892348103642673730021116285", "0.0", "0.4697054725196008327572409833584846963902758501051857778858", "0.5", "-0.1438135030266039872812752137539892348103642673730021116285", "-0.4225104213043878068625981375435852744620048119659366838592", "-0.5184363216725267978035999542185276833064261444492343782382", "0.8450208426087756137251962750871705489240096239318733677184", "0.0", "-0.4225104213043878068625981375435852744620048119659366838592", "0.5184363216725267978035999542185276833064261444492343782382" ], "G": "1", "normalized_full_period_closure": "1.519096317758272968672697452613579072469125644560348929679e-36", "closest_distance_numerically_refined": 0.012890317910019019, "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": 2.6734014779705717e-08, "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_001128_independent160.json", "sha256": "d70881fb7081a178dbb5736a1ce6fa3de52f24be56a88a3a1edc2f43d8e15328" }, "native_topology": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/novelty/raw_iso_10_001128_topology192.json", "sha256": "f8df708e6a1db02c1008de0963dca1ab785c0ab83a520ce535b522214c10c139" }, "trajectory_audit": { "path": "/Users/ludwig/Documents/Codex/2026-09-08/you/work/round4/validation/raw_iso_10_001128_trajectory_audit.json", "sha256": "5d1fb047fd37ff010b6797c6b564294d65ef8580f80d71576bbbbe92034941e7" } }, "visual_reviewed_by_assistant": true, "display_label": "Linearly stable orbit \u2014 isolated unequal-mass family", "viewer_period_at_E_minus_one": 16.958476838108957, "ancestry_status": "closed_equal_outer_mass_family_mapped_numerically", "family_ancestry_resolution": { "id": "raw_iso_10_001128", "status": "numerical_symmetric_family_ancestry_mapped", "classification": "Closed isolated continuation loop (isola) for equal outer masses, containing a linearly elliptic non-power topology segment and a genuine figure-eight-cube topology segment separated by binary-collision limits.", "masses": [ "1", "0.612356088827994835162485140041506525569967171792435513056814", "1" ], "stable_word": "AABAbbaabaBB", "cube_word": "ABabABabABab", "mass_minimum": "0.468917981330796344439248757837263330313623986856215826270916", "mass_maximum": "0.634604250806254920719975211351370866138663796548664189098896", "equal_mass_point_on_traced_component": false, "join_max_parameter_difference": "1.89442891895776269505109485461800416147033156297582651525734e-29", "join_opposite_tangent_dot": "-0.999999999999999999999999999999999999999999999999999999998989", "collision_mass_estimates": { "up": "0.629437018998624554212490572767533115054311151431727235349228", "down": "0.506554932881657927367856296501994415458880557618022907220259" }, "stability": "Independently verified planar linear ellipticity; no nonlinear/KAM proof claimed.", "novelty": "No counterpart identified in audited sources. Strong numerical evidence for an uncatalogued isolated unequal-mass branch. Global publication priority is not established.", "scope": "The closed-loop result concerns the Euler-half-twist, zero-angular-momentum continuation with masses(1,mu,1). It does not exclude every possible route through symmetry-breaking bifurcations or other mass paths.", "prior_report_correction": "The old jump atmu=.660356 changed the primitive word toAABAbABB. Its endpoint atmu=.716137 did not belong to a demonstrated continuation of1128. The last pre-jump accepted mass was.632356.", "proof_type": "High-precision numerical evidence, not an interval existence or global continuation theorem.", "completed_utc": "2026-09-09T10:07:18.831228+00:00", "evidence": [ { "path": "closed_branch_join.json", "sha256": "0c6f7e91eeec6c3e896792a1a756c2670fe965cb06cd35a3088cb7c648d3ac55" }, { "path": "mass_minimum.json", "sha256": "57f19be9f744757114ca034ab322b418a1895c93b09821e84adf713e5035f7be" }, { "path": "mass_maximum.json", "sha256": "995f62f2febbfab11ba5ee7dcf9f175ff95fa2102cea0fe654c3fdf061d7ab26" }, { "path": "collision_up.json", "sha256": "5ffdc0524e5f91876f5ae32d23b258cc08a07f5048dfea56569e1bef1db02223" }, { "path": "collision_down.json", "sha256": "882ba9fa2ffb91302ad209d678c01c761e3ea5d44909176fcd43d931ec81f5d0" }, { "path": "old_path_topology_audit.json", "sha256": "3b82966b910fc570132fc00d6e13abeff5dbf33fa3c7128f1a398569e64a7bc5" }, { "path": "validation/join_mu055_independent160.json", "sha256": "9667311deef1f7874f18f7e966fcd1b9c7937990b5c25a9c9cebf700a9d70c2c" }, { "path": "validation/mass_minimum_independent160.json", "sha256": "2c1a2878958e9862c0029cd4ba681cd1ac0107a36d37cb78844fc7998e10a6ce" } ] }, "followup_report": "stable_orbit_ancestry/ancestry_report.md" } ]