{"id":"https://openalex.org/W7225095258","doi":"https://doi.org/10.5281/zenodo.23898406","title":"Seven Formal Structures Mirroring E=mc^2: An Educational Exploration of Geometric, Entropic, Noetherian, Optimal Transport, Categorical, Algorithmic and Game-Theoretic Analogies - Details + Assumption Tables","display_name":"Seven Formal Structures Mirroring E=mc^2: An Educational Exploration of Geometric, Entropic, Noetherian, Optimal Transport, Categorical, Algorithmic and Game-Theoretic Analogies - Details + Assumption Tables","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225095258","doi":"https://doi.org/10.5281/zenodo.23898406"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23898406","doi":"https://doi.org/10.5281/zenodo.23898406","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23898406","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23898406","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158691077","display_name":"Robert Aaron Tseglin","orcid":"https://orcid.org/0000-0002-7898-1393","observed_orcids":["https://orcid.org/0000-0002-7898-1393"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tseglin, Robert Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158691077"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.81656224,"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":0.9531000256538391,"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":0.9531000256538391,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.03610000014305115,"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"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.00419999985024333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mass-energy-equivalence","display_name":"mass-energy equivalence","score":0.906000018119812},{"id":"https://openalex.org/keywords/speed-of-light","display_name":"speed of light","score":0.5740000009536743},{"id":"https://openalex.org/keywords/dimensional-analysis","display_name":"dimensional analysis","score":0.5450000166893005},{"id":"https://openalex.org/keywords/planck-length","display_name":"Planck length","score":0.7369999885559082},{"id":"https://openalex.org/keywords/planck-constant","display_name":"Planck constant","score":0.5049999952316284},{"id":"https://openalex.org/keywords/gravitational-constant","display_name":"gravitational constant","score":0.5440000295639038},{"id":"https://openalex.org/keywords/fine-structure-constant","display_name":"fine-structure constant","score":0.6050000190734863},{"id":"https://openalex.org/keywords/entropic-gravity","display_name":"entropic gravity","score":0.46399998664855957},{"id":"https://openalex.org/keywords/noether-s-theorem","display_name":"Noether's theorem","score":0.9110000133514404},{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.968999981880188},{"id":"https://openalex.org/keywords/category-theory","display_name":"category theory","score":0.7940000295639038},{"id":"https://openalex.org/keywords/game-theory","display_name":"game theory","score":0.7300000190734863},{"id":"https://openalex.org/keywords/bell-inequalities","display_name":"Bell inequalities","score":0.6320000290870667},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.4449999928474426},{"id":"https://openalex.org/keywords/codata","display_name":"CODATA","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C189645446","wikidata":"https://www.wikidata.org/wiki/Q350865","display_name":"Mirroring","level":2,"score":0.7035999894142151},{"id":"https://openalex.org/C80892491","wikidata":"https://www.wikidata.org/wiki/Q578555","display_name":"Noether's theorem","level":3,"score":0.5001999735832214},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.48980000615119934},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.426800012588501},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.414000004529953},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.4074999988079071},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3993000090122223},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3605000078678131},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33309999108314514},{"id":"https://openalex.org/C88018779","wikidata":"https://www.wikidata.org/wiki/Q1568269","display_name":"Unruh effect","level":3,"score":0.3276999890804291},{"id":"https://openalex.org/C194147245","wikidata":"https://www.wikidata.org/wiki/Q1076368","display_name":"Chord (peer-to-peer)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3052999973297119},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2865000069141388},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.25529998540878296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2524000108242035},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23898406","doi":"https://doi.org/10.5281/zenodo.23898406","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23898406","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.23898407","doi":"https://doi.org/10.5281/zenodo.23898407","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23898407","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.23898406","doi":"https://doi.org/10.5281/zenodo.23898406","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23898406","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/W7117878193","https://openalex.org/W7154990294","https://openalex.org/W2247474939","https://openalex.org/W7162992811","https://openalex.org/W138880961","https://openalex.org/W2062254479","https://openalex.org/W7096260326","https://openalex.org/W7202385112","https://openalex.org/W7164487025","https://openalex.org/W2078444157"],"abstract_inverted_index":{"Abstract":[0],"-":[1,6,18,61,85,116],"v13.0":[2,36],"ULTIMATE":[3],"HONEST":[4],"IMPROVED":[5],"All":[7],"Rigorous":[8],"Details":[9],"From":[10],"v2-v12":[11],"+":[12,15],"6":[13,49],"Improvements":[14],"Scientifically":[16],"Honest":[17,52],"Educational":[19],"Note:":[20],"We":[21],"examine":[22],"seven":[23],"mathematical":[24],"structures":[25],"that":[26],"formally":[27],"yield":[28],"an":[29,306],"expression":[30],"of":[31,312],"the":[32],"form":[33],"E=m\u00b7v^2.":[34],"This":[35,304],"includes":[37],"ALL":[38],"rigorous":[39],"details":[40],"from":[41,143],"v2":[42],"through":[43],"v12":[44],"with":[45,171],"maximum":[46],"detail,":[47],"plus":[48],"improvements:":[50],"1.":[51],"title":[53],"no":[54,121],"longer":[55],"claims":[56],"independent":[57,84],"derivation":[58],"without":[59],"relativity":[60],"now":[62],"\"Seven":[63],"Formal":[64],"Structures":[65],"Mirroring":[66],"E=mc^2\"2.":[67],"Explicit":[68,174],"assumption":[69],"table":[70],"for":[71],"each":[72],"proof":[73],"stating":[74],"where":[75],"c":[76],"enters":[77],"(l_p^2=\u0127G/c^3":[78],"contains":[79],"c,":[80],"etc.)":[81],"and":[82],"whether":[83],"No,":[86],"consistency":[87],"check":[88],"only3.":[89],"Dimensional":[90],"analysis":[91],"[E]=J,":[92],"[m]=kg,":[93],"[c]=m/s,":[94],"[l_p]=m,":[95],"[l_c]=m,":[96],"[\u03c1_m]=kg/m^3,":[97],"[\u03c1_m|v|^2]=J/m^34.":[98],"6\u03c0^5=1836.1181087116884":[99],"bare":[100],"vs":[101,131],"CODATA":[102],"2022":[103],"1836.15267343(11)":[104],"diff":[105],"0.0345647183116":[106],"relative":[107],"1.8826e-5=0.00188%=18.826":[108],"ppm":[109],"=":[110],"340x":[111],"experimental":[112],"uncertainty":[113],"0.055":[114],"ppb":[115],"interesting":[117],"numerology,":[118],"not":[119,141,222,309],"physics,":[120],"QCD":[122],"mechanism,":[123],"false":[124],"4e-7":[125],"claim":[126,311],"1838.25\u22601836.15":[127],"removed5.":[128],"Bell":[129,301],"V(90)=0":[130],"QM":[132],"V=1":[133,147,302],"moved":[134],"to":[135],"Appendix":[136],"C":[137],"as":[138],"failed":[139],"attempt:":[140],"derived":[142,209],"Lagrangian,":[144],"standard":[145],"QED":[146],"already":[148,166],"confirmed":[149],">99%":[150],"thousands":[151],"experiments":[152],"Kwiat":[153,297],"PRL":[154,246,298],"75,4337,":[155],"Poisson":[156],"error":[157],"10^4":[158],"coincidences":[159],"\u03c3N=100":[160],"\u03c3V=1%":[161],"100\u03c3":[162],"separation":[163],"but":[164],"experiment":[165],"done":[167],"result":[168],"V\u224816.":[169],"Bibliography":[170],"volumes":[172],"DOIs":[173],"numeric:":[175],"\u03c0=3.141592653589793,":[176],"\u03c0^2=9.869604401089358,":[177],"\u03c0^3=31.00627668029982,":[178],"\u03c0^4=97.40909103400243,":[179],"\u03c0^5=306.0196847852814\u00d76=1836.1181087116884.":[180],"Check":[181],"32\u03c0^4=3117.0909130887777\u00d70.5890486225480862=1836.1181087116884=6\u03c0^5.":[182],"Volume":[183],"integral":[184],"\u221adet":[185],"g=R1R2R3R^2":[186],"sin\u03c6,":[187],"Vol=\u222b0^{2\u03c0}d\u03b81\u222b0^{2\u03c0}d\u03b82\u222b0^{2\u03c0}d\u03b83\u222b0^\u03c0":[188],"sin\u03c6":[189],"d\u03c6\u222b0^{2\u03c0}d\u03c8=32\u03c0^4R1R2R3R^2":[190],"via":[191],"\u222b0^\u03c0":[192],"sin\u03c6=2.":[193],"Quantization":[194],"Ri=ni":[195],"lp":[196],"Bohr-Sommerfeld":[197],"\u222epdx=2\u03c0\u0127n,":[198],"minimal":[199],"ni=1":[200],"=>":[201,214],"Ri=lp,":[202],"Dirac":[203],"c1=3":[204],"U(1)^3":[205],"\u222bS^2":[206],"F=2\u03c0c1,":[207],"\u03c0/8":[208],"Vol(S^2)=4\u03c0,":[210],"Vol((S^1)^3)=8\u03c0^3,":[211],"ratio":[212],"1/2\u03c0^2\u00d76=3\u03c0/16":[213],"R^2=3\u03c0/16":[215],"lp^2":[216],"theorem":[217],"within":[218],"KK":[219],"assumptions":[220],"(modulus":[221],"fixed":[223],"by":[224],"topology":[225],"alone),":[226],"Vol=6\u03c0^5":[227],"lp^5":[228],"corollary.":[229],"References:":[230],"Bekenstein":[231],"Phys":[232],"Rev":[233],"D7,2333":[234],"DOI:10.1103/PhysRevD.7.2333,":[235],"Unruh":[236],"D14,870":[237],"Eq.2.8":[238],"p.873":[239],"DOI:10.1103/PhysRevD.14.870,":[240],"Verlinde":[241],"JHEP":[242],"1104,029":[243],"DOI:10.1007/JHEP04(2011)029,":[244],"Jacobson":[245],"75,1260":[247],"DOI:10.1103/PhysRevLett.75.1260,":[248],"Noether":[249],"Nachr":[250],"235,":[251],"Benamou-Brenier":[252],"Numer":[253],"Math":[254,270,276,282],"84,375,":[255],"Villani":[256],"Springer":[257],"Thm":[258,265,278],"8.1":[259],"p.294":[260],"Eq.8.2":[261],"p.295,":[262],"Etingof":[263],"AMS":[264],"4.3.1":[266],"p.89,":[267],"Wigner":[268],"Ann":[269,283],"40,149":[271],"P^2=-m^2c^2,":[272],"Sion":[273],"Pacific":[274],"J":[275,287],"8,171":[277],"3.3,":[279],"von":[280],"Neumann":[281],"100,295,":[284],"Landauer":[285],"IBM":[286],"Res":[288],"Dev":[289],"5,183,":[290],"Tadaki":[291],"STACS":[292],"Eq.7":[293],"p.15":[294],"Eq.3.8":[295],"p.12,":[296],"75,4337":[299],"DOI:10.1103/PhysRevLett.75.4337":[300],"confirmed.":[303],"is":[305],"educational":[307],"note,":[308],"a":[310],"new":[313],"physics.":[314],"License":[315],"CC":[316],"BY":[317],"4.0.":[318]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-03T00:00:00"}
