{"id":"https://openalex.org/W7204044764","doi":"https://doi.org/10.5281/zenodo.22065781","title":"Foundation Studies of the Curvature-Spacecraft Theory (I): Realization of Nonnegative-Energy Curvature Bubbles\\\\Explicit Construction of Ordinary-Matter Initial-Data Configurations and a Sharp Shaping Window}","display_name":"Foundation Studies of the Curvature-Spacecraft Theory (I): Realization of Nonnegative-Energy Curvature Bubbles\\\\Explicit Construction of Ordinary-Matter Initial-Data Configurations and a Sharp Shaping Window}","publication_year":2026,"publication_date":"2026-08-23","ids":{"openalex":"https://openalex.org/W7204044764","doi":"https://doi.org/10.5281/zenodo.22065781"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22065781","doi":"https://doi.org/10.5281/zenodo.22065781","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22065781","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.22065781","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133872609","display_name":"Peng Li","orcid":"https://orcid.org/0000-0001-8780-5554","observed_orcids":["https://orcid.org/0000-0001-8780-5554","https://orcid.org/0009-0004-4519-3261"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Peng","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-4519-3261","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133872609"],"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.48829999566078186,"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":0.48829999566078186,"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":0.44749999046325684,"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":0.018400000408291817,"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/warp-drive","display_name":"warp drive","score":0.6420000195503235},{"id":"https://openalex.org/keywords/negative-energy","display_name":"negative energy","score":0.6200000047683716},{"id":"https://openalex.org/keywords/weak-energy-condition","display_name":"weak energy condition","score":0.8970000147819519},{"id":"https://openalex.org/keywords/time-symmetric-initial-data","display_name":"time-symmetric initial data","score":0.8690000176429749},{"id":"https://openalex.org/keywords/conformally-flat-spacetimes","display_name":"conformally flat spacetimes","score":0.6179999709129333},{"id":"https://openalex.org/keywords/lichnerowicz-equation","display_name":"Lichnerowicz equation","score":0.9549999833106995},{"id":"https://openalex.org/keywords/positive-mass-theorem","display_name":"positive mass theorem","score":0.8009999990463257},{"id":"https://openalex.org/keywords/throat-area","display_name":"throat area","score":0.3720000088214874},{"id":"https://openalex.org/keywords/quadrupole-moment","display_name":"quadrupole moment","score":0.6150000095367432}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6291000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4875999987125397},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4530999958515167},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4302000105381012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.414900004863739},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C14257148","wikidata":"https://www.wikidata.org/wiki/Q558066","display_name":"Gravitational field","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.289900004863739},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2567000091075897},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2540000081062317}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.22065781","doi":"https://doi.org/10.5281/zenodo.22065781","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22065781","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.22065782","doi":"https://doi.org/10.5281/zenodo.22065782","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22065782","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.22731338","doi":"https://doi.org/10.5281/zenodo.22731338","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22731338","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.22065781","doi":"https://doi.org/10.5281/zenodo.22065781","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22065781","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/W7116859324","https://openalex.org/W4412714160","https://openalex.org/W4416588181","https://openalex.org/W7021109090","https://openalex.org/W7220699419","https://openalex.org/W2997565737","https://openalex.org/W2977324641","https://openalex.org/W1857372675","https://openalex.org/W7213249101","https://openalex.org/W7169884092"],"abstract_inverted_index":{"Traditional":[0],"warp-driven":[1],"configurations":[2],"require":[3],"negative":[4],"energy":[5,24],"to":[6,27,201,582],"sustain":[7],"a":[8,55,73,115,191,206,235,284,462,499],"bubble-like":[9],"spacetime;":[10],"on":[11,216],"time-symmetric":[12,106],"initial":[13],"data,":[14],"this":[15,62,278,421,441],"paper":[16,422,442],"proves":[17],"that":[18,37],"ordinary":[19],"matter":[20,45],"satisfying":[21],"the":[22,39,43,48,59,66,80,90,105,110,126,134,145,149,164,184,196,202,211,217,221,242,247,251,256,261,265,270,274,280,289,297,302,309,315,336,340,343,355,359,364,373,390,397,404,449,475,481,487,495,511,518,521,523,535,543,547,570,576,583],"weak":[23,360],"condition":[25],"suffices":[26],"construct":[28,38],"static":[29,281,367,455,577],"curvature":[30,571],"bubbles,":[31],"and":[32,42,96,122,155,250,273,301,388,403,433,446,490,546],"provides":[33,443],"theoretical":[34],"realization":[35,434,447],"methods":[36],"complete":[40,488],"spacetime":[41,489],"shell":[44,491],"directly":[46,541],"from":[47,144,198,480],"target":[49,482],"triple":[50,483],"(mass,":[51,484],"texture,":[52,485],"redshift),":[53,486],"realizing":[54],"flat":[56,108],"cabin":[57],"in":[58,104,348,358],"interior.":[60],"To":[61],"end,":[63],"we":[64],"establish":[65],"\\textbf{Anyang":[67],"Elliptic":[68],"Constraint":[69],"Mapping":[70],"theory":[71,76],"(AECM)},":[72],"boundary":[74,146,244],"encoding":[75,170],"grown":[77],"out":[78,161],"of":[79,83,89,129,133,148,220,224,237,246,260,293,369,420,439,461,501,515,520,534,551,569],"constraint":[81,111],"equations":[82,112],"general":[84,561],"relativity":[85],"(the":[86,465],"elliptic":[87,153],"sector":[88],"3+1":[91],"decomposition,":[92],"which":[93,119,527],"precedes":[94,171],"evolution":[95,101],"must":[97],"be":[98],"satisfied":[99],"before":[100],"can":[102],"unfold):":[103],"conformally":[107],"sector,":[109],"compress":[113],"into":[114,190,240,458],"single":[116,192],"Lichnerowicz":[117],"equation,":[118],"under":[120],"$u=\\psi-1$":[121],"$\\sigma=\\rho\\psi^5/2$":[123],"becomes,":[124],"verbatim,":[125],"Poisson":[127],"equation":[128,514],"AECM":[130],"(two":[131],"names":[132],"same":[135,231,356],"equation).":[136],"The":[137,230,418,531,567],"exterior":[138],"geometry":[139,204],"is":[140,168,376,423,497,539,580],"then":[141],"uniquely":[142],"determined":[143],"data":[147],"diagnostic":[150],"surface":[151,321],"by":[152,314,352,378,542],"development,":[154],"all":[156,415,454],"global":[157],"quantities":[158],"are":[159,414,509,529,558,563],"read":[160],"mode-by-mode":[162,257],"along":[163],"Dirichlet-to-Neumann":[165],"spectrum:":[166],"\\textbf{constraint":[167],"encoding;":[169],"evolution}.":[172],"This":[173],"reveals":[174],"two":[175,459],"counterintuitive":[176],"facts:":[177],"first,":[178],"Newton's":[179],"structure":[180,464],"survives":[181],"exactly":[182],"at":[183,575],"coding":[185],"level":[186],"(Einstein's":[187],"nonlinearity":[188],"compressed":[189],"algebraic":[193],"factor":[194],"$\\sigma=\\rho\\psi^5/2$;":[195],"map":[197],"physical":[199,344],"density":[200,345],"external":[203],"remains":[205],"nonlinear":[207],"fixed":[208],"point);":[209],"second,":[210],"shaping":[212],"capacity":[213],"depends":[214],"only":[215,505],"angular":[218],"distribution":[219],"source,":[222],"independent":[223],"radial":[225],"details":[226],"(radial":[227],"degeneracy":[228],"theorem).":[229],"spectral":[232],"readout":[233],"unifies":[234,453],"family":[236,401,500],"classical":[238],"problems":[239],"corollaries:":[241],"explicit":[243,316,380],"versions":[245],"positive":[248,253],"mass":[249,254,466],"charged":[252,398,406],"($M\\ge|Q_e|$),":[255],"pricing":[258],"$4(\\ell+2)$":[259],"Penrose":[262],"texture":[263,371],"deficit,":[264],"throat":[266],"area":[267],"correction":[268],"$\\kappa=-128/35$,":[269],"static-extension":[271],"rigidity,":[272],"CF--Bartnik":[275],"mass.":[276],"Along":[277],"framework,":[279],"precursor":[282],"receives":[283],"threefold":[285],"verdict.":[286],"\\textbf{(i)":[287],"Feasible}:":[288],"quadrupole":[290,370],"moment":[291,330],"ratio":[292,331],"WEC":[294],"sources":[295,325],"satisfies":[296],"universal":[298],"window":[299,306,341],"$[-\\frac12,1]$":[300],"spectrally":[303],"pure":[304],"sharp":[305],"$[-\\frac15,\\frac25]$":[307],"(in":[308],"closure":[310],"sense),":[311],"saturated":[312],"pointwise":[313],"extremal":[317],"configuration":[318],"$\\sigma\\propto3\\cos^2\\theta$":[319],"(thin-shell":[320],"source;":[322],"smooth":[323],"volume":[324],"approximate":[326],"but":[327,428],"never":[328],"attain)\\footnote{The":[329],"$\\epsilon_\\ell=a_\\ell/(M_{\\rm":[332],"math}R^\\ell)$":[333],"holds":[334],"for":[335,342],"effective":[337],"source":[338],"$\\sigma$;":[339],"$\\rho$":[346],"follows":[347],"Corollary":[349],"\\ref{cor:rho-window}":[350],"(normalized":[351],"$M_{\\rm":[353,469],"ADM}$,":[354],"interval":[357],"field).};":[361],"\\textbf{(ii)":[362],"Blocked}:":[363],"purely":[365],"gravitational":[366],"extension":[368],"inside":[372],"CF":[374],"class":[375,438],"refuted":[377],"an":[379],"obstruction":[381],"tensor":[382],"(point":[383],"value":[384],"$1/3888$);":[385],"\\textbf{(iii)":[386],"Existence":[387],"escape}:":[389],"spherically":[391,399],"symmetric":[392,400],"neutral":[393,537],"bubble":[394,408,572],"(full-spacetime":[395],"WEC),":[396],"($e/m\\in[0,1]$),":[402],"arbitrarily-shaped":[405,536],"MP":[407],"(strictly":[409],"Minkowski":[410],"cabin,":[411],"full-spacetime":[412],"WEC/DEC)":[413],"exact":[416],"solutions.":[417],"endpoint":[419],"not":[424],"abstract":[425],"existence":[426,432,445,533,554],"theorems,":[427],"\\textbf{physical":[429],"realizability}:":[430],"constructive":[431,532],"methods.":[435],"For":[436],"each":[437],"targets,":[440],"\\textbf{constructive":[444],"methods}:":[448],"negative-frame":[450,544],"locking":[451,545],"theorem":[452],"flat-cabin":[456],"bubbles":[457],"branches":[460],"conductor-potential":[463],"function":[467],"law":[468],"ADM}=f(N)C(\\Sigma)$,":[470],"$\\ln(1/N)$":[471],"neutral,":[472],"$1/N-1$":[473],"charged);":[474],"five-step":[476],"construction":[477,548],"algorithm":[478],"builds,":[479],"matter;":[492],"unique":[493],"when":[494,504],"shape":[496],"given,":[498],"equivalent":[502],"realizations":[503],"finitely":[506],"many":[507],"moments":[508],"given;":[510],"geometrically":[512],"induced":[513],"state":[516],"identifies":[517],"material":[519],"shell;":[522],"realization-domain":[524],"criterion":[525],"delimits":[526],"targets":[528],"feasible.":[530],"cell":[538],"given":[540],"algorithm,":[549],"\\textbf{independent":[550],"any":[552],"hypothetical":[553],"theorem}":[555],"(axisymmetric":[556],"shapes":[557,562],"strict":[559],"theorems;":[560],"numerically":[564],"verified,":[565],"\\S19).":[566],"ship":[568],"floats":[573],"first":[574],"level;":[578],"navigation":[579],"left":[581],"follow-up":[584],"series.":[585]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-24T00:00:00"}