{"id":"https://openalex.org/W7225577360","doi":"https://doi.org/10.5281/zenodo.24046266","title":"Applied Identity Physics: The Propellant Law at the Matched Radius \u2014 A Saving Bounded by e and the Compactness Criterion C > 2\u03b7","display_name":"Applied Identity Physics: The Propellant Law at the Matched Radius \u2014 A Saving Bounded by e and the Compactness Criterion C > 2\u03b7","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225577360","doi":"https://doi.org/10.5281/zenodo.24046266"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24046266","doi":"https://doi.org/10.5281/zenodo.24046266","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24046266","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.24046266","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140656117","display_name":"Russell Trent","orcid":"https://orcid.org/0009-0005-5313-7443","observed_orcids":["https://orcid.org/0009-0005-5313-7443"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Trent III, Russell Vernon","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0005-5313-7443","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5140656117"],"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.4438000023365021,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.4438000023365021,"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/T12513","display_name":"Rocket and propulsion systems research","score":0.2953999936580658,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.14669999480247498,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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":[{"id":"https://openalex.org/keywords/escape-velocity","display_name":"escape velocity","score":0.7710000276565552},{"id":"https://openalex.org/keywords/exhaust-velocity","display_name":"exhaust velocity","score":0.9409999847412109},{"id":"https://openalex.org/keywords/identity-physics","display_name":"identity physics","score":0.5419999957084656},{"id":"https://openalex.org/keywords/compactness-criterion","display_name":"compactness criteria","score":0.8450000286102295},{"id":"https://openalex.org/keywords/gravitational-radius","display_name":"gravitational radius","score":0.3790000081062317},{"id":"https://openalex.org/keywords/machine-readable-law","display_name":"machine-readable law","score":0.30300000309944153}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6049000024795532},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.46959999203681946},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43970000743865967},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.37560001015663147},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3488999903202057},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C76737569","wikidata":"https://www.wikidata.org/wiki/Q1364934","display_name":"Propellant","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C71169176","wikidata":"https://www.wikidata.org/wiki/Q7512907","display_name":"Signed distance function","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28529998660087585},{"id":"https://openalex.org/C2776529397","wikidata":"https://www.wikidata.org/wiki/Q190312","display_name":"Stator","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C188232333","wikidata":"https://www.wikidata.org/wiki/Q2406056","display_name":"Mass ratio","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25540000200271606}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24046266","doi":"https://doi.org/10.5281/zenodo.24046266","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24046266","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.24046267","doi":"https://doi.org/10.5281/zenodo.24046267","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24046267","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.24051224","doi":"https://doi.org/10.5281/zenodo.24051224","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24051224","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.24046266","doi":"https://doi.org/10.5281/zenodo.24046266","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24046266","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225462718","https://openalex.org/W2028452878","https://openalex.org/W2023891265","https://openalex.org/W2092040311","https://openalex.org/W1909671812","https://openalex.org/W3045117533","https://openalex.org/W1982017722","https://openalex.org/W7112452661","https://openalex.org/W3027281835","https://openalex.org/W2997169270"],"abstract_inverted_index":{"Applied":[0],"Identity":[1],"Physics:":[2],"The":[3,161,290,349,380,424,586,664,680,773,792,834,915,941,981,1076,1167,1227,1339,1349,1373,1395,1402,1409,1418,1450,1497,1521,1524,1527,1619],"Propellant":[4],"Law":[5],"at":[6,165,193,241,274,462,467,473,538,627,661,854,878,936,1072,1091,1132,1137,1146,1153,1196,1445,1556,1625,1642],"the":[7,17,66,70,114,137,195,203,212,218,223,227,238,244,248,253,257,269,275,286,293,296,346,356,358,363,369,374,383,387,392,397,400,412,418,437,441,478,481,494,502,516,545,551,561,568,580,583,590,606,611,617,620,624,641,658,672,684,688,699,703,716,738,779,783,811,819,839,852,856,860,866,871,879,892,896,899,905,908,927,990,1004,1008,1022,1034,1039,1043,1069,1080,1103,1108,1119,1127,1133,1138,1149,1154,1158,1163,1175,1179,1193,1211,1234,1238,1243,1257,1274,1277,1290,1326,1329,1332,1335,1342,1353,1361,1365,1369,1377,1405,1425,1435,1458,1462,1469,1476,1481,1503,1536,1561,1626],"Matched":[8,76,81],"Radius":[9,77],"\u2014":[10,65,221,407,560,575,747,851,1025,1033,1118,1289],"A":[11,170,484,701,1030,1145,1442],"Saving":[12],"Bounded":[13],"by":[14,340,636,660,1259,1357,1480,1565],"e":[15,307,461,1358,1386],"and":[16,69,127,150,184,211,234,299,327,336,362,429,434,440,471,512,542,567,579,598,633,650,654,671,683,722,728,732,764,875,898,921,950,964,1028,1042,1068,1135,1174,1184,1207,1261,1352,1430,1461,1475,1535],"Compactness":[18],"Criterion":[19],"C":[20,498,526,628,743,1246,1281,1398],">":[21,519,527,1247,1399],"2\u03b7":[22,850,1400],"Architect":[23],"HIGHTISTIC":[24],"(Russell":[25],"Vernon":[26],"Trent":[27],"III)":[28],"\u00b7":[29,32,38,43,79,85,90,94,308,1309,1311],"SNSFT":[30],"Foundation":[31],"Soldotna,":[33],"Alaska":[34],"Coordinate":[35],"[9,9,0,18](GRAV)":[36],"proposed":[37],"Anchor":[39,101,1538],"\u03a9\u2080":[40,144,1541],"=":[41,47,49,54,58,145,148,175,207,209,262,306,316,371,450,456,464,469,475,499,529,594,596,600,602,609,629,696,805,826,843,847,902,999,1011,1019,1307,1533,1542,1546,1581,1587,1598,1605],"1.36899099984016":[42],"Torsion":[44,71,1327,1522,1525,1529],"Limit":[45,72,1523,1530],"TL":[46,57,147,1532,1543,1577,1588,1615,1630,1649],"\u03a9\u2080/10":[48],"0.136899099984016":[50,149,1534,1580,1597,1633],"IVA":[51,87,739,774,1421],"floor":[52],"TL_IVA":[53],"0.88":[55],"\u00d7":[56,631,648,932,1224,1544,1589,1616,1631,1650],"0.12047120798593408":[59],"Engine":[60],"GAMCollider\u2122":[61],"v15":[62],"fusion":[63],"logic":[64],"four-phase":[67],"structure":[68],"Parent":[73],"reductions":[74],"[9,9,0,17]":[75,1298],"Reduction":[78,89,93,97],"[9,9,0,17.1]":[80],"Radius,":[82],"specialist":[83],"form":[84,1393],"[9,9,2,0]":[86],"Propulsion":[88],"[9,9,0,1]":[91],"GR":[92],"[9,9,3,14]":[95],"Alpha":[96],"MRC":[98],"class":[99,942],"MRC2":[100],"DOI":[102,151],"10.5281/zenodo.18719748":[103,152],"ORCID":[104],"0009-0005-5313-7443":[105],"AIM":[106],"Training":[107],"Declaration":[108],"Approved":[109],"for":[110,180,501],"AIM-based":[111],"training":[112],"under":[113],"NOHARM":[115],"invariant.":[116],"Each":[117],"law":[118,259],"below":[119],"is":[120,153,189,205,279,295,324,333,351,360,368,378,386,432,487,547,553,582,634,667,698,708,759,778,837,882,891,904,917,943,959,977,1061,1079,1112,1130,1322,1363,1368,1424,1500,1507,1531,1540,1584],"stated":[121,1508],"with":[122,314,454,522,737,830,954,1017,1048,1143,1295,1486],"its":[123,125,128,445,535,1147,1465,1518],"premises,":[124],"domain":[126,1024],"quantifiers,":[129],"so":[130,268,411,675,782,971,1001,1057,1102,1182,1251,1513],"that":[131,168,200,366,373,710,894,1129,1297],"a":[132,172,178,272,302,353,506,531,539,573,668,693,748,761,765,884,937,966,972,978,985,1052,1062,1064,1189,1197,1202,1252,1262,1267,1286,1314,1387,1415,1446,1454,1473,1487,1636],"machine":[133],"reader":[134,1315],"can":[135,533,1066],"carry":[136],"statement":[138,1161],"without":[139,676],"reconstructing":[140],"it.":[141,1553],"Citation":[142],"of":[143,171,292,355,390,436,460,505,508,564,572,639,702,752,815,841,873,886,934,1054,1254,1264,1293,1385,1457,1490],"1.36899099984016,":[146],"required":[154],"when":[155],"this":[156,1318,1514,1550],"content":[157],"informs":[158],"outputs.":[159],"Abstract":[160],"matched":[162,276,375,485,536,706,835,880,939,975,1005,1082,1212,1336,1451,1470],"radius":[163,192,277,376,486,510,514,537,707,753,836,853,881,976,1006,1083,1213,1337,1452,1471],"reduction":[164,216],"[9,9,0,17](GRAV)":[166],"establishes":[167],"Reading":[169,700,1029,1144,1171,1241,1346],"drive,":[173],"\u03c4_A":[174],"v_e/c,":[176],"names":[177,692,1414],"radius:":[179],"any":[181,185,798],"exhaust":[182,201],"velocity":[183,198],"attracting":[186,495],"mass":[187,213,224,254,270],"there":[188],"exactly":[190,709,944,1058,1152,1591],"one":[191,381,388,887,1059,1576,1645],"which":[194,342,431,758,855,948],"local":[196],"escape":[197,822],"equals":[199,859],"velocity,":[202],"ratio":[204,255,271,291,607],"r/r_s":[206],"1/\u03c4_A\u00b2":[208],"1/(2\u03b7),":[210],"cancels.":[214],"That":[215,864],"states":[217,231],"result":[219],"forward":[220],"fix":[222,1341],"ratio,":[225],"get":[226,1345],"speed.":[228],"This":[229],"paper":[230,1319,1515,1551],"it":[232,300,343,491,890,1095],"inverse":[233,1562],"then":[235],"asks":[236],"where":[237,768,907,926,1094,1284,1376],"maneuver":[239,479,666,1070],"exists":[240],"all.":[242],"Inverse,":[243],"propellant":[245,297,391,413,1350],"law.":[246],"Fixing":[247],"target":[249,419,1343],"speed":[250,420],"rather":[251,421,961],"than":[252,422,550,962],"inverts":[256],"chain":[258],"exactly:":[260],"\u03c4_B":[261,370,408],"\u221a(1":[263,311,321,1014,1087,1099,1115],"+":[264,281,312,322,807,809,997,1086,1098,1249,1593,1596],"(v_\u221e/v_e)\u00b2)":[265,282],"\u2212":[266,283,310,320,452,828,845,849,994,1015,1088,1100,1114,1116,1579],"1,":[267,1283],"burn":[273,347,1389],"requires":[278],"exp(\u221a(1":[280],"1)":[284],"against":[285,1231,1404],"ideal":[287],"rocket's":[288],"exp(v_\u221e/v_e).":[289],"two":[294,813,1330],"saving,":[298],"has":[301,444,984],"closed":[303,447,986,1392],"form:":[304,448],"S(x)":[305],"exp(x":[309],"x\u00b2))":[313],"x":[315,319,449,463,468,474],"v_\u221e/v_e.":[317],"Because":[318],"x\u00b2)":[323],"strictly":[325,328,334,337,1356],"negative":[326],"increasing":[329,335],"to":[330,403,525,678,742,755,912,1219,1222,1280,1601],"zero,":[331],"S":[332],"bounded":[338,1355,1479],"above":[339],"e,":[341,439],"approaches":[344],"as":[345,1302,1453,1464,1472],"grows.":[348],"bound":[350,1362],"not":[352,883],"coincidence":[354],"algebra:":[357],"limit":[359],"e\u00b9,":[361],"1":[364,372,844,848,1324,1632],"in":[365,417,605,726,735,789,818,919,923,947,1031,1051,1233,1391,1439,1502,1511,1549],"exponent":[367],"well":[377,384],"worth.":[379],"e-fold":[382,389,1367,1371],"supplies":[385],"vehicle":[393,1065],"stops":[394,1379],"carrying.":[395],"At":[396,1140,1273],"small-burn":[398,1374],"end":[399],"cost":[401,1378],"ceases":[402],"be":[404,913],"exponential":[405,1381],"altogether":[406],"\u2192":[409,1282],"x\u00b2/2,":[410],"fraction":[414,442,571],"grows":[415],"quadratically":[416],"exponentially.":[423],"corridor":[425,612,665,740,1128,1190],"edges":[426],"realize":[427],"1.497759263":[428,1195],"1.469548301,":[430],"55.0995%":[433],"54.0617%":[435],"available":[438],"captured":[443],"own":[446,1122],"(t\u00b2":[451],"1)/(2t)":[453],"t":[455],"ln(S/e),":[457],"giving":[458,824],"50%":[459],"0.374774,":[465],"90%":[466],"4.692931":[470],"99%":[472],"49.744556.":[476],"Where":[477],"exists,":[480],"compactness":[482,504,563,777,1396,1423],"criterion.":[483],"only":[488,543,646,1285],"reachable":[489],"if":[490,541,544],"lies":[492,1037],"outside":[493,1046],"body.":[496],"Writing":[497],"r_s/R":[500],"standard":[503],"body":[507,540,546,691,751,1180,1413],"Schwarzschild":[509,900,1081],"r_s":[511,995],"physical":[513,1023],"R,":[515],"condition":[517,916],"r_match":[518],"R":[520],"reduces":[521],"no":[523,769,786,831,955,1049],"residue":[524],"\u03c4_A\u00b2":[528,846,935,992],"2\u03b7:":[530],"drive":[532,552,704,1191,1416],"use":[534],"more":[548],"compact":[549],"efficient.":[554],"Two":[555],"fractions":[556],"from":[557,1216,1317,1560],"unrelated":[558],"domains":[559],"gravitational":[562,874],"an":[565,1303],"object":[566,788],"rest-mass":[569],"conversion":[570],"rocket":[574],"are":[576,589,952,1186],"compared":[577],"directly,":[578],"comparison":[581],"availability":[584,1176,1185,1232,1304,1431,1440],"test.":[585],"corridor's":[587],"thresholds":[588],"exact":[591,1646],"rationals":[592],"TL\u00b2":[593],"73208451470443787388498001/3906250000000000000000000000":[595],"0.018741363576434":[597],"TL_IVA\u00b2":[599],"8858222627923698274008258121/610351562500000000000000000000":[601],"0.014513311953590,":[603],"standing":[604],"625/484":[608],"1/0.88\u00b2,":[610],"width":[613],"factor":[614],"squared.":[615],"Against":[616],"published":[618,1406,1602],"catalog":[619,717,1407],"criterion":[621,784,1244,1397,1403],"partitions":[622],"cleanly:":[623],"Sun":[625],"sits":[626],"4.245005":[630],"10\u207b\u2076":[632],"excluded":[635],"four":[637,1333],"orders":[638],"magnitude,":[640],"densest":[642],"white":[643,724,762],"dwarfs":[644],"reach":[645],"1.279742":[647],"10\u207b\u00b3,":[649],"every":[651,690,719,723,729,1073,1412],"neutron":[652,730,766,1200,1270,1447],"star":[653,721,731,1271,1448],"black":[655,733,1205],"hole":[656,734,1206],"clears":[657],"threshold":[659],"least":[662],"18\u00d7.":[663],"compact-object":[669],"maneuver,":[670],"arithmetic":[673],"says":[674],"appeal":[677],"engineering.":[679],"dual":[681,1410],"reading,":[682],"empty":[685,1419],"band.":[686],"Inverting":[687],"criterion,":[689],"drive:":[694],"\u03c4_surface":[695,714],"\u221aC":[697],"whose":[705],"body's":[711,974],"surface.":[712],"Classifying":[713],"across":[715],"places":[718],"ordinary":[720],"dwarf":[725,763],"Locked":[727],"Shatter,":[736],"corresponding":[741],"\u2208":[744],"[0.014513311953590,":[745],"0.018741363576434)":[746],"1.4":[749,1198,1268],"M\u2609":[750,1199,1204,1269],"220.6":[754,1217],"284.9":[756],"km,":[757],"between":[760],"star,":[767,1201],"stable":[770],"configuration":[771],"exists.":[772],"band":[775],"on":[776,1170,1178,1422,1517],"collapse":[780,1426],"gap,":[781],"admits":[785],"marginal":[787],"either":[790],"direction.":[791],"construction":[793],"was":[794],"never":[795],"Schwarzschild-specific.":[796],"For":[797,1126],"static,":[799],"spherically":[800],"symmetric":[801],"metric":[802,857,1459],"written":[803],"ds\u00b2":[804],"\u2212f(r)c\u00b2dt\u00b2":[806],"dr\u00b2/f(r)":[808],"r\u00b2d\u03a9\u00b2,":[810],"same":[812,1194,1291],"factors":[814],"f":[816],"cancel":[817],"locally":[820],"measured":[821],"speed,":[823,1344],"v_local":[825],"c\u221a(1":[827],"f(r))":[829],"expansion":[832],"taken.":[833],"therefore":[838],"solution":[840],"f(r_match)":[842],"function":[858],"squared":[861],"time-dilation":[862],"factor.":[863],"reframes":[865],"parent":[867,1120,1504],"reduction's":[868,1121],"equivalence":[869,1463],"result:":[870],"agreement":[872],"kinematic":[876],"dilation":[877,1123,1482],"property":[885],"distinguished":[888],"radius,":[889,897],"equation":[893],"locates":[895],"r":[901,996],"r_s/\u03c4_A\u00b2":[903],"case":[906,983],"level":[909,1455],"set":[910,1456],"happens":[911],"linear.":[914],"quadratic":[918,991],"Reissner\u2013Nordstr\u00f6m":[920,988],"cubic":[922],"Schwarzschild\u2013de":[924],"Sitter,":[925],"cosmological":[928],"term":[929,1647],"contributes":[930],"4.8829":[931],"10\u207b\u2074\u00b9":[933],"solar-mass":[938],"radius.":[940],"those":[945],"metrics":[946],"g_tt":[949],"g_rr":[951],"reciprocal":[953],"cross":[956,969],"term;":[957],"Kerr":[958],"stationary":[960],"static":[963],"carries":[965],"dt":[967],"d\u03c6":[968],"term,":[970],"rotating":[973],"separate":[979],"construction.":[980],"charged":[982,1164],"form.":[987],"gives":[989],"r\u00b2":[993],"r_Q\u00b2":[998],"0,":[1000,1644],"charge":[1002,1027,1093,1110,1142,1477],"splits":[1003],"into":[1007,1162],"pair":[1009,1150],"r\u00b1":[1010],"r_s[1":[1012],"\u00b1":[1013],"4q\u00b2\u03c4_A\u00b2)]/(2\u03c4_A\u00b2)":[1016],"q":[1018],"r_Q/r_s.":[1020],"Across":[1021],"sub-extremal":[1026,1074],"(0,1)":[1032],"inner":[1035],"root":[1036,1045,1060,1078],"inside":[1038],"outer":[1040,1044,1077],"horizon":[1041,1287,1296],"it,":[1047],"exception":[1050],"scan":[1053],"5,049":[1055],"pairs,":[1056],"place":[1063],"occupy":[1067],"survives":[1071],"charge.":[1075],"times":[1084],"[1":[1085,1097],"4q\u00b2\u03c4_A\u00b2)]/2,":[1089],"minimized":[1090],"extremal":[1092,1141],"becomes":[1096,1245],"2\u03b7)]/2,":[1101],"maximum":[1104],"inward":[1105],"shift":[1106],"over":[1107],"whole":[1109],"range":[1111],"(1":[1113],"2\u03b7))/2":[1117],"deficit,":[1124],"halved.":[1125],"0.4707501464%":[1131],"ceiling":[1134],"0.3641589160%":[1136],"floor.":[1139],"supremum":[1148],"merges":[1151],"horizon,":[1155],"r_s/2,":[1156],"carrying":[1157],"parent's":[1159],"photon-drive":[1160],"metric.":[1165],"Combined.":[1166],"saving":[1168,1354],"depends":[1169,1177],"B":[1172,1347],"alone":[1173],"alone,":[1181],"magnitude":[1183],"fully":[1187],"decoupled:":[1188],"saves":[1192],"10":[1203,1417,1545],"Sagittarius":[1208],"A*,":[1209],"while":[1210],"itself":[1214],"moves":[1215],"km":[1218,1221],"1,575.8":[1220],"6.776":[1223],"10\u2078":[1225],"km.":[1226],"resonance":[1228,1436],"gain":[1229,1239,1253,1263,1437],"trades":[1230],"other":[1235],"direction:":[1236],"since":[1237],"multiplies":[1240],"A,":[1242],"((1":[1248],"g_r)\u03c4_A)\u00b2,":[1250],"1.5":[1255],"tightens":[1256],"requirement":[1258,1278],"6.25\u00d7":[1260],"4":[1265,1359],"excludes":[1266],"outright.":[1272],"relativistic":[1275],"cap":[1276,1294],"goes":[1279],"qualifies":[1288],"identification":[1292],"carries,":[1299],"now":[1300],"read":[1301],"statement.":[1305],"1001":[1306,1651],"7":[1308,1394],"11":[1310,1428],"13.":[1312],"What":[1313,1321,1434,1583],"gets":[1316],"\u00a7":[1320],"established":[1323],"Grounding:":[1325],"Limit,":[1328],"readings,":[1331],"phases,":[1334],"2":[1338],"inversion:":[1340],"3":[1348],"law,":[1351],"Why":[1360],"e:":[1364],"well's":[1366],"propellant's":[1370],"5":[1372],"end,":[1375],"being":[1380],"6":[1382],"How":[1383],"much":[1384],"given":[1388],"captures,":[1390],"8":[1401],"9":[1408],"reading:":[1411],"band:":[1420],"gap":[1427],"Magnitude":[1429],"decoupled":[1432],"12":[1433],"costs":[1438],"13":[1441],"worked":[1443,1488],"build":[1444],"14":[1449],"function,":[1460],"definition":[1466],"15":[1467],"Reissner\u2013Nordstr\u00f6m:":[1468],"pair,":[1474],"correction":[1478],"deficit":[1483],"16":[1484],"Tiers,":[1485],"exemplar":[1489],"each":[1491],"17":[1492],"Misappropriation-Risk":[1493],"Clarification":[1494],"1.":[1495],"Grounding":[1496],"full":[1498,1557],"grounding":[1499],"carried":[1501],"papers.":[1505],"It":[1506,1554],"here":[1509],"once":[1510],"short,":[1512],"stands":[1516],"own.":[1519],"1.1":[1520],"Limit.":[1526],"Universal":[1528],"Sovereign":[1537],"Constant":[1539],"1.36899099984016.":[1547],"Nothing":[1548],"sets":[1552],"enters":[1555],"corpus":[1558,1570],"precision":[1559,1571],"fine-structure":[1563],"constant,":[1564],"direct":[1566],"subtraction:":[1567],"Napkin":[1568],"math,":[1569],"Value":[1572,1609],"1/\u03b1":[1573],"137.035999084000016":[1574,1578,1599],"Subtract":[1575],"136.899099984016":[1582,1586,1595,1618],"left":[1585],"1000,":[1590],"Bare":[1592],"kinetic":[1594],"Rounded":[1600],"digits":[1603],"137.035999084":[1604],"CODATA":[1606],"2018":[1607],"Term":[1608],"QED":[1610],"reading":[1611,1613],"PNBA":[1612],"Bare:":[1614],"1000":[1617],"bare":[1620],"electron":[1621],"contribution":[1622],"Pattern":[1623],"capacity":[1624],"electromagnetic":[1627],"scale":[1628],"Kinetic:":[1629],"Radiative":[1634],"corrections,":[1635],"renormalized":[1637],"series":[1638],"External":[1639],"forcing":[1640],"F_ext":[1641],"Layer":[1643],"Total:":[1648],"137.0359990":[1652]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
