Axiom Zero: Laws, Principles, and Rules of Structure Article Swipe
This paper is a structural companion to the foundational Axiom Zero manuscript “Axiom Zero: Structural Irreducibility and the Unpredictability of Primes.” It assumes familiarity with the core AZ framework (survivors, cover sets, horizon windows, the triadic law, and completeness) and is not intended as a first introduction. New readers should begin with the main AZ paper and then return here as needed for definitions and structural laws. Working within the Axiom Zero viewpoint, this note makes explicit the “laws of motion” that govern survivors and horizons. It collects and systematizes a small set of additional principles—uniformity, non-extinction, finite-injury, and related structural rules—that control how survivors distribute across residue classes, how channels behave across horizons, and how local updates interact with global density. From these, together with the original AZ axioms, it derives horizon mass laws, variance and discrepancy bounds in residue classes, additive horizon decompositions, and carrier–shadow descriptions. The aim is not to settle any specific classical conjecture here, but to provide a reusable structural toolkit for later AZ applications to additive questions, correlation patterns, and gap phenomena in the primes. For orientation and cross-references, readers may also wish to consult the companion AZ studies: Axiom Zero: Structural Irreducibility and the Unpredictability of Primes — DOI: 10.5281/zenodo.16998285 Conservativity of Axiom Zero over N — DOI: 10.5281/zenodo.17073211 Analytic Conservativity of Axiom Zero — DOI: 10.5281/zenodo.17073257 Contribution Classes and Horizon Contribution — DOI: 10.5281/zenodo.17110018 Euclid–Euler in Axiom Zero: Even Perfect Numbers from Structural Arithmetic — DOI: 10.5281/zenodo.17728314 Lagrange in Axiom Zero: Four Squares from Structural Arithmetic -- DOI: 10.5281/zenodo.17728407 Together, these works position Axiom Zero as a structural complement to classical analytic and sieve-theoretic approaches, rather than a replacement. For questions or comments, contact: [email protected] Version update note. This version does not change any of the underlying mathematics, computations, or stated results. The update is purely logical and expository: The former “Non-Extinction Axiom” is now presented as a Non-Extinction Theorem, proved from the existing AZ structural machinery together with standard classical inputs. The former “Uniformity Axiom” and “Finite-Injury Schema” are now explicitly labeled as the Uniformity Conjecture and Finite-Injury Conjecture, respectively. Their statements are unchanged in spirit, but their status is now clearly conjectural rather than axiomatic. References, terminology, and dependency labels in the main text and appendices have been adjusted to match this bookkeeping (e.g. results now state precisely when they depend on the Non-Extinction Theorem and/or on the Uniformity / Finite-Injury conjectures). All previously claimed theorems, numerical examples, and structural laws remain the same; the revision is intended to make the logical landscape more transparent and to avoid asking readers to accept additional axioms on faith.
Related Topics
Concepts
Mathematics
Axiom
Axiom of choice
Zermelo–Fraenkel set theory
Conjecture
Urelement
Irreducibility
Zero (linguistics)
Set (abstract data type)
Continuum hypothesis
Mathematical economics
Axiom independence
Discrete mathematics
Core (optical fiber)
Pure mathematics
Core model
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.5281/zenodo.17842876
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7109649628
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W7109649628Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.5281/zenodo.17842876Digital Object Identifier
- Title
-
Axiom Zero: Laws, Principles, and Rules of StructureWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-12-06Full publication date if available
- Authors
-
Chiles, NathanList of authors in order
- Landing page
-
https://doi.org/10.5281/zenodo.17842876Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17842876Direct OA link when available
- Concepts
-
Mathematics, Axiom, Axiom of choice, Zermelo–Fraenkel set theory, Conjecture, Urelement, Irreducibility, Zero (linguistics), Set (abstract data type), Continuum hypothesis, Mathematical economics, Axiom independence, Discrete mathematics, Core (optical fiber), Pure mathematics, Core modelTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
Full payload
| id | https://openalex.org/W7109649628 |
|---|---|
| doi | https://doi.org/10.5281/zenodo.17842876 |
| ids.doi | https://doi.org/10.5281/zenodo.17842876 |
| ids.openalex | https://openalex.org/W7109649628 |
| fwci | |
| type | preprint |
| title | Axiom Zero: Laws, Principles, and Rules of Structure |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C33923547 |
| concepts[0].level | 0 |
| concepts[0].score | 0.7519177198410034 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[0].display_name | Mathematics |
| concepts[1].id | https://openalex.org/C167729594 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7275226712226868 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q17736 |
| concepts[1].display_name | Axiom |
| concepts[2].id | https://openalex.org/C151797676 |
| concepts[2].level | 4 |
| concepts[2].score | 0.581447958946228 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q179692 |
| concepts[2].display_name | Axiom of choice |
| concepts[3].id | https://openalex.org/C51460 |
| concepts[3].level | 5 |
| concepts[3].score | 0.5581449866294861 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q191849 |
| concepts[3].display_name | Zermelo–Fraenkel set theory |
| concepts[4].id | https://openalex.org/C2780990831 |
| concepts[4].level | 2 |
| concepts[4].score | 0.4351917803287506 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q319141 |
| concepts[4].display_name | Conjecture |
| concepts[5].id | https://openalex.org/C78550038 |
| concepts[5].level | 5 |
| concepts[5].score | 0.4270363450050354 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1896657 |
| concepts[5].display_name | Urelement |
| concepts[6].id | https://openalex.org/C2776823524 |
| concepts[6].level | 2 |
| concepts[6].score | 0.40489524602890015 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q6073561 |
| concepts[6].display_name | Irreducibility |
| concepts[7].id | https://openalex.org/C2780813799 |
| concepts[7].level | 2 |
| concepts[7].score | 0.40459927916526794 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q3274237 |
| concepts[7].display_name | Zero (linguistics) |
| concepts[8].id | https://openalex.org/C177264268 |
| concepts[8].level | 2 |
| concepts[8].score | 0.38465046882629395 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q1514741 |
| concepts[8].display_name | Set (abstract data type) |
| concepts[9].id | https://openalex.org/C96488702 |
| concepts[9].level | 2 |
| concepts[9].score | 0.36579179763793945 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q208416 |
| concepts[9].display_name | Continuum hypothesis |
| concepts[10].id | https://openalex.org/C144237770 |
| concepts[10].level | 1 |
| concepts[10].score | 0.3633808195590973 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q747534 |
| concepts[10].display_name | Mathematical economics |
| concepts[11].id | https://openalex.org/C170088968 |
| concepts[11].level | 3 |
| concepts[11].score | 0.3626919090747833 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q4830547 |
| concepts[11].display_name | Axiom independence |
| concepts[12].id | https://openalex.org/C118615104 |
| concepts[12].level | 1 |
| concepts[12].score | 0.3546092212200165 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[12].display_name | Discrete mathematics |
| concepts[13].id | https://openalex.org/C2164484 |
| concepts[13].level | 2 |
| concepts[13].score | 0.3472740054130554 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q5170150 |
| concepts[13].display_name | Core (optical fiber) |
| concepts[14].id | https://openalex.org/C202444582 |
| concepts[14].level | 1 |
| concepts[14].score | 0.28008437156677246 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[14].display_name | Pure mathematics |
| concepts[15].id | https://openalex.org/C2780366209 |
| concepts[15].level | 2 |
| concepts[15].score | 0.2794540524482727 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q5170200 |
| concepts[15].display_name | Core model |
| keywords[0].id | https://openalex.org/keywords/axiom |
| keywords[0].score | 0.7275226712226868 |
| keywords[0].display_name | Axiom |
| keywords[1].id | https://openalex.org/keywords/axiom-of-choice |
| keywords[1].score | 0.581447958946228 |
| keywords[1].display_name | Axiom of choice |
| keywords[2].id | https://openalex.org/keywords/zermelo–fraenkel-set-theory |
| keywords[2].score | 0.5581449866294861 |
| keywords[2].display_name | Zermelo–Fraenkel set theory |
| keywords[3].id | https://openalex.org/keywords/conjecture |
| keywords[3].score | 0.4351917803287506 |
| keywords[3].display_name | Conjecture |
| keywords[4].id | https://openalex.org/keywords/urelement |
| keywords[4].score | 0.4270363450050354 |
| keywords[4].display_name | Urelement |
| keywords[5].id | https://openalex.org/keywords/irreducibility |
| keywords[5].score | 0.40489524602890015 |
| keywords[5].display_name | Irreducibility |
| language | en |
| locations[0].id | doi:10.5281/zenodo.17842876 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400562 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Zenodo (CERN European Organization for Nuclear Research) |
| locations[0].source.host_organization | https://openalex.org/I67311998 |
| locations[0].source.host_organization_name | European Organization for Nuclear Research |
| locations[0].source.host_organization_lineage | https://openalex.org/I67311998 |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | |
| locations[0].raw_type | article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | False |
| locations[0].is_published | |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | https://doi.org/10.5281/zenodo.17842876 |
| indexed_in | datacite |
| authorships[0].author.id | |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Chiles, Nathan |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Chiles, Nathan |
| authorships[0].is_corresponding | True |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.5281/zenodo.17842876 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-12-07T00:00:00 |
| display_name | Axiom Zero: Laws, Principles, and Rules of Structure |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-12-07T23:44:45.987378 |
| primary_topic | |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | doi:10.5281/zenodo.17842876 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400562 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Zenodo (CERN European Organization for Nuclear Research) |
| best_oa_location.source.host_organization | https://openalex.org/I67311998 |
| best_oa_location.source.host_organization_name | European Organization for Nuclear Research |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I67311998 |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | |
| best_oa_location.raw_type | article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | https://doi.org/10.5281/zenodo.17842876 |
| primary_location.id | doi:10.5281/zenodo.17842876 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400562 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Zenodo (CERN European Organization for Nuclear Research) |
| primary_location.source.host_organization | https://openalex.org/I67311998 |
| primary_location.source.host_organization_name | European Organization for Nuclear Research |
| primary_location.source.host_organization_lineage | https://openalex.org/I67311998 |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | |
| primary_location.raw_type | article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | https://doi.org/10.5281/zenodo.17842876 |
| publication_date | 2025-12-06 |
| publication_year | 2025 |
| referenced_works_count | 0 |
| abstract_inverted_index./ | 399 |
| abstract_inverted_index.N | 212 |
| abstract_inverted_index.a | 3, 44, 90, 162, 264, 275, 315 |
| abstract_inverted_index.-- | 254 |
| abstract_inverted_index.AZ | 27, 54, 128, 168, 193, 322 |
| abstract_inverted_index.It | 21, 86 |
| abstract_inverted_index.as | 43, 60, 263, 314, 341 |
| abstract_inverted_index.in | 139, 178, 233, 246, 353, 370 |
| abstract_inverted_index.is | 2, 40, 150, 302, 311, 358, 416 |
| abstract_inverted_index.it | 130 |
| abstract_inverted_index.of | 19, 79, 93, 202, 208, 218, 292 |
| abstract_inverted_index.on | 391, 396, 434 |
| abstract_inverted_index.or | 279, 297 |
| abstract_inverted_index.to | 6, 152, 160, 170, 189, 267, 379, 418, 426, 430 |
| abstract_inverted_index.All | 402 |
| abstract_inverted_index.For | 181, 277 |
| abstract_inverted_index.New | 47 |
| abstract_inverted_index.The | 148, 300, 307, 330 |
| abstract_inverted_index.aim | 149 |
| abstract_inverted_index.and | 16, 37, 39, 56, 64, 84, 88, 98, 114, 136, 145, 175, 183, 199, 226, 270, 305, 334, 345, 367, 374, 408, 425 |
| abstract_inverted_index.any | 154, 291 |
| abstract_inverted_index.are | 337, 351 |
| abstract_inverted_index.but | 159, 355 |
| abstract_inverted_index.for | 62, 166 |
| abstract_inverted_index.gap | 176 |
| abstract_inverted_index.how | 103, 109, 115 |
| abstract_inverted_index.may | 186 |
| abstract_inverted_index.not | 41, 151, 289 |
| abstract_inverted_index.now | 312, 338, 359, 385 |
| abstract_inverted_index.set | 92 |
| abstract_inverted_index.the | 7, 17, 25, 34, 52, 69, 77, 126, 179, 191, 200, 293, 320, 342, 371, 392, 397, 412, 414, 420 |
| abstract_inverted_index.— | 204, 213, 221, 229, 242 |
| abstract_inverted_index.DOI: | 205, 214, 222, 230, 243, 255 |
| abstract_inverted_index.Even | 236 |
| abstract_inverted_index.Four | 249 |
| abstract_inverted_index.From | 122 |
| abstract_inverted_index.This | 0, 286 |
| abstract_inverted_index.Zero | 10, 71, 210, 220, 262 |
| abstract_inverted_index.also | 187 |
| abstract_inverted_index.been | 377 |
| abstract_inverted_index.core | 26 |
| abstract_inverted_index.does | 288 |
| abstract_inverted_index.from | 239, 251, 319 |
| abstract_inverted_index.have | 376 |
| abstract_inverted_index.here | 59 |
| abstract_inverted_index.law, | 36 |
| abstract_inverted_index.laws | 410 |
| abstract_inverted_index.main | 53, 372 |
| abstract_inverted_index.make | 419 |
| abstract_inverted_index.mass | 133 |
| abstract_inverted_index.more | 423 |
| abstract_inverted_index.note | 74 |
| abstract_inverted_index.over | 211 |
| abstract_inverted_index.text | 373 |
| abstract_inverted_index.than | 274, 363 |
| abstract_inverted_index.that | 81 |
| abstract_inverted_index.then | 57 |
| abstract_inverted_index.they | 389 |
| abstract_inverted_index.this | 73, 381 |
| abstract_inverted_index.when | 388 |
| abstract_inverted_index.wish | 188 |
| abstract_inverted_index.with | 24, 51, 119, 125, 326 |
| abstract_inverted_index.(e.g. | 383 |
| abstract_inverted_index.Axiom | 9, 70, 195, 209, 219, 234, 247, 261 |
| abstract_inverted_index.Their | 349 |
| abstract_inverted_index.Zero: | 13, 196, 235, 248 |
| abstract_inverted_index.avoid | 427 |
| abstract_inverted_index.begin | 50 |
| abstract_inverted_index.cover | 30 |
| abstract_inverted_index.first | 45 |
| abstract_inverted_index.here, | 158 |
| abstract_inverted_index.later | 167 |
| abstract_inverted_index.laws, | 134 |
| abstract_inverted_index.laws. | 66 |
| abstract_inverted_index.local | 116 |
| abstract_inverted_index.makes | 75 |
| abstract_inverted_index.match | 380 |
| abstract_inverted_index.note. | 285 |
| abstract_inverted_index.paper | 1, 55 |
| abstract_inverted_index.same; | 413 |
| abstract_inverted_index.sets, | 31 |
| abstract_inverted_index.small | 91 |
| abstract_inverted_index.state | 386 |
| abstract_inverted_index.their | 356 |
| abstract_inverted_index.these | 258 |
| abstract_inverted_index.works | 259 |
| abstract_inverted_index.Primes | 203 |
| abstract_inverted_index.accept | 431 |
| abstract_inverted_index.across | 106, 112 |
| abstract_inverted_index.and/or | 395 |
| abstract_inverted_index.asking | 428 |
| abstract_inverted_index.axioms | 433 |
| abstract_inverted_index.behave | 111 |
| abstract_inverted_index.bounds | 138 |
| abstract_inverted_index.change | 290 |
| abstract_inverted_index.depend | 390 |
| abstract_inverted_index.faith. | 435 |
| abstract_inverted_index.former | 308, 331 |
| abstract_inverted_index.global | 120 |
| abstract_inverted_index.govern | 82 |
| abstract_inverted_index.labels | 369 |
| abstract_inverted_index.needed | 61 |
| abstract_inverted_index.proved | 318 |
| abstract_inverted_index.purely | 303 |
| abstract_inverted_index.rather | 273, 362 |
| abstract_inverted_index.remain | 411 |
| abstract_inverted_index.return | 58 |
| abstract_inverted_index.settle | 153 |
| abstract_inverted_index.should | 49 |
| abstract_inverted_index.stated | 298 |
| abstract_inverted_index.status | 357 |
| abstract_inverted_index.these, | 123 |
| abstract_inverted_index.update | 284, 301 |
| abstract_inverted_index.within | 68 |
| abstract_inverted_index.Classes | 225 |
| abstract_inverted_index.Horizon | 227 |
| abstract_inverted_index.Numbers | 238 |
| abstract_inverted_index.Perfect | 237 |
| abstract_inverted_index.Squares | 250 |
| abstract_inverted_index.Theorem | 394 |
| abstract_inverted_index.Version | 283 |
| abstract_inverted_index.Working | 67 |
| abstract_inverted_index.assumes | 22 |
| abstract_inverted_index.axioms, | 129 |
| abstract_inverted_index.claimed | 404 |
| abstract_inverted_index.clearly | 360 |
| abstract_inverted_index.consult | 190 |
| abstract_inverted_index.control | 102 |
| abstract_inverted_index.derives | 131 |
| abstract_inverted_index.horizon | 32, 132, 143 |
| abstract_inverted_index.inputs. | 329 |
| abstract_inverted_index.labeled | 340 |
| abstract_inverted_index.logical | 304, 421 |
| abstract_inverted_index.primes. | 180 |
| abstract_inverted_index.provide | 161 |
| abstract_inverted_index.readers | 48, 185, 429 |
| abstract_inverted_index.related | 99 |
| abstract_inverted_index.residue | 107, 140 |
| abstract_inverted_index.results | 384 |
| abstract_inverted_index.spirit, | 354 |
| abstract_inverted_index.toolkit | 165 |
| abstract_inverted_index.triadic | 35 |
| abstract_inverted_index.updates | 117 |
| abstract_inverted_index.version | 287 |
| abstract_inverted_index.“laws | 78 |
| abstract_inverted_index.Analytic | 216 |
| abstract_inverted_index.Axiom” | 310, 333 |
| abstract_inverted_index.Lagrange | 245 |
| abstract_inverted_index.Theorem, | 317 |
| abstract_inverted_index.additive | 142, 171 |
| abstract_inverted_index.adjusted | 378 |
| abstract_inverted_index.analytic | 269 |
| abstract_inverted_index.channels | 110 |
| abstract_inverted_index.classes, | 108, 141 |
| abstract_inverted_index.collects | 87 |
| abstract_inverted_index.contact: | 281 |
| abstract_inverted_index.density. | 121 |
| abstract_inverted_index.existing | 321 |
| abstract_inverted_index.explicit | 76 |
| abstract_inverted_index.intended | 42, 417 |
| abstract_inverted_index.interact | 118 |
| abstract_inverted_index.original | 127 |
| abstract_inverted_index.position | 260 |
| abstract_inverted_index.results. | 299 |
| abstract_inverted_index.reusable | 163 |
| abstract_inverted_index.revision | 415 |
| abstract_inverted_index.specific | 155 |
| abstract_inverted_index.standard | 327 |
| abstract_inverted_index.studies: | 194 |
| abstract_inverted_index.together | 124, 325 |
| abstract_inverted_index.variance | 135 |
| abstract_inverted_index.windows, | 33 |
| abstract_inverted_index.“Axiom | 12 |
| abstract_inverted_index.Schema” | 336 |
| abstract_inverted_index.Together, | 257 |
| abstract_inverted_index.classical | 156, 268, 328 |
| abstract_inverted_index.comments, | 280 |
| abstract_inverted_index.companion | 5, 192 |
| abstract_inverted_index.examples, | 407 |
| abstract_inverted_index.framework | 28 |
| abstract_inverted_index.horizons, | 113 |
| abstract_inverted_index.horizons. | 85 |
| abstract_inverted_index.landscape | 422 |
| abstract_inverted_index.machinery | 324 |
| abstract_inverted_index.motion” | 80 |
| abstract_inverted_index.numerical | 406 |
| abstract_inverted_index.patterns, | 174 |
| abstract_inverted_index.phenomena | 177 |
| abstract_inverted_index.precisely | 387 |
| abstract_inverted_index.presented | 313 |
| abstract_inverted_index.questions | 278 |
| abstract_inverted_index.survivors | 83, 104 |
| abstract_inverted_index.theorems, | 405 |
| abstract_inverted_index.unchanged | 352 |
| abstract_inverted_index.Arithmetic | 241, 253 |
| abstract_inverted_index.Conjecture | 344 |
| abstract_inverted_index.Primes.” | 20 |
| abstract_inverted_index.Structural | 14, 197, 240, 252 |
| abstract_inverted_index.Uniformity | 343, 398 |
| abstract_inverted_index.additional | 94, 432 |
| abstract_inverted_index.appendices | 375 |
| abstract_inverted_index.axiomatic. | 364 |
| abstract_inverted_index.complement | 266 |
| abstract_inverted_index.conjecture | 157 |
| abstract_inverted_index.dependency | 368 |
| abstract_inverted_index.distribute | 105 |
| abstract_inverted_index.explicitly | 339 |
| abstract_inverted_index.manuscript | 11 |
| abstract_inverted_index.previously | 403 |
| abstract_inverted_index.questions, | 172 |
| abstract_inverted_index.statements | 350 |
| abstract_inverted_index.structural | 4, 65, 100, 164, 265, 323, 409 |
| abstract_inverted_index.underlying | 294 |
| abstract_inverted_index.viewpoint, | 72 |
| abstract_inverted_index.(survivors, | 29 |
| abstract_inverted_index.Conjecture, | 347 |
| abstract_inverted_index.References, | 365 |
| abstract_inverted_index.approaches, | 272 |
| abstract_inverted_index.bookkeeping | 382 |
| abstract_inverted_index.conjectural | 361 |
| abstract_inverted_index.correlation | 173 |
| abstract_inverted_index.definitions | 63 |
| abstract_inverted_index.discrepancy | 137 |
| abstract_inverted_index.expository: | 306 |
| abstract_inverted_index.familiarity | 23 |
| abstract_inverted_index.orientation | 182 |
| abstract_inverted_index.transparent | 424 |
| abstract_inverted_index.Contribution | 224, 228 |
| abstract_inverted_index.applications | 169 |
| abstract_inverted_index.foundational | 8 |
| abstract_inverted_index.mathematics, | 295 |
| abstract_inverted_index.replacement. | 276 |
| abstract_inverted_index.rules—that | 101 |
| abstract_inverted_index.systematizes | 89 |
| abstract_inverted_index.terminology, | 366 |
| abstract_inverted_index.Finite-Injury | 346, 400 |
| abstract_inverted_index.completeness) | 38 |
| abstract_inverted_index.computations, | 296 |
| abstract_inverted_index.conjectures). | 401 |
| abstract_inverted_index.descriptions. | 147 |
| abstract_inverted_index.introduction. | 46 |
| abstract_inverted_index.respectively. | 348 |
| abstract_inverted_index.“Uniformity | 332 |
| abstract_inverted_index.Conservativity | 207, 217 |
| abstract_inverted_index.Euclid–Euler | 232 |
| abstract_inverted_index.Irreducibility | 15, 198 |
| abstract_inverted_index.Non-Extinction | 316, 393 |
| abstract_inverted_index.finite-injury, | 97 |
| abstract_inverted_index.decompositions, | 144 |
| abstract_inverted_index.non-extinction, | 96 |
| abstract_inverted_index.sieve-theoretic | 271 |
| abstract_inverted_index.Unpredictability | 18, 201 |
| abstract_inverted_index.carrier–shadow | 146 |
| abstract_inverted_index.“Finite-Injury | 335 |
| abstract_inverted_index.cross-references, | 184 |
| abstract_inverted_index.“Non-Extinction | 309 |
| abstract_inverted_index.10.5281/zenodo.16998285 | 206 |
| abstract_inverted_index.10.5281/zenodo.17073211 | 215 |
| abstract_inverted_index.10.5281/zenodo.17073257 | 223 |
| abstract_inverted_index.10.5281/zenodo.17110018 | 231 |
| abstract_inverted_index.10.5281/zenodo.17728314 | 244 |
| abstract_inverted_index.10.5281/zenodo.17728407 | 256 |
| [email protected] | 282 |
| abstract_inverted_index.principles—uniformity, | 95 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |