{"id":"https://openalex.org/W7163549331","doi":"https://doi.org/10.20944/preprints202604.0949.v3","title":"The Identity of Motion and Geometry: A Rigorous Mathematical Proof That Spacetime is the Kinetic Field","display_name":"The Identity of Motion and Geometry: A Rigorous Mathematical Proof That Spacetime is the Kinetic Field","publication_year":2026,"publication_date":"2026-06-03","ids":{"openalex":"https://openalex.org/W7163549331","doi":"https://doi.org/10.20944/preprints202604.0949.v3"},"language":"en","primary_location":{"id":"doi:10.20944/preprints202604.0949.v3","doi":"https://doi.org/10.20944/preprints202604.0949.v3","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202604.0949.v3","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.20944/preprints202604.0949.v3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120939444","display_name":"RAHEB ALI MOHAMMED SALEH AOUDH","orcid":"https://orcid.org/0009-0002-8141-8152","observed_orcids":["https://orcid.org/0009-0002-8141-8152"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Raheb Ali Mohammed Saleh Aoudh","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0002-8141-8152","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5120939444"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.9452999830245972,"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":0.9452999830245972,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.04610000178217888,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.006000000052154064,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spacetime-metric","display_name":"spacetime metric","score":0.9210000038146973},{"id":"https://openalex.org/keywords/einstein-field-equations","display_name":"Einstein field equations","score":0.7450000047683716},{"id":"https://openalex.org/keywords/weak-field-limit","display_name":"weak-field limit","score":0.6470000147819519},{"id":"https://openalex.org/keywords/flrw-cosmology","display_name":"FRW cosmology","score":0.7620000243186951},{"id":"https://openalex.org/keywords/modified-friedmann-equations","display_name":"modified Friedmann equations","score":0.9750000238418579},{"id":"https://openalex.org/keywords/dark-energy","display_name":"dark energy","score":0.8939999938011169},{"id":"https://openalex.org/keywords/gravitational-waves","display_name":"gravitational waves","score":0.9110000133514404},{"id":"https://openalex.org/keywords/gravitational-lensing","display_name":"gravitational lensing","score":0.7319999933242798},{"id":"https://openalex.org/keywords/sparc-galaxies","display_name":"SPARC galaxies","score":0.5260000228881836},{"id":"https://openalex.org/keywords/modified-gravity","display_name":"modified gravity","score":0.38199999928474426},{"id":"https://openalex.org/keywords/effective-speed-of-light","display_name":"effective speed of light","score":0.4050000011920929},{"id":"https://openalex.org/keywords/modified-dispersion-relations","display_name":"modified dispersion relations","score":0.367000013589859}],"concepts":[{"id":"https://openalex.org/C30864177","wikidata":"https://www.wikidata.org/wiki/Q742982","display_name":"Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker metric","level":3,"score":0.6929000020027161},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.6873000264167786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5598000288009644},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.5241000056266785},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C2780791080","wikidata":"https://www.wikidata.org/wiki/Q273711","display_name":"Einstein field equations","level":3,"score":0.4560999870300293},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.42309999465942383},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.4004000127315521},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.399399995803833},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C8466233","wikidata":"https://www.wikidata.org/wiki/Q757269","display_name":"Metric tensor","level":3,"score":0.3806000053882599},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3359000086784363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3118000030517578},{"id":"https://openalex.org/C134328617","wikidata":"https://www.wikidata.org/wiki/Q546984","display_name":"Linearized gravity","level":3,"score":0.30559998750686646},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C2779228454","wikidata":"https://www.wikidata.org/wiki/Q6410802","display_name":"Kinetic term","level":3,"score":0.30140000581741333},{"id":"https://openalex.org/C172790937","wikidata":"https://www.wikidata.org/wiki/Q18343","display_name":"Dark energy","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C149324446","wikidata":"https://www.wikidata.org/wiki/Q43514","display_name":"Theory of relativity","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.258899986743927}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.20944/preprints202604.0949.v3","doi":"https://doi.org/10.20944/preprints202604.0949.v3","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202604.0949.v3","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.20944/preprints202604.0949.v3","doi":"https://doi.org/10.20944/preprints202604.0949.v3","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202604.0949.v3","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"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/W7154246287","https://openalex.org/W7142548340","https://openalex.org/W6960210967","https://openalex.org/W7141206292","https://openalex.org/W7130565511","https://openalex.org/W7160376534","https://openalex.org/W7117378919","https://openalex.org/W7126172831","https://openalex.org/W7116093593","https://openalex.org/W6949678437"],"abstract_inverted_index":{"We":[0,337],"present":[1],"a":[2,193,203,234,373],"rigorous":[3],"mathematical":[4],"proof":[5,139],"that":[6,141,323,369],"the":[7,15,21,38,45,79,93,99,125,135,145,156,173,182,208,212,223,249,256,272,300,312,315,332,353,377,381],"spacetime":[8,72,370],"metric":[9,73,114,190,253],"$g_{\\mu\\nu}$":[10,74,169],"of":[11,20,37,98,134,155,238,248,271,334,357,380],"General":[12],"Relativity":[13],"and":[14,83,185,233,359],"fundamental":[16,146,374],"kinetic":[17,80,206,224,250,273,382],"field":[18,81,127,179,195,225,251],"$\\nu^\\mu$":[19],"Fundamental":[22],"Speed":[23],"Theory":[24],"(FST)":[25],"are":[26,265],"not":[27,372],"two":[28,33,177],"distinct":[29,178],"entities,":[30],"but":[31,376],"rather":[32],"mathematically":[34],"equivalent":[35],"descriptions":[36],"same":[39,183,209],"underlying":[40],"physical":[41],"reality.":[42],"Starting":[43],"from":[44,92,112,166],"foundational":[46,100,136,157,355],"FST":[47,94,126,285,324],"paper---validated":[48],"on":[49],"171":[50],"SPARC":[51,293],"galaxies":[52,294],"with":[53,129,222,295,363],"$\\chi^2_\\nu":[54],"=":[55,117,149,261],"0.170$":[56],"across":[57],"five":[58,354],"hierarchical":[59],"validation":[60],"levels---we":[61],"establish":[62,368],"six":[63],"central":[64],"theorems:":[65],"The":[66,71,102,107,138,159,164,197,216,240,275,366],"Metric-Kinetic":[67],"Map":[68],"(Theorem":[69,105,162,200,244,279],"1):":[70],"is":[75,152,170,307,319,371],"uniquely":[76],"determined":[77],"by":[78,132],"$\\tilde{\\nu}$":[82,123,167],"its":[84],"gradients":[85],"via":[86],"an":[87,228],"explicit,":[88],"closed-form":[89],"expression":[90],"derived":[91],"velocity":[95],"relation":[96,147],"(Eq.~28":[97],"paper).":[101],"Einstein":[103,108],"Correspondence":[104,243],"2):":[106],"tensor":[109],"$G_{\\mu\\nu}$":[110],"computed":[111],"this":[113,142],"satisfies":[115],"$G_{\\mu\\nu}":[116],"\\frac{8\\pi":[118],"G}{c^4}":[119],"T_{\\mu\\nu}^{(V)}$":[120],"exactly":[121],"when":[122],"obeys":[124],"equation,":[128,347],"$T_{\\mu\\nu}^{(V)}$":[130],"given":[131],"Eq.~(6)":[133],"paper.":[137,158],"establishes":[140],"correspondence":[143],"requires":[144],"$\\beta_{\\text{eff}}":[148],"|\\lambda|\\nu_0^2/(6c_1)$,":[150],"which":[151],"precisely":[153],"Eq.~(18)":[154],"Invertibility":[160],"Theorem":[161,278],"3):":[163],"map":[165,210],"to":[168,192,352],"bijective":[171],"in":[172,342],"weak-field":[174,187],"regime;":[175],"no":[176],"configurations":[180],"produce":[181,252],"metric,":[184],"every":[186,346],"spherically":[188],"symmetric":[189],"corresponds":[191],"unique":[194],"configuration.":[196],"Cosmological":[198],"Extension":[199],"4):":[201],"For":[202,291],"homogeneous,":[204],"time-dependent":[205],"field,":[207],"generates":[211],"FLRW":[213],"cosmological":[214],"metric.":[215],"modified":[217],"Friedmann":[218],"equations":[219,356],"emerge":[220],"naturally,":[221],"providing":[226],"both":[227],"effective":[229],"dark":[230,289,329],"energy":[231],"density":[232],"slowly":[235],"evolving":[236],"equation":[237,258],"state.":[239],"Gravitational":[241,263,276],"Wave":[242],"5):":[245],"Linear":[246],"perturbations":[247,254,270],"satisfying":[255],"wave":[257],"$\\Box":[259],"h_{\\mu\\nu}^{\\text{TT}}":[260],"0$.":[262],"waves":[264],"thus":[266],"identified":[267],"as":[268],"propagating":[269],"field.":[274,383],"Lensing":[277],"6):":[280],"Weak":[281],"lensing":[282,298,327],"masses":[283,287],"equal":[284],"dynamical":[286],"without":[288,328],"matter.":[290],"19":[292],"published":[296],"weak":[297],"masses,":[299],"median":[301,313],"lensing-to-dynamical":[302],"mass":[303],"ratio":[304],"at":[305],"$300\\,\\text{kpc}$":[306],"$\\mathbf{1.09}$":[308],"(all":[309],"galaxies),":[310],"while":[311],"for":[314,331,345],"15-galaxy":[316],"reliable":[317],"subset":[318],"$\\mathbf{0.88}$.":[320],"This":[321],"demonstrates":[322],"explains":[325],"gravitational":[326],"matter":[330],"majority":[333],"well-measured":[335],"galaxies.":[336],"provide":[338],"complete":[339],"dimensional":[340],"analysis":[341],"SI":[343],"units":[344],"trace":[348],"all":[349],"derivations":[350],"back":[351],"FST,":[358],"supply":[360],"exhaustive":[361],"appendices":[362],"step-by-step":[364],"calculations.":[365],"results":[367],"entity":[375],"perceptual":[378],"manifestation":[379]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-06-05T00:00:00"}