{"id":"https://openalex.org/W7225187449","doi":"https://doi.org/10.5281/zenodo.23929277","title":"The Unwritten Page: The First-Order Variation of the Henneaux\u2013Teitelboim Einstein\u2013Cartan Action, and the Solution Space of Experiment Two in Unimodular Gauge","display_name":"The Unwritten Page: The First-Order Variation of the Henneaux\u2013Teitelboim Einstein\u2013Cartan Action, and the Solution Space of Experiment Two in Unimodular Gauge","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225187449","doi":"https://doi.org/10.5281/zenodo.23929277"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23929277","doi":"https://doi.org/10.5281/zenodo.23929277","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23929277","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.23929277","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159396451","display_name":"William Alexander Aldred","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aldred, William Alexander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1215-577X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159396451"],"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.9077000021934509,"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":0.9077000021934509,"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":0.04690000042319298,"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"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.0348999984562397,"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/einstein-cartan-theory","display_name":"Einstein-Cartan theory","score":0.8709999918937683},{"id":"https://openalex.org/keywords/unimodular-gravity","display_name":"unimodular gravity","score":0.9639999866485596},{"id":"https://openalex.org/keywords/torsion","display_name":"torsion","score":0.5130000114440918},{"id":"https://openalex.org/keywords/solution-space","display_name":"solution space","score":0.7129999995231628},{"id":"https://openalex.org/keywords/boundary-terms","display_name":"boundary terms","score":0.460999995470047},{"id":"https://openalex.org/keywords/first-order-formalism","display_name":"first-order formalism","score":0.44699999690055847},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.9455000162124634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5735999941825867},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5699999928474426},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C147727578","wikidata":"https://www.wikidata.org/wiki/Q7706297","display_name":"Tetrad","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C2993043157","wikidata":"https://www.wikidata.org/wiki/Q4949967","display_name":"Boundary line","level":2,"score":0.3594000041484833},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2980000078678131},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2653000056743622},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2779017129","wikidata":"https://www.wikidata.org/wiki/Q660651","display_name":"Memorandum","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C202532154","wikidata":"https://www.wikidata.org/wiki/Q4374193","display_name":"Problem statement","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23929277","doi":"https://doi.org/10.5281/zenodo.23929277","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23929277","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.23929278","doi":"https://doi.org/10.5281/zenodo.23929278","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23929278","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.23929277","doi":"https://doi.org/10.5281/zenodo.23929277","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23929277","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/W2785893110","https://openalex.org/W4402386247","https://openalex.org/W2561561375","https://openalex.org/W7100024790","https://openalex.org/W4205605395","https://openalex.org/W4417210149","https://openalex.org/W1979738913","https://openalex.org/W3151735493","https://openalex.org/W7155212086","https://openalex.org/W2761992601"],"abstract_inverted_index":{"Paper":[0],"#2":[1,133],"of":[2,92,151,254,263,311,449,469,549,568,593],"this":[3,302,342],"corpus,":[4],"Two":[5],"Bounds":[6],"and":[7,25,33,40,61,116,161,176,198,236,317,341,377,453,457,501,536,574,581,590],"an":[8,34,413,524,529],"Integration":[9],"Constant,":[10],"states":[11],"its":[12,46,81,242,362,428,439,495,533],"unimodular":[13,108,126,264,331],"Einstein\u2013Cartan":[14,230,517],"construction":[15],"in":[16,45,59,80,125,131,202,208,301,329,347,598],"four":[17],"lines":[18],"\u2014":[19,39,159,175,245,319,340,374,382,471,586,595],"vary":[20],"the":[21,26,29,42,76,93,97,102,111,118,128,148,152,179,183,185,192,194,209,215,222,228,233,255,259,266,270,275,281,285,290,304,308,320,330,337,355,359,378,383,391,402,450,458,498,502,510,521,537,547,552,559,563,569,575,582,587,591,604],"Henneaux\u2013Teitelboim":[22],"(HT)":[23],"action":[24,153],"traceless":[27,98,223,267,298],"equations,":[28],"unmodified":[30],"Cartan":[31,99,299,309,499],"equation,":[32,273,500],"integration":[35],"constant":[36,464],"fall":[37],"out":[38],"flags":[41],"general":[43,50],"derivation":[44,52],"own":[47,363],"text:":[48],"\"the":[49],"first-order":[51,87,149],"for":[53,121,368,405,509],"arbitrary":[54],"geometries":[55],"is":[56,110,241,269,278,296,352,366,390,409,475,519,523,528],"companion":[57],"work":[58],"preparation,":[60],"no":[62,297,324,397,505,515],"claim":[63],"below":[64],"depends":[65],"on":[66,354,427,491],"it.\"":[67],"The":[68],"design":[69],"memorandum":[70],"deposited":[71],"with":[72,396,412,480,532],"paper":[73,132,142,237,312,343],"#6":[74],"names":[75],"same":[77,286],"page":[78],"twice":[79],"one-week":[82],"build":[83,605],"plan:":[84],"\"(1)":[85],"full":[86,203,229,477],"(tetrad":[88],"+":[89],"connection)":[90],"variation":[91,150,166,218,277,306],"HT-EC":[94,478],"action,":[95],"displaying":[96],"equation":[100,224,231,268,300,310],"alongside":[101],"metric":[103],"one":[104,112,463],"(the":[105,350],"spin":[106,162,325,338,376,380,392,483,488,507],"sector's":[107],"behaviour":[109],"genuinely":[113],"unwritten":[114],"page)\"":[115],"\"(2)":[117],"solution-space":[119,180,403],"statement":[120,181,253,404],"Experiment":[122,406],"Two's":[123,407],"families":[124,408],"gauge,\"":[127],"second":[129],"flagged":[130],"as":[134,139,155,247,251,541,603],"\"a":[135],"to-verify,":[136],"not":[137,191,220,279,416,579,600],"asserted":[138],"proven.\"":[140],"This":[141],"writes":[143],"that":[144,492],"page.":[145],"It":[146],"carries":[147,423],"exactly":[154,455,602],"I":[156,212,372],"print":[157],"it":[158,177,226,542],"tetrad":[160,217,272],"connection":[163,305],"independent,":[164],"every":[165,168,420],"shown,":[167],"boundary":[169],"term":[170,322,385],"displayed":[171],"rather":[172,204],"than":[173,205],"dropped":[174],"proves":[178],"at":[182,399],"precision":[184],"memos":[186],"need.":[187],"Three":[188],"findings":[189],"are":[190,200,447,454,460,596],"ones":[193],"memos'":[195],"shorthand":[196],"suggests,":[197],"they":[199],"printed":[201,440],"harmonized.":[206],"First,":[207],"HT":[210,321,425],"form":[211,262,349],"actually":[213],"use,":[214],"direct":[216],"does":[219],"yield":[221],"alone:":[225],"yields":[227,307],"carrying":[232],"multiplier":[234],"field,":[235],"#2's":[238],"Eq.":[239,314,345],"(9)":[240],"trace-free":[243],"projection":[244],"correct":[246],"a":[248,252,410,417,473,476,481,487],"projection,":[249],"incomplete":[250],"whole":[256,271,316],"variation.":[257],"(In":[258],"strict,":[260],"constrained-determinant":[261],"gravity":[265,573],"because":[274],"trace":[276,360,384],"free;":[280],"two":[282],"forms":[283],"have":[284],"solution":[287,479,518],"space":[288],"under":[289],"conditions":[291],"proved":[292],"here.)":[293],"Second,":[294],"there":[295],"action:":[303],"#2,":[313],"(10),":[315],"unprojected":[318],"contains":[323],"connection,":[326],"so":[327,388],"nothing":[328],"sector":[332,339],"touches,":[333],"traces,":[334],"or":[335,561,565],"projects":[336],"solves":[344,434],"(10)":[346],"closed":[348],"operator":[351],"invertible":[353],"24-dimensional":[356],"torsion":[357,389],"space;":[358],"coefficient":[361],"contraction":[364],"forces":[365],"1/4;":[367],"both":[369],"source":[370,484],"classes":[371],"use":[373],"Dirac":[375],"Weyssenhoff":[379],"fluid":[381],"vanishes":[386],"identically,":[387],"tensor":[393,489,508],"times":[394],"\u03ba\u00b2":[395],"correction":[398],"all).":[400],"Third,":[401],"theorem":[411],"obstruction":[414],"attached,":[415],"blanket":[418],"verification:":[419],"family":[421,522],"member":[422,474],"explicit":[424],"data":[426],"stationary":[429],"chart":[430],"(\u03c4^t":[431],"=":[432,436],"t\u00b7e":[433],"\u2202_\u03bc\u03c4^\u03bc":[435],"e":[437],"there),":[438],"completion":[441],"numbers":[442],"(horizons,":[443],"surface":[444],"gravities,":[445],"a_max)":[446],"functionals":[448],"geometry":[451,493],"alone":[452],"unchanged,":[456],"lifts":[459],"fibered":[461],"by":[462],"\u039b_int":[465,594],"per":[466],"connected":[467],"component":[468],"spacetime":[470],"but":[472],"physical":[482],"only":[485],"if":[486],"exists":[490],"reproducing":[494],"pressures":[496],"through":[497],"record":[503],"owns":[504],"such":[506],"rotating":[511,516],"members":[512],"(paper":[513],"#1:":[514],"known;":[520],"ansatz).":[525],"That":[526],"step":[527],"obstruction,":[530],"named":[531],"missing":[534],"input,":[535],"proof":[538],"stops":[539],"there,":[540],"must.":[543],"Nothing":[544],"here":[545],"derives":[546],"value":[548,564],"\u039b_int,":[550],"matches":[551],"conjugate":[553],"pair":[554],"(\u039b_int,":[555],"\u222be":[556],"d\u2074x)":[557],"across":[558],"bounce,":[560],"touches":[562],"coincidence":[566],"tiers":[567],"vacuum":[570,576],"problem;":[571],"quantum":[572,584],"catastrophe":[577],"remain":[578],"solved,":[580,601],"memorandum's":[583],"caveats":[585],"path-integral":[588],"measure":[589],"superselection":[592],"stated":[597],"\u00a78,":[599],"plan":[606],"ordered.":[607]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}
