{"id":"https://openalex.org/W7225729410","doi":"https://doi.org/10.5281/zenodo.24101816","title":"The Dual-Channel Annihilation-Field Model: Model Outline and Core Observational Evidence","display_name":"The Dual-Channel Annihilation-Field Model: Model Outline and Core Observational Evidence","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225729410","doi":"https://doi.org/10.5281/zenodo.24101816"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24101816","doi":"https://doi.org/10.5281/zenodo.24101816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101816","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":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24101816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152297603","display_name":"weihui lu","orcid":"https://orcid.org/0009-0002-9230-9525","observed_orcids":["https://orcid.org/0009-0002-9230-9525"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"lu, weihui","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0002-9230-9525","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152297603"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.5967000126838684,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.5967000126838684,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.15610000491142273,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.0835999995470047,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C201941533","wikidata":"https://www.wikidata.org/wiki/Q188721","display_name":"Annihilation","level":2,"score":0.7652000188827515},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6589999794960022},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6312999725341797},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.5910000205039978},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5529000163078308},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.47859999537467957},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.45570001006126404},{"id":"https://openalex.org/C547195049","wikidata":"https://www.wikidata.org/wiki/Q1725664","display_name":"Terminology","level":2,"score":0.4494999945163727},{"id":"https://openalex.org/C63630878","wikidata":"https://www.wikidata.org/wiki/Q902336","display_name":"Creation and annihilation operators","level":3,"score":0.4343000054359436},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.38589999079704285},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3736000061035156},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.29660001397132874},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2946000099182129},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2583000063896179}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24101816","doi":"https://doi.org/10.5281/zenodo.24101816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101816","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":"article-journal"},{"id":"doi:10.5281/zenodo.24101817","doi":"https://doi.org/10.5281/zenodo.24101817","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101817","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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24101816","doi":"https://doi.org/10.5281/zenodo.24101816","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101816","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":"article-journal"},"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":[],"abstract_inverted_index":{"The":[0,26,407,510,555,596,706,866,961,980,1174,1195,1210,1280,1322],"Dual-Channel":[1,27,254,646],"Annihilation-Field":[2,255],"Model:":[3],"Model":[4,29,256],"Outline":[5],"and":[6,72,125,154,190,204,224,237,278,323,345,355,388,413,428,441,469,537,549,574,577,609,631,669,681,696,723,732,783,806,816,845,853,870,900,940,955,977,1016,1034,1113,1141,1144,1158,1166,1220,1255,1268,1283,1317,1346,1366,1405,1408,1418,1476,1481],"Core":[7,641,653,790,859,947,1291,1465],"Observational":[8,1146],"Evidence":[9],"Author:":[10],"Weihui":[11,14],"LuCorresponding":[12],"author:":[13],"Lu":[15],"(affiliation":[16],"not":[17,45,123,127,147,518,584,621,713,728,1131,1304],"listed)":[18],"Email:":[19],"fast1py@163.com":[20],"ORCID:":[21],"0009-0002-9230-9525Version:":[22],"v1.8":[23],"(2026-11)":[24],"Appendix":[25,634],"Quantum-Well":[28],"\u2014":[30],"Key":[31],"Physical":[32],"Interpretations":[33],"(Verbatim":[34],"Statements)":[35],"Draft":[36],"terminology":[37],"(not":[38],"to":[39,47,170,221,239,292,302,320,433,877,1287,1310],"be":[40,156,321,565,604,735,927,1288],"rewritten)":[41],"This":[42,246,1453],"model":[43,265,379,396,511,543,556,597,966,1327,1458],"is":[44,120,122,168,174,248,263,325,332,446,727,739,750,885,967,1036,1125,1181,1202,1328,1385,1437,1455],"intended":[46],"\u201cfight\u201d":[48],"any":[49,520,561],"theory,":[50],"nor":[51,1451],"does":[52,64,126,517,712,1303],"it":[53,68,267,516,726],"posit":[54],"a":[55,161,191,525,532,558,591,702,760,784,826,833,836,931,987,1046,1127,1132,1307,1329,1440,1444],"hierarchy":[56],"of":[57,83,110,151,178,186,226,230,252,339,371,377,438,534,541,571,626,640,644,659,704,708,721,762,803,832,881,888,910,918,933,937,943,964,974,1019,1030,1138,1154,1171,1177,1198,1298,1400,1423,1471],"\u201cfirst":[58,139],"principles":[59],"/":[60,141,369,374,380,1081,1083,1092,1098,1193,1218,1238],"second":[61,95,142,891],"principles.\u201d":[62],"It":[63],"one":[65,198,774],"thing":[66],"only:":[67],"places":[69],"quantum":[70,166,188,235,241,439,449,478,539,572,607,660,671,673,677,683,699,753,834,843,867,920,938,1172,1179,1200,1251,1264,1314,1319,1402,1412,1427,1433],"wells":[71,98,114,274,440,540,573,608,663,674,678,684,700,895,939,1157,1180,1201,1252,1265,1315,1320],"annihilation":[73,111,179,182,193,231,279,442,480,579,610,779,804,818,828,838,873,913,944,1021,1335,1342,1355,1374,1392],"pairs":[74,232,280,580,611,780,805,811,874,1336,1343,1356,1375,1393],"side":[75,77],"by":[76,107,386,546,553,606,730,907,969,1183,1325,1390,1420],"as":[78,419,451,473,524,590,688,930,1121,1204],"the":[79,84,86,90,101,108,130,148,187,200,210,222,227,240,249,253,264,284,288,306,314,333,348,351,356,382,389,395,401,424,435,447,467,542,568,575,615,627,645,686,709,744,747,769,771,776,807,823,849,871,878,882,898,908,911,934,941,965,970,975,1013,1020,1027,1031,1037,1042,1051,1055,1103,1111,1123,1155,1226,1230,1242,1276,1299,1301,1326,1348,1352,1360,1371,1380,1382,1398,1409,1421,1424,1431,1457,1460,1472],"two":[80,87,259,270,403,981,1043,1156,1231,1277],"basic":[81],"objects":[82],"universe;":[85,883],"are":[88,105,146,311,318,360,430,470,612,620,664,685,812,905,1012,1026,1163,1214,1232,1278,1285,1337,1376,1388,1415],"jointly":[89,875],"first":[91,879,889],"element,":[92],"with":[93,298,567,1117],"no":[94,410,415,740,886],"element.":[96],"Quantum":[97,113,647,662,894],"provide":[99,896],"only":[100,116,220,269,432,472,589,717,897],"arena;":[102],"all":[103,319,903,1169,1286],"properties":[104,904,1170],"realized":[106,906],"reactions":[109,909],"pairs.":[112,819,945],"undergo":[115],"topological":[117,764,786,1406],"deformation;":[118,1407],"structure":[119,243,787,869],"constant\u2014it":[121],"crushed":[124],"disappear.":[128],"Wherever":[129,209],"terms":[131,211,1018,1029],"\u201cstructural":[132],"realism,\u201d":[133],"\u201cultimate":[134],"truth,\u201d":[135],"\u201contological":[136],"establishment,\u201d":[137],"or":[138,158,164,215,327,422],"principle":[140],"principle\u201d":[143],"appear,":[144,217],"they":[145,218,1387],"original":[149],"wording":[150],"this":[152,378,454,691,1311],"draft":[153],"should":[155],"deleted":[157],"revised.":[159],"When":[160,1370],"central,":[162],"black-hole-center,":[163],"origin-center":[165],"well":[167,242,450,754,868,1403,1413,1434],"subjected":[169],"pressure,":[171],"what":[172,1456],"happens":[173],"an":[175],"in-and-out":[176,808],"pairing":[177],"pairs\u2014a":[180],"positive":[181,203,536,576,695,815,827,852,919,976,1178,1250,1313,1334,1354,1373,1401,1426],"pair":[183,194,533,829,839],"jumps":[184,196,830,840],"out":[185,831,1339,1378],"well,":[189,835],"negative":[192,205,538,578,676,698,817,837,854,978,1032,1199,1263,1318,1341,1391,1411],"immediately":[195,1350],"in;":[197],"exits,":[199,848],"other":[201,411,850,985],"enters,":[202,851],"accompanying":[206,855],"each":[207,299,363,856,984],"other.":[208,857],"\u201ccrushing,\u201d":[212],"\u201crupture,\u201d":[213],"\u201cbreaking,\u201d":[214],"\u201ccollapse\u201d":[216],"refer":[219],"dismantling":[223],"release":[225],"aggregation":[228,917,1015,1175,1187],"form":[229,703],"inside":[233],"neutral":[234,448,670,682],"wells,":[236],"never":[238,465],"itself.":[244],"Abstract":[245],"paper":[247,408],"formal":[250],"version":[251],"(DCAF),":[257],"in":[258,305,365,453,614,690,1345],"parts.":[260],"Part":[261,330],"I":[262,1480],"outline:":[266],"posits":[268,409],"irreducible":[271],"primordial":[272,404,535],"entities\u2014quantum":[273],"(positive,":[275,281],"negative,":[276,668],"neutral)":[277],"negative)\u2014and":[282],"compresses":[283],"complete":[285],"chain":[286],"from":[287,313,400,531],"underlying":[289,872,912],"field":[290,953,972],"equations":[291,954,973],"macroscopic":[293],"phenomena":[294,601],"into":[295,666,814,841,1306],"concise":[296],"statements,":[297],"conclusion":[300],"annotated":[301],"its":[303,513,756,763,1107],"source":[304],"existing":[307,315],"topical":[308],"drafts;":[309],"formulas":[310,390],"transcribed":[312],"drafts,":[316],"coefficients":[317,1281],"calibrated,":[322],"nothing":[324,901],"rewritten":[326,929],"newly":[328],"invented.":[329],"II":[331],"core":[334,358,507,962],"observational":[335],"evidence:":[336],"four":[337,366],"sets":[338],"public":[340],"observations":[341],"(black-hole":[342],"shadow":[343],"size":[344,715,733],"EHT":[346,1145],"measurements,":[347],"Hubble":[349,502],"constant,":[350],"baryonic":[352],"Tully\u2013Fisher":[353,504],"relation,":[354,462],"dwarf-galaxy":[357,506],"problem)":[359],"listed":[361],"separately,":[362],"written":[364],"parts\u2014\u201cobservational":[367],"fact":[368],"difficulties":[370],"standard":[372],"theory":[373],"step-by-step":[375],"derivation":[376,383,468],"conclusion\u201d\u2014with":[381],"given":[384,968,1182,1324],"step":[385,387,552],"used":[391,431],"marked,":[392],"showing":[393],"how":[394],"derives":[397,550],"them":[398],"naturally":[399,1126],"above":[402],"entities":[405,417],"alone.":[406],"postulates":[412,654],"introduces":[414],"additional":[416],"such":[418],"spacetime,":[420],"vacuum,":[421],"space;":[423],"words":[425],"\u201cspacetime,\u201d":[426],"\u201cvacuum,\u201d":[427],"\u201cspace\u201d":[429],"describe":[434],"distribution":[436,942],"forms":[437],"pairs,":[443,914],"where":[444,1229],"\u201cvacuum\u201d":[445],"defined":[452,689],"model.":[455],"External":[456],"results":[457],"(Schwarzschild":[458],"radius,":[459],"Heisenberg":[460],"uncertainty":[461],"6\u221a3,":[463],"etc.)":[464],"enter":[466],"allowed":[471],"order-of-magnitude":[474,594],"rulers.":[475],"Keywords:":[476],"dual-channel":[477],"well;":[479,844],"pair;":[481],"reaction\u2013diffusion":[482],"equation;":[483],"soliton":[484,959,1056],"solution;":[485],"black-hole":[486,494,496,500],"horizon;":[487],"dynamic":[488],"electron;":[489],"dark":[490],"layer;":[491],"onion":[492],"structure;":[493],"particle;":[495],"jet;":[497],"gravitational-wave":[498],"echo;":[499],"shadow;":[501],"constant;":[503],"relation;":[505],"1":[508,635],"Introduction":[509],"changes":[512],"starting":[514,527],"point:":[515],"take":[519],"external":[521],"ready-made":[522],"formula":[523,563],"guiding":[526],"point,":[528],"but":[529,716],"starts":[530],"itself,":[544],"driven":[545],"corresponding":[547,1028,1211],"equations,":[548],"conclusions":[551],"step.":[554],"follows":[557,598],"hard":[559],"rule:":[560],"physical":[562],"must":[564],"combined":[566,586],"three":[569,710,745],"types":[570,658,711,802],"within":[581],"them;":[582],"anything":[583],"so":[585,1367],"can":[587,603,926],"serve":[588],"ruler":[592],"for":[593,1246,1259,1439],"comparison.":[595],"another":[599],"principle:":[600],"that":[602,618,842,1394],"explained":[605],"included":[613],"model;":[616],"those":[617],"cannot":[619,1167],"included.":[622],"[Source]":[623,789,858,946,1135,1290,1464],"\u201cDetailed":[624,1469],"Derivation":[625,1137,1470],"Central":[628,1473],"Critical":[629,1474],"Criterion":[630,1475],"Singularity":[632,1477],"Resolution,\u201d":[633,1478],"(hard":[636],"rule);":[637],"\u201cCore":[638],"III\u2014Record":[639],"Dynamical":[642],"Deductions":[643],"Well":[648],"Model\u201d":[649],"(inclusion":[650],"principle)":[651],"2":[652],"Postulate":[655,799],"I:":[656],"Three":[657],"wells.":[661,921,1428],"divided":[665,813],"positive,":[667],"wells\u2014positive":[672],"aggregate,":[675],"diffuse":[679],"outward,":[680],"vacuum":[687],"model,":[692,1312],"containing":[693],"half":[694,697],"internally,":[701],"nesting.":[705],"calibration":[707],"consider":[714],"nesting":[718,935,1435],"level":[719],"(number":[720],"layers)":[722],"internal":[724],"number;":[725],"limited":[729],"volume,":[731],"may":[734],"assigned":[736],"arbitrarily.":[737],"There":[738],"transition":[741],"layer":[742],"between":[743,892,1041],"types;":[746],"property":[748],"switch":[749],"definite.":[751],"A":[752,1192,1217,1282],"has":[755],"valve":[757,777,797,1383],"value,":[758,1384],"i.e.,":[759],"change":[761],"shape:":[765],"when":[766,825],"transitioning":[767],"toward":[768],"center":[770,1112,1124,1302,1454,1462],"density":[772,1105,1129,1436],"rises":[773],"level,":[775],"opens,":[778],"jump":[781,1344,1395],"out,":[782],"new":[785],"forms.":[788],"III,":[791,860,948,1292,1466],"Secs.":[792,1148],"2.1/2.2;":[793],"oral":[794],"statement":[795],"(2026-11-07,":[796],"value)":[798],"II:":[800],"Two":[801],"pairing.":[809],"Annihilation":[810],"In-and-out":[820],"pairing:":[821],"whatever":[822],"cause,":[824],"vice":[846],"versa\u2014one":[847],"opening":[861],"emphasis":[862],"paragraph":[863],"First":[864],"attribute.":[865],"belong":[876],"attribute":[880],"there":[884],"distinction":[887],"versus":[890],"them.":[893],"arena":[899],"else;":[902],"including":[915],"gravity\u2014the":[916],"Any":[922],"description":[923,932],"involving":[924],"\u201cspacetime\u201d":[925],"equivalently":[928],"levels":[936,1404,1414],"Sec.":[949,1293,1467],"4.3":[950],"3":[951],"Underlying":[952],"spherically":[956,1047,1185],"symmetric":[957,1048,1186],"steady-state":[958],"solution":[960],"dynamics":[963],"reaction\u2013diffusion-type":[971],"channels.":[979,1044],"channels":[982],"balance":[983],"through":[986,1450],"mutual-repulsion":[988,1038],"coupling":[989,1039],"term:":[990],"\u2202\u03c1\u208a/\u2202t":[991],"=":[992,1000,1072,1079,1090,1096,1191,1206,1216,1222,1236,1274],"D\u208a\u2207\u00b2\u03c1\u208a":[993],"+":[994,1006,1068],"\u03b1\u208a\u03c1\u208a\u00b2":[995,1009,1069],"\u2212":[996,998,1002,1004,1010,1024,1070],"\u03b2\u208a\u03c1\u208a":[997,1011,1071],"\u03b7\u03c1\u208a\u03c1\u208b\u2202\u03c1\u208b/\u2202t":[999],"D\u208b\u2207\u00b2\u03c1\u208b":[1001],"\u03b1\u208b\u03c1\u208b\u00b2":[1003],"\u03b2\u208b\u03c1\u208b":[1005,1025],"\u03b7\u03c1\u208a\u03c1\u208b":[1007,1035],"Here":[1008],"self-catalytic":[1014],"dissipation":[1017],"pairs;":[1022],"\u2212\u03b1\u208b\u03c1\u208b\u00b2":[1023],"channel;":[1033],"term":[1040],"Taking":[1045],"steady":[1049],"state,":[1050],"positive-energy":[1052,1104],"channel":[1053],"gives":[1054],"solution:":[1057,1077],"\u00b7":[1058,1062,1064,1066,1075,1086,1208,1224],"Steady-state":[1059],"equation:":[1060],"D\u208a":[1061],"(1/r\u00b2)":[1063],"(d/dr)(r\u00b2":[1065],"d\u03c1\u208a/dr)":[1067],"0":[1073],"(1-5)":[1074],"Soliton":[1076],"\u03c1\u208a(r)":[1078],"\u03c1\u2080":[1080,1095,1109],"cosh\u00b2(r":[1082],"L)":[1084],"(1-6)":[1085],"Characteristic":[1087],"quantities:":[1088],"L":[1089,1120],"\u221a(D\u208a":[1091],"\u03b2\u208a)":[1093],"(1-7),":[1094],"\u03b2\u208a":[1097],"\u03b1\u208a":[1099],"(1-8)":[1100],"That":[1101],"is,":[1102],"takes":[1106],"maximum":[1108],"at":[1110,1272,1443],"decays":[1114],"rapidly":[1115],"outward":[1116,1269,1358],"characteristic":[1118],"length":[1119],"cosh\u00b2;":[1122],"bounded":[1128,1332],"peak,":[1130],"divergent":[1133],"cusp.":[1134],"\u201cSelf-Consistent":[1136],"Black-Hole":[1139],"Horizon":[1140],"Shadow":[1142],"Diameter":[1143],"Verification,\u201d":[1147],"1.1,":[1149],"1.2":[1150],"4":[1151],"Action":[1152],"scales":[1153],"scale":[1159,1243],"segmentation":[1160,1244],"(the":[1161],"following":[1162],"particular":[1164],"solutions":[1165],"determine":[1168],"wells)":[1173],"action":[1176,1197],"three-dimensional":[1184],"flux":[1188],"conservation:":[1189],"F\u208a(R)":[1190],"R\u00b2.":[1194],"diffusion":[1196],"set":[1203],"F\u208b(R)":[1205],"B":[1207,1223,1284],"R^(1/3).":[1209],"reaction":[1212],"speeds":[1213],"v\u208a":[1215],"R\u00b2":[1219],"v\u208b(R)":[1221],"R^(2/3);":[1225],"intersection":[1227],"radius":[1228],"equal":[1233],"is:":[1234,1245],"R*":[1235],"(A":[1237],"B)^(3/8)":[1239],"(5-13)":[1240],"Accordingly,":[1241],"R":[1247,1260,1273],"<":[1248],"R,":[1249,1262],"react":[1253,1266],"faster":[1254,1267],"centripetal":[1256],"dominance":[1257,1270],"prevails;":[1258,1271],">":[1261],"R*,":[1275],"equal.":[1279],"calibrated.":[1289],"5.4":[1294],"5":[1295],"Dynamic":[1296],"equilibrium":[1297],"center:":[1300],"collapse":[1305],"singularity":[1308,1461],"According":[1309],"aggregate":[1316],"diffuse.":[1321],"mechanism":[1323],"black-hole-type":[1330],"eruption\u2013replenishment":[1331],"oscillation:":[1333],"squeezed":[1338,1377],"\u2192":[1340,1351,1359,1365],"fill":[1347],"spot":[1349],"squeezed-out":[1353],"overflow":[1357],"peripheral":[1361],"creation":[1362],"system":[1363],"replenishes":[1364],"on":[1368],"alternately.":[1369],"central":[1372,1432],"(i.e.,":[1379],"threshold,":[1381],"reached),":[1386],"replaced":[1389],"in,":[1396],"weakening":[1397],"tendency":[1399],"increased":[1410],"pressed":[1416],"back":[1417],"restored":[1419],"pressure":[1422],"outer":[1425],"Repeating":[1429],"this,":[1430],"locked":[1438],"long":[1441],"time":[1442],"stable":[1445],"extremely":[1446],"high":[1447],"value\u2014neither":[1448],"collapsing":[1449],"dispersing.":[1452],"calls":[1459],"layer.":[1463],"5.5;":[1468],"Parts":[1479],"VIII":[1482],"6":[1483],"Black-hole":[1484],"h":[1485]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}
