{"id":"https://openalex.org/W7130851671","doi":"https://doi.org/10.5281/zenodo.18724775","title":"Information Manifolds and Pencil Projections: Structural Rigidity and Symmetry Invariants in the Prime Lattice Modulo-12","display_name":"Information Manifolds and Pencil Projections: Structural Rigidity and Symmetry Invariants in the Prime Lattice Modulo-12","publication_year":2026,"publication_date":"2026-02-21","ids":{"openalex":"https://openalex.org/W7130851671","doi":"https://doi.org/10.5281/zenodo.18724775"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.18724775","doi":"https://doi.org/10.5281/zenodo.18724775","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18724775","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.18724775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065759296","display_name":"Silvio Gabbianelli","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gabbianelli, Silvio","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0007-3329-5270","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5065759296"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.0003000000142492354,"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":0.0,"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/prime-numbers","display_name":"prime numbers","score":0.8679999709129333},{"id":"https://openalex.org/keywords/prime-number-distribution","display_name":"prime number distribution","score":0.8920000195503235},{"id":"https://openalex.org/keywords/composite-numbers","display_name":"composite numbers","score":0.7929999828338623},{"id":"https://openalex.org/keywords/twin-primes","display_name":"twin primes","score":0.7269999980926514},{"id":"https://openalex.org/keywords/goldbach-partitions","display_name":"Goldbach partitions","score":0.9169999957084656},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.9079999923706055},{"id":"https://openalex.org/keywords/structural-rigidity","display_name":"structural rigidity","score":0.7179999947547913}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6376000046730042},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5792999863624573},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.45260000228881836},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44749999046325684},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.4284999966621399},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42250001430511475},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.4203000068664551},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C143352335","wikidata":"https://www.wikidata.org/wiki/Q110863","display_name":"Twin prime","level":3,"score":0.3375999927520752},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.3325999975204468},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C120561534","wikidata":"https://www.wikidata.org/wiki/Q724975","display_name":"Gaussian integer","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.3052999973297119},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30309998989105225},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.251800000667572},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5281/zenodo.18724775","doi":"https://doi.org/10.5281/zenodo.18724775","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18724775","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.18724776","doi":"https://doi.org/10.5281/zenodo.18724776","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18724776","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.18733106","doi":"https://doi.org/10.5281/zenodo.18733106","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18733106","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.19458069","doi":"https://doi.org/10.5281/zenodo.19458069","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19458069","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.18724775","doi":"https://doi.org/10.5281/zenodo.18724775","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18724775","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7125912795","https://openalex.org/W7143428071","https://openalex.org/W7139985054","https://openalex.org/W7156852064","https://openalex.org/W7104393623","https://openalex.org/W7171866711","https://openalex.org/W7162989074","https://openalex.org/W7222798277","https://openalex.org/W7162947214","https://openalex.org/W7117360319"],"abstract_inverted_index":{"For":[0],"over":[1],"two":[2],"millennia,":[3],"prime":[4,116],"numbers":[5],"have":[6],"been":[7],"regarded":[8],"as":[9,104],"the":[10,29,36,44,68,72,92,105,113,120,123,153,164,175,181,191,203],"ebellious":[11],"\u201catoms\u201d":[12],"of":[13,31,39,71,95,115,135,145,158,166,177,183,190],"arithmetic,":[14],"whose":[15],"distribution":[16,30],"is":[17,155],"governed":[18],"by":[19],"probabilistic":[20],"laws":[21],"or":[22],"inherent":[23],"chaos.":[24],"This":[25,138,194],"paper":[26],"demonstrates":[27],"that":[28,111,152,174],"primes":[32,167,179],"is,":[33],"in":[34,210],"fact,":[35],"deterministic":[37,150,199],"consequence":[38],"a":[40,60,88,100,133,141,149,169,197],"precise":[41],"geometric":[42,188],"architecture:":[43],"Manifold":[45],"12.":[46],"By":[47],"mapping":[48],"every":[49],"positive":[50],"odd":[51],"integer":[52],"n":[53],"(excluding":[54],"3":[55],"and":[56,180,206],"its":[57],"multiples)":[58],"to":[59,132],"discrete":[61],"position":[62],"p":[63],"=":[64,76],"(n\u22121)/2,":[65],"we":[66,98],"analyze":[67],"obstructing":[69],"action":[70],"\u201cPencilof":[73],"Lines\u201d":[74],"y":[75],"kx":[77],"+":[78],"(k":[79],"\u2212":[80],"1)/2\u2014the":[81],"parametric":[82],"function":[83],"representing":[84],"composite":[85],"numbers.":[86],"Through":[87],"deep-scan":[89],"analysis":[90],"at":[91],"trans-computational":[93],"scale":[94],"10^100":[96],"(Googol),":[97],"identify":[99],"structural":[101],"phenomenon":[102],"defined":[103],"raking":[106],"Effect.":[107],"Computational":[108],"evidence":[109],"confirms":[110],"while":[112],"density":[114,125],"singularities":[117],"decreases":[118],"logarithmically,":[119],"derivative":[121],"f":[122],"obstruction":[124],"(\u03a6\u2032)":[126],"vanishes":[127],"asymptotically":[128],"(\u2248":[129],"10^\u2212107),":[130],"leading":[131],"state":[134],"Geometric":[136],"Inertia.":[137],"effect":[139],"ensures":[140],"stabilized":[142],"residual":[143],"porosity":[144],"\u2248":[146],"0.0025%,":[147],"providing":[148],"proof":[151],"Pencil":[154],"structurally":[156],"incapable":[157],"achieving":[159],"total":[160],"saturation.These":[161],"results":[162],"transform":[163],"study":[165],"into":[168],"rigorous":[170],"topological":[171],"framework,":[172],"proving":[173],"infinitude":[176],"twin":[178],"persistence":[182],"Goldbach":[184],"partitions":[185],"are":[186],"mandatory":[187],"consequences":[189],"lattice":[192],"symmetry.":[193],"model":[195],"offers":[196],"new":[198],"pathway":[200],"for":[201],"resolving":[202],"Riemann":[204],"Hypothesis":[205],"other":[207],"long-standing":[208],"enigmas":[209],"number":[211],"theory":[212]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-02-22T00:00:00"}