{"id":"https://openalex.org/W7224396772","doi":"https://doi.org/10.5281/zenodo.23755473","title":"Held, Rocking, Locked: The Islands of a Light Star Around an Eccentric Binary","display_name":"Held, Rocking, Locked: The Islands of a Light Star Around an Eccentric Binary","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224396772","doi":"https://doi.org/10.5281/zenodo.23755473"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23755473","doi":"https://doi.org/10.5281/zenodo.23755473","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23755473","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23755473","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137619378","display_name":"Matthew Schulz","orcid":"https://orcid.org/0009-0000-0956-5743","observed_orcids":["https://orcid.org/0009-0000-0956-5743"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Schulz, Matthew","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-0956-5743","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5137619378"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.0020000000949949026,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/three-body-problem","display_name":"three-body problem","score":0.5690000057220459},{"id":"https://openalex.org/keywords/eccentric-binary-stars","display_name":"eccentric binary stars","score":0.5929999947547913},{"id":"https://openalex.org/keywords/orbital-resonance","display_name":"orbital resonance","score":0.4020000100135803},{"id":"https://openalex.org/keywords/mean-motion-resonance","display_name":"mean motion resonance","score":0.5070000290870667},{"id":"https://openalex.org/keywords/chaotic-diffusion","display_name":"chaotic diffusion","score":0.3499999940395355},{"id":"https://openalex.org/keywords/resonance-islands","display_name":"resonance islands","score":0.40799999237060547},{"id":"https://openalex.org/keywords/orbital-stability","display_name":"orbital stability","score":0.3059999942779541},{"id":"https://openalex.org/keywords/orbital-precession","display_name":"orbital precession","score":0.42399999499320984},{"id":"https://openalex.org/keywords/eccentricity-evolution","display_name":"eccentricity evolution","score":0.3610000014305115},{"id":"https://openalex.org/keywords/period-ratio","display_name":"period ratio","score":0.3179999887943268},{"id":"https://openalex.org/keywords/numerical-integration-error","display_name":"numerical integration error","score":0.37700000405311584}],"concepts":[{"id":"https://openalex.org/C190538878","wikidata":"https://www.wikidata.org/wiki/Q50013","display_name":"Eccentricity (behavior)","level":2,"score":0.8705000281333923},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.781000018119812},{"id":"https://openalex.org/C150846664","wikidata":"https://www.wikidata.org/wiki/Q7602306","display_name":"Stars","level":2,"score":0.6880000233650208},{"id":"https://openalex.org/C125311221","wikidata":"https://www.wikidata.org/wiki/Q208474","display_name":"Orbital eccentricity","level":3,"score":0.6262999773025513},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.54830002784729},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5206999778747559},{"id":"https://openalex.org/C100784341","wikidata":"https://www.wikidata.org/wiki/Q1340491","display_name":"Eccentric","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C59108619","wikidata":"https://www.wikidata.org/wiki/Q2261398","display_name":"Circular orbit","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C193786831","wikidata":"https://www.wikidata.org/wiki/Q50053","display_name":"Binary star","level":3,"score":0.3961000144481659},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C32224563","wikidata":"https://www.wikidata.org/wiki/Q37640","display_name":"Orbital period","level":3,"score":0.3544999957084656},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.3411000072956085},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.3352000117301941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32659998536109924},{"id":"https://openalex.org/C173990265","wikidata":"https://www.wikidata.org/wiki/Q2268240","display_name":"Elliptic orbit","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C81502235","wikidata":"https://www.wikidata.org/wiki/Q104225","display_name":"Precession","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C97784730","wikidata":"https://www.wikidata.org/wiki/Q272626","display_name":"Orbital elements","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23755473","doi":"https://doi.org/10.5281/zenodo.23755473","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23755473","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23755474","doi":"https://doi.org/10.5281/zenodo.23755474","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23755474","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23755473","doi":"https://doi.org/10.5281/zenodo.23755473","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23755473","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1184603","https://openalex.org/W200938426","https://openalex.org/W2140637239","https://openalex.org/W92435691","https://openalex.org/W3021845257","https://openalex.org/W2073210744","https://openalex.org/W2476560452","https://openalex.org/W4226022897","https://openalex.org/W3027093506","https://openalex.org/W2918045107"],"abstract_inverted_index":{"We":[0],"follow":[1],"a":[2,93,175,232,237,241,322,338,350,354,359,366,373,376,437,449,465,478,484,492,496,505,513,546,624,670,731,758,787,797,807,1018,1022,1041,1045,1052,1055,1079,1095,1119,1147,1244,1250,1281,1291,1321,1362,1367,1386,1390,1405,1433,1436,1440,1468,1486,1492,1516,1522],"planet-mass":[3],"body":[4],"around":[5],"an":[6,413,665],"eccentric":[7],"pair":[8,619],"of":[9,75,120,140,231,341,451,467,480,516,520,562,602,672,728,796,803,854,956,1020,1031,1133,1137,1302,1352,1439,1532,1570],"equal":[10],"stars,":[11,155,684],"near":[12,287,472,699],"the":[13,51,55,69,87,91,95,121,135,150,162,164,201,207,223,225,260,269,280,289,302,306,310,327,345,379,385,400,407,411,445,563,578,582,596,614,618,629,637,656,679,691,693,735,737,745,752,762,801,804,838,845,848,859,861,864,889,897,921,928,952,959,972,1010,1027,1034,1037,1058,1064,1075,1088,1093,1101,1116,1131,1134,1138,1150,1154,1173,1180,1183,1194,1226,1234,1256,1269,1273,1374,1393,1397,1410,1429,1449,1475,1489,1530,1543,1563,1573,1578],"7:1":[14],"and":[15,81,101,149,187,193,216,244,286,309,336,343,371,402,406,448,459,544,581,608,640,678,721,747,771,779,783,817,833,867,902,925,958,981,1050,1125,1136,1172,1185,1190,1192,1217,1268,1324,1380,1403,1418,1458,1474,1537,1540,1553,1572],"8:1":[16],"period":[17,973],"ratios,":[18],"by":[19,196,353,424,487,555,675,709,998,1044,1347,1472],"direct":[20,176,1348],"three-body":[21],"integration":[22],"for":[23,744,1567,1577],"up":[24,30,1353],"to":[25,28,158,211,228,239,284,471,687,756,786,809,893,1016,1029,1123,1354,1361,1435],"60,000":[26,1073,1355],"orbits,":[27,109,816,1049,1074,1356],"see":[29],"close":[31],"why":[32],"three":[33,249,822],"bodies":[34],"are":[35,652,1306],"hard.":[36],"The":[37,256,389,632,790,835,915,983,1170,1300],"star":[38,300,347,438,1036,1252,1406],"is":[39,66,194,314,444,537,963,1077,1109,1255,1340,1510,1515],"held":[40,507,765,1283],"where":[41,178,717,927,1118,1130,1377,1381],"two":[42,468,1090],"clocks":[43],"keep":[44,585],"time":[45,586],"together:":[46],"one":[47,102,442,568,1344,1466],"angle,":[48,569],"\u03c6_N,":[49,570],"comparing":[50],"pair's":[52,122,136,311,386,564,579,657,753,960,1065],"orbit":[53,414,580,1005],"with":[54,68,265,344,384,396,545,876,1006,1063,1177,1357,1455,1504,1508,1521,1529],"star's":[56,70,208,261,281,583,597,849,890,922,1477],"lap,":[57],"stays":[58,571],"put":[59,572],"while":[60,573],"every":[61,218,331,535,574,935,993,1158,1358],"other":[62,575],"angle":[63,576],"turns.":[64],"Escape":[65],"one-sided:":[67],"eccentricity":[71,137,209,598,658,875],"at":[72,134,206,236,279,372,461,599,751,769,774,806,852,871,888,932,970,1051,1389,1432],"0.20,":[73,600,757],"163":[74,601],"166":[76,603],"recorded":[77,604],"escapes,":[78,605],"from":[79,86,482,606,613,622,1452],"light":[80,607],"heavy":[82,298,346,609,944,1035,1476],"stars":[83,105,610,641],"alike,":[84,611],"leave":[85,612],"island's":[88,202,615,846,916],"side":[89,616],"nearest":[90,617],"pair,":[92],"door":[94,626,638,1388],"published":[96,633,1398],"stability":[97,111,634,1394,1399,1411],"rules":[98,635,1400],"smooth":[99,636,1401],"over,":[100,639],"that":[103,152,324,453,651,681,764,1254,1261,1279,1289,1364,1421,1491],"41":[104],"started":[106,642,1407],"on":[107,259,394,426,441,628,793,1009,1146,1237,1266,1366,1488],"circular":[108,643],"as":[110,251,253,421,495,533,664,824,826,1212,1233,1243,1333,1335,1409,1425,1479],"maps":[112,395,1176,1412,1423],"start":[113,220,937,1413],"theirs,":[114,1414],"did":[115,1215],"not":[116,645,1216,1220,1416,1518],"find":[117,646],"in":[118,477,491,1092,1097,1112,1157,1272,1286,1294,1343,1373,1498,1535,1541],"10\u2075":[119],"periods.":[123],"An":[124],"island":[125,224,666,746,860],"read":[126,460,663,1424,1552],"over":[127,272,356,668,814,882,1047,1072,1350,1402,1460],"600":[128,166,661,695,883],"orbits":[129,167,275,475,662,696,884],"can":[130,985],"be":[131,1221],"slow":[132,339,351,380,653,1042,1059,1419],"chaos:":[133],"0.25,":[138,659],"22":[139],"28":[141],"inner":[142],"starts":[143],"lose":[144],"their":[145,528,1207,1311,1341],"hold":[146,257,836],"within":[147,185,190,240,276,715,725,741,810,885],"6,000,":[148,669],"room":[151,680],"keeps":[153,415,682,1127],"its":[154,179,182,188,683,748,855,880,1128,1568],"births":[156,685],"7.465":[157,686],"7.505,":[159,688],"lies":[160,689],"below":[161,305,690,951],"centre":[163,203,692,847,917],"first":[165,392,694],"point":[168,697,1319],"to.":[169],"Mardling's":[170,263,705,868,1371,1453],"(2013)":[171],"resonance":[172,987,1309,1391,1499],"pendulum":[173,929,1372],"passes":[174,1338],"test":[177,377,1056,1159,1245],"assumptions":[180,719],"hold,":[181,720],"rate\u2013width":[183,712],"relation":[184,506,713,738,1282],"1.1%":[186,716],"widths":[189,723],"about":[191,248,277,315,726,742,821,886,964,999,1078],"30%,":[192],"off":[195,490],"measured":[197,1012,1304],"amounts":[198],"outside":[199],"them:":[200],"doubles":[204,918],"once,":[205,919],"0.348":[210,924],"0.350":[212],"rather":[213],"than":[214,510],"0.41,":[215],"then":[217,294,840,913,934],"nearby":[219,936],"escapes.":[221,938],"Inside":[222],"rocking":[226,333,791,995],"locks":[227,792,1446],"simple":[229,794],"fractions":[230,246,795,819],"cycle":[233,798,1441],"per":[234,416,566,799,1004,1442],"orbit,":[235,567,800,1008,1443],"fifth":[238,808,1434],"few":[242,788,1437],"billionths,":[243],"odd":[245,818],"fill":[247,820,1447],"times":[250,317,823,966,1069,1081,1285],"often":[252,509,825],"even":[254,827],"ones.":[255,828],"drags":[258,330,837],"ellipse:":[262],"coefficient,":[264,869],"nothing":[266,877,1456],"fitted,":[267,878],"gives":[268,879],"drag's":[270,1450],"slope":[271,881],"six":[273],"hundred":[274,1080],"6%":[278,887],"eccentricities":[282,754,891,923],"0.20":[283,892],"0.26,":[285],"0.28":[288,896],"centre's":[290,898,1274],"ellipse":[291,850,899],"stands":[292,900],"still,":[293,901,1106],"turns":[295,841,851,905],"backward.":[296,906],"A":[297,539,592,943],"third":[299,355,945,1046],"moves":[301,1087],"islands":[303,948],"just":[304,950],"whole":[307,953],"numbers,":[308],"short-period":[312,961,1481],"swing":[313,962],"1.12":[316,965],"Georgakarakos's":[318,967,1480],"(2003)":[319,968],"formula.":[320],"At":[321,655,844,989,1083],"tolerance":[323,362,463,991,1025,1493],"looks":[325,1495],"tight,":[326],"integrator's":[328],"arithmetic":[329,984],"unlocked":[332,994],"rate":[334,996],"down":[335,431,526,1242],"fakes":[337,1497],"slide":[340,1019],"locks,":[342],"it":[348,842,904,1086,1108,1114,1126,1378,1382,1463,1484,1506,1581],"shortens":[349,1040],"beat":[352,381,1043,1060,1270],"30,000":[357,1048],"orbits;":[358],"hundredfold":[360,1023],"tighter":[361,1024,1070],"removes":[363],"both,":[364],"though":[365,1107],"far":[367,630,1334],"smaller":[368],"drift":[369,1039,1490],"remains,":[370],"second":[374,625,1053,1103,1148],"birth":[375,1054,1098],"finds":[378,1057,1385],"keeping":[382,1061],"pace":[383,1062],"falling":[387,1066],"eccentricity.":[388,1067],"method":[390,1181],"was":[391,435,1248,1527,1551,1556],"checked":[393],"known":[397,1178,1511],"answers,":[398],"reproducing":[399],"frictionless":[401,1184],"damped":[403,1186],"period-doubling":[404],"constants":[405],"dial":[408,1195],"between":[409,920,1196],"them,":[410],"area":[412],"trip.":[417],"Many":[418],"tests":[419,1370],"began":[420,1232],"marks":[422,1236],"made":[423,760],"eye":[425,1227],"plain":[427,1238],"pictures,":[428,1239],"each":[429,872,1007,1240,1548],"written":[430,525,1205,1241],"before":[432,527,1161,1206,1246],"any":[433],"number":[434,1359],"read:":[436],"polygon":[439,1253],"drawn":[440],"picture":[443],"inscribed-angle":[446,1257],"theorem,":[447,1258],"scatter":[450],"readings":[452],"looked":[454],"chaotic":[455,676,732,1312],"is,":[456,667],"zoomed":[457],"out":[458,470,532,1211],"relative":[462,990],"10\u207b\u00b9\u00b2,":[464],"rotation":[466],"angles,":[469],"returns":[473],"31,063":[474],"apart":[476],"run":[479,1363],"60,000,":[481],"which":[483,1396,1404,1444,1494],"twin":[485,499],"nudged":[486],"10\u207b\u00b9\u2070":[488],"drifts":[489,1132],"straight":[493],"line,":[494],"regular":[497],"orbit's":[498,1089],"does;":[500],"sorted":[501],"blind,":[502,1277],"reads":[503,511],"naming":[504,512],"more":[508],"shape,":[514],"19":[515,1284],"30":[517],"against":[518],"11":[519,832,1293],"28.":[521,1295],"Of":[522,1202],"490":[523,1203],"predictions":[524,1204],"runs,":[529,1208],"236":[530,1209],"came":[531,1210],"written;":[534],"miss":[536],"kept.":[538],"preprint,":[540,1517],"without":[541],"peer":[542,1519],"review":[543],"limited":[547,1523],"literature":[548,1337,1524],"pass.":[549,1525],"What":[550,1329],"this":[551,1330],"paper":[552,1331],"found:":[553],"Held":[554],"coupled":[556],"clocks.":[557],"Near":[558,895],"seven":[559],"(or":[560],"eight)":[561],"periods":[565],"turns:":[577],"lap":[584],"together.":[587],"(Section":[588,648,701,829,907,939,977,1166,1198,1223,1296,1327],"5;":[589],"Figure":[590,703,909,941,1200,1298],"7.)":[591],"one-sided":[593,1387],"door.":[594],"With":[595,1033],"(Figure":[620],"1);":[621],"0.30":[623],"opens":[627,1503],"side.":[631],"do":[644],"it.":[647,1229,1513],"6.)":[649],"Islands":[650],"chaos.":[654],"what":[660,1505,1509],"row":[671],"rooms":[673],"divided":[674],"threads,":[677],"to,":[698],"7.525.":[700],"6;":[702],"9.)":[704],"pendulum,":[706],"tested":[707,767],"piece":[708],"piece.":[710],"Its":[711,947],"holds":[714,739,1379],"her":[718,722],"come":[724],"30%":[727],"ours.":[729],"Once":[730],"layer":[733,749],"eats":[734],"island,":[736],"instead,":[740],"10%,":[743],"together":[750],"0.05":[755],"reading":[759],"after":[761],"fact":[763],"when":[766],"forward":[768],"0.225":[770],"missed":[772],"narrowly":[773],"0.25.":[775],"(Sections":[776],"5,":[777],"6":[778],"10;":[780,940],"Appendices":[781],"B":[782],"C.)":[784],"Locks":[785],"billionths.":[789],"core":[802],"lock":[805,1431],"3.5":[811],"\u00d7":[812,1001],"10\u207b\u2079":[813,992],"6,000":[815],"8;":[830],"Figures":[831,979],"12.)":[834],"ellipse,":[839],"back.":[843],"two-thirds":[853],"free":[856],"rate.":[857],"Across":[858],"drag":[862],"follows":[863],"hold's":[865],"grip,":[866],"taken":[870],"line's":[873],"mean":[874],"0.26.":[894],"above":[903],"9;":[908],"13.)":[910],"One":[911],"doubling,":[912],"escape.":[914],"0.350,":[926],"would":[930],"only":[931],"0.41;":[933],"14.)":[942],"star.":[946],"sit":[949],"numbers":[954],"instead":[955],"above,":[957],"formula,":[969],"half":[971],"ratio":[974],"he":[975,1263],"tested.":[976],"11;":[978],"15":[980],"16.)":[982],"fake":[986,1017],"physics.":[988],"falls":[997],"2.8":[1000],"10\u207b\u2078":[1002],"cycles":[1003],"line":[1011,1104],"most":[1013],"closely,":[1014],"enough":[1015],"locks;":[1021],"shrinks":[1026],"fall":[1028],"0.0093":[1030],"itself.":[1032],"same":[1038,1155],"Ten":[1068],"again,":[1071],"creep":[1076],"smaller.":[1082],"looser":[1084],"tolerances":[1085],"rates":[1091],"proportion":[1094],"nudge":[1096,1111,1120],"does,":[1099],"leaving":[1100],"eccentricity's":[1102],"almost":[1105],"no":[1110],"birth:":[1113],"drains":[1115],"energy":[1117,1135],"outward":[1121],"adds":[1122],"it,":[1124],"sign":[1129],"angular":[1139],"momentum":[1140],"both":[1141],"change":[1142],"theirs.":[1143],"Made":[1144],"again":[1145],"machine,":[1149],"long":[1151],"runs":[1152,1262,1351],"gave":[1153],"verdict":[1156],"registered":[1160],"they":[1162],"were":[1163],"sent":[1164],"there.":[1165],"3;":[1167,1297],"Appendix":[1168],"A.5.)":[1169],"bench":[1171],"guesses.":[1174],"On":[1175],"answers":[1179],"reproduced":[1182],"doubling":[1187,1325,1470],"constants,":[1188],"8.721082":[1189],"4.669197,":[1191],"found":[1193,1228],"them":[1197],"4;":[1199],"6).":[1201],"written,":[1213],"211":[1214],"43":[1218],"could":[1219],"read.":[1222],"3.)":[1224],"How":[1225],"Several":[1230],"results":[1231],"author's":[1235,1564,1574],"anything":[1247],"measured:":[1249],"clockwork":[1251],"dead":[1259],"zones":[1260],"never":[1264],"drew":[1265],"avoid,":[1267],"hidden":[1271],"rocking.":[1275],"Sorted":[1276],"picture-reads":[1278],"name":[1280,1290],"30,":[1287],"those":[1288],"shape":[1292],"4.)":[1299],"kinds":[1301],"thing":[1303],"here":[1305],"known:":[1307],"mean-motion":[1308],"islands,":[1310],"edges,":[1313],"secondary":[1314],"resonances,":[1315],"slices":[1316],"whose":[1317],"highest":[1318],"resembles":[1320],"vanishing":[1322],"twist,":[1323],"centres":[1326],"14).":[1328],"adds,":[1332],"our":[1336],"found,":[1339,1507],"measurement":[1342],"circumbinary":[1345],"setting":[1346],"integration,":[1349],"tied":[1360],"reproduces":[1365],"laptop.":[1368],"It":[1369,1384,1427,1526,1561],"test-particle":[1375],"limit,":[1376,1395],"misses.":[1383],"beyond":[1392],"circular,":[1408],"does":[1415],"find;":[1417],"chaos":[1420],"600-orbit":[1422],"islands.":[1426],"measures":[1428],"rocking's":[1430],"billionths":[1438],"fractions'":[1445],"most,":[1448],"size":[1451,1487],"coefficient":[1454],"fitted":[1457],"where,":[1459],"longer":[1461],"records,":[1462],"stops":[1464],"being":[1465],"number;":[1467],"single":[1469],"followed":[1471],"escape;":[1473],"tide":[1478],"response.":[1482],"And":[1483],"puts":[1485],"tight":[1496],"frequencies.":[1500],"Each":[1501],"section":[1502],"beside":[1512],"This":[1514],"reviewed,":[1520],"built":[1528],"assistance":[1531],"Claude":[1533,1555],"(Anthropic)":[1534],"algorithm":[1536],"program":[1538],"development":[1539],"drafting;":[1542],"declaration":[1544],"page":[1545],"says":[1546],"how":[1547,1554],"cited":[1549],"work":[1550],"used.":[1557],"CC":[1558],"BY":[1559],"4.0.":[1560],"cites":[1562],"field":[1565],"guide":[1566],"way":[1569],"working":[1571],"Crossover":[1575],"Atlas":[1576],"circle-valued":[1579],"counting":[1580],"relies":[1582],"on.":[1583],"Matthew":[1584],"\u201cBear\u201d":[1585],"Schulz":[1586],"\u00b7":[1587,1590,1593,1596,1598],"Independent":[1588],"Researcher":[1589],"Belmont,":[1591],"CA":[1592],"ORCID":[1594],"0009-0000-0956-5743":[1595],"mattschulz97@protonmail.com":[1597],"matthewschulz.net":[1599]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-30T00:00:00"}