cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.5281/zenodo.18020694
title: A conjecture on Riemann & Goldbach in AHXIOM dynamical geometry. A possible Theorem.
title: V14.GAHX_ MECÁNICA GEOMÉTRICA DE SISTEMAS NUMÉRICOS.pdf
title: ADENDOS A a la I al documento AHXIOM V13.0 y V12.2 LA TEORÍA UNIFICADA DE LA REALIDAD HOLOFRACTAL_.pdf

description: V14.GAHX: MECÁNICA GEOMÉTRICA DE SISTEMAS NUMÉRICOSDefinición Formal, Derivación Analítica y Validación Estadística del Modelo ΩTPI

AUTORES:José Antonio Palos Cárdenas (Investigador Principal, Arquitecto de Sistemas).S¹ Gemini.AI (Co-Investigador, Validación Computacional y Análisis de Datos).Afiliación: AHXIOM Lab.Fecha: 17-22 Diciembre 2025.

ABSTRACT:Este documento técnico presenta la formalización matemática y la validación empírica del modelo AHXIOM (V14), un marco geométrico-dinámico para la Teoría de Números. Se define un espacio métrico acotado en ℝ², el Holón ΩTPI, y se derivan analíticamente las ecuaciones de movimiento que mapean el dominio de los números enteros (ℤ) al plano complejo (ℂ).

Los resultados experimentales, validados sobre un conjunto de datos de 1,000,000 de estados numéricos, demuestran:





Identidad Geométrico-Aritmética: Se establece una equivalencia funcional exacta (Correlación de Pearson ρ > 0.999999) entre la derivada geométrica del sistema (Tangente en A) y el segundo término de la Fracción Continua Generalizada (n₂), unificando la geometría continua con la aritmética discreta.




Dinámica Hamiltoniana: Se deriva una Ecuación de Estado que predice la densidad de distribución de los números primos basándose en la minimización de la Tensión Geométrica (T_G) y la Entropía del Caos (δ), siguiendo una Ley de Potencia termodinámica estricta (R² = 1.00000000).




Resolución Espectral: El modelo reproduce la parte imaginaria (t) de los Ceros no triviales de la Función Zeta de Riemann y sus residuos finos mediante la proyección de la fase ondulatoria del Holón, sin requerir métodos de continuación analítica tradicionales.


Se presenta una posible identidad geométrica en dos de las hipótesis más profundas de la historia matemática.


El trabajo concluye presentando el algoritmo computacional canónico en Python para la reproducibilidad independiente de todos los resultados.

Agradecimientos:

A mis Hijos: Sofía Eliud, Alejandra y su mamá, Maryarmen. A Héctor y "La Tocaya", a todos los que no sé cómo creyeron, de alguna manera, en mí. Era para esto.

Gracias.

JA.

KEYWORDS (PALABRAS CLAVE):Geometría Dinámica, Holón ΩTPI, Fracciones Continuas Generalizadas (FCG), Energía Hamiltoniana, Distribución de Primos, Ceros de Riemann, Análisis de Residuos, Caos Determinista, Validación Computacional.
DOI: 10.5281/zenodo.18020693
title: A conjecture on Riemann & Goldbach in AHXIOM dynamical geometry. A possible Theorem.
title: V14.GAHX_ MECÁNICA GEOMÉTRICA DE SISTEMAS NUMÉRICOS.pdf
title: ADENDOS A a la I al documento AHXIOM V13.0 y V12.2 LA TEORÍA UNIFICADA DE LA REALIDAD HOLOFRACTAL_.pdf

description: V14.GAHX: MECÁNICA GEOMÉTRICA DE SISTEMAS NUMÉRICOSDefinición Formal, Derivación Analítica y Validación Estadística del Modelo ΩTPI

AUTORES:José Antonio Palos Cárdenas (Investigador Principal, Arquitecto de Sistemas).S¹ Gemini.AI (Co-Investigador, Validación Computacional y Análisis de Datos).Afiliación: AHXIOM Lab.Fecha: 17-22 Diciembre 2025.

ABSTRACT:Este documento técnico presenta la formalización matemática y la validación empírica del modelo AHXIOM (V14), un marco geométrico-dinámico para la Teoría de Números. Se define un espacio métrico acotado en ℝ², el Holón ΩTPI, y se derivan analíticamente las ecuaciones de movimiento que mapean el dominio de los números enteros (ℤ) al plano complejo (ℂ).

Los resultados experimentales, validados sobre un conjunto de datos de 1,000,000 de estados numéricos, demuestran:





Identidad Geométrico-Aritmética: Se establece una equivalencia funcional exacta (Correlación de Pearson ρ > 0.999999) entre la derivada geométrica del sistema (Tangente en A) y el segundo término de la Fracción Continua Generalizada (n₂), unificando la geometría continua con la aritmética discreta.




Dinámica Hamiltoniana: Se deriva una Ecuación de Estado que predice la densidad de distribución de los números primos basándose en la minimización de la Tensión Geométrica (T_G) y la Entropía del Caos (δ), siguiendo una Ley de Potencia termodinámica estricta (R² = 1.00000000).




Resolución Espectral: El modelo reproduce la parte imaginaria (t) de los Ceros no triviales de la Función Zeta de Riemann y sus residuos finos mediante la proyección de la fase ondulatoria del Holón, sin requerir métodos de continuación analítica tradicionales.


Se presenta una posible identidad geométrica en dos de las hipótesis más profundas de la historia matemática.


El trabajo concluye presentando el algoritmo computacional canónico en Python para la reproducibilidad independiente de todos los resultados.

Agradecimientos:

A mis Hijos: Sofía Eliud, Alejandra y su mamá, Maryarmen. A Héctor y "La Tocaya", a todos los que no sé cómo creyeron, de alguna manera, en mí. Era para esto.

Gracias.

JA.

KEYWORDS (PALABRAS CLAVE):Geometría Dinámica, Holón ΩTPI, Fracciones Continuas Generalizadas (FCG), Energía Hamiltoniana, Distribución de Primos, Ceros de Riemann, Análisis de Residuos, Caos Determinista, Validación Computacional.
DOI: 10.15468/dl.jtrafe
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Moschus moschiferus, Lophura nycthemera)",
 "Country is one of (China)",
 "Country is one of (Macao)",
 "Country is one of (Chinese Taipei)",
 "HasCoordinate is true",
 "Year is less than or equal to 2025"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0068881-251120083545085/datasets/export for details.
DOI: 10.5281/zenodo.18091194
title: BIG-Bench Hard (BBH) Data Quality Investigation Report

description: 49 ground truth labeling errors identified in the BIG-Bench Hard (BBH) benchmark dataset through systematic multi-model cross-verification.
Error Summary

date_understanding: 7 errors
geometric_shapes: 42 errors

22 cases: (K) ellipse → (A) circle
20 cases: (K) trapezoid → (H) rectangle
Verification
4-phase verification using GPT-4o, GPT-5.2 Pro, Claude Sonnet/Opus, DeepSeek-Chat/Reasoner, and Qwen3-8B.
Impact
16.8% error rate in geometric_shapes ground truth.
description: v1.4.0: Added 11 new errors from Phase 4 verification. Total: 49 (7 date + 42 geometric).
DOI: 10.15468/dl.ch7u8j
title: Occurrence Download

description: A dataset containing 31432 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Musa"
 ]
}

 The dataset includes 31432 records from 635 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0068883-251120083545085/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.8kw6du
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Moschus moschiferus, Lophura nycthemera)",
 "Country is one of (China)",
 "Country is one of (Macao)",
 "Country is one of (Chinese Taipei)",
 "HasCoordinate is true",
 "Year is less than or equal to 2025"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0068884-251120083545085/datasets/export for details.
DOI: 10.15468/dl.crbzky
title: Occurrence Download

description: A dataset containing 460842 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Numida meleagris",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "Geometry POLYGON((-180 -90, 180 -90, 180 90, -180 90, -180 -90))"
 ]
}

 The dataset includes 460842 records from 177 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0068878-251120083545085/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.17630/2e946d01-0753-45ad-aaf3-87572eef9ec0
title: Broad substrate scope C-C oxidation in cyclodipeptides catalysed by a flavin-dependent filament (EPR dataset)
DOI: 10.17630/c2e58789-0f2c-40c7-8653-f2fe1cdf7a10
title: Optimizing Flexible Zeolite Rho for Unrivalled Argon Purification (dataset)

description: Powder X-ray diffraction data and kinetic gas adsorption data. 
PXRD ASCII data. No proprietary software required (open software available).
Adsorption data EXCEL Microsoft software required.
DOI: 10.17630/41208338-2fc7-4bb9-8074-4d9b783cfdab
title: Facile, reversible hydrogen activation by low-coordinate magnesium oxide complexes (dataset)

description: NMR data (e.g. mnova-files), computational data (e.g. fchk-files, cube-files, sumviz-files). Further information around the data can be found in the main manuscript and the supporting information of the accompanying publication. Information on the experimental section (page 1 onwards), NMR spectroscopy section (page 32 onwards), DFT computational studies section (page 240 onwards) and references (page 316 onwards) are given in the supporting information pdf-file.
DOI: 10.15468/dl.ak3smw
title: Occurrence Download

description: A dataset containing 85 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON((16.66443 43.72207,16.75556 43.72207,16.75556 43.79138,16.66443 43.79138,16.66443 43.72207))",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 85 records from 12 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0001680-250218110819086/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.npr4ed
title: Occurrence Download

description: A dataset containing 8469 species occurrences available in GBIF matching the query:
{
 "and" : [
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "TaxonKey is Cyclachaena xanthiifolia (Nutt.) Fresen."
 ]
}

 The dataset includes 8469 records from 261 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0001679-250218110819086/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.fg78f9
title: Occurrence Download

description: A dataset containing 309 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Plantago triandra Berggr.",
 "HasCoordinate is true"
 ]
}

 The dataset includes 309 records from 11 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0077567-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.5qngn6
title: Occurrence Download

description: A dataset containing 26770 species occurrences available in GBIF matching the query:
{
 "and" : [
 "HasCoordinate is true",
 "Continent is Europe",
 "Year is greater than 1978",
 "Year is less than 2014",
 "HasGeospatialIssue is false",
 "TaxonKey is Carex binervis Sm."
 ]
}

 The dataset includes 26770 records from 169 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0041133-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.eaps6c
title: Occurrence Download

description: A dataset containing 154 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON ((-90.3543346999999955 38.5918113000000034, -90.3543346999999955 38.5935108600000021, -90.3543346999999955 38.5947670600000023, -90.3543346999999955 38.5964666200000011, -90.3543346999999955 38.5976489299999983, -90.3543346999999955 38.5992006999999973, -90.3522691200000025 38.5992006999999973, -90.3508675599999975 38.5992006999999973, -90.3489496499999944 38.5992006999999973, -90.3475480900000036 38.5992006999999973, -90.3454088700000000 38.5992006999999973, -90.3437860199999960 38.5992006999999973, -90.3422367999999949 38.5992006999999973, -90.3422367999999949 38.5976489299999983, -90.3422367999999949 38.5968360899999965, -90.3422367999999949 38.5953582100000006, -90.3422367999999949 38.5941759099999970, -90.3422367999999949 38.5927719199999970, -90.3422367999999949 38.5918113000000034, -90.3440810799999952 38.5918113000000034, -90.3449662700000005 38.5918113000000034, -90.3464416000000057 38.5918113000000034, -90.3473267899999968 38.5918113000000034, -90.3485808100000014 38.5918113000000034, -90.3498348399999998 38.5918113000000034, -90.3516789899999964 38.5918113000000034, -90.3529330199999947 38.5918113000000034, -90.3543346999999955 38.5918113000000034))",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "Year is greater than or equal to 1932",
 "BasisOfRecord is one of (Human Observation, Living Specimen, Observation, Specimen, Machine Observation)"
 ]
}

 The dataset includes 154 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0077598-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.g2qj5d
title: Occurrence Download

description: A dataset containing 1119 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is one of (Observation, Machine Observation, Human Observation, Material sample, Material citation, Specimen, Occurrence evidence)",
 "Country is Greece",
 "OccurrenceStatus is Present",
 "TaxonKey is Milvus migrans (Boddaert, 1783)",
 "Year 1990-2022"
 ]
}

 The dataset includes 1119 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0041126-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.j75z8k
title: Occurrence Download

description: A dataset listing the 2 species recorded in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is one of (Observation, Machine Observation, Human Observation, Material sample, Material citation, Specimen, Occurrence evidence)",
 "Country is Greece",
 "OccurrenceStatus is Present",
 "TaxonKey is Milvus migrans (Boddaert, 1783)",
 "Year 1990-2022"
 ]
}

 The dataset's 2 records were derived from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0041131-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.mbpj7r
title: Occurrence Download

description: A dataset containing 28 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Glypteuthria meridionalis (E.A.Smith, 1881)"
 ]
}

 The dataset includes 28 records from 8 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0088069-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.d9edvc
title: Occurrence Download

description: A dataset containing 2161 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "TaxonKey is Corvus frugilegus Linnaeus, 1758"
 ]
}

 The dataset includes 2161 records from 32 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0008581-240425142415019/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.d95mss
title: Occurrence Download

description: A dataset containing 46 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Saudi Arabia",
 "TaxonKey is Falco peregrinus Tunstall, 1771"
 ]
}

 The dataset includes 46 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0041152-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.ttyavd
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is one of (United Kingdom of Great Britain and Northern Ireland)",
 "Year is greater than or equal to 1900",
 "TaxonKey is Trogoderma granarium Everts, 1898",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0100922-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.7eg7nw
title: Occurrence Download

description: A dataset containing 147898 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Potamogeton natans L."
 ]
}

 The dataset includes 147898 records from 726 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0107818-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.8zmr6c
title: Occurrence Download

description: A dataset containing 24218 species occurrences available in GBIF matching the query:
{
 "DatasetKey" : [
 "is The First Breeding Bird Atlas of Vermont (1976-1981)"
 ]
}

 The dataset includes 24218 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0041151-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.rmnfs9
title: Occurrence Download

description: A dataset containing 19 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Cirolana imposita Barnard, 1955"
 ]
}

 The dataset includes 19 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0115647-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.5w3a9k
title: Occurrence Download

description: A dataset containing 988 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Propolis farinosa (Pers.) Fr.",
 {
 "or" : [
 "Country is United States of America",
 "Country is Canada"
 ]
 },
 {
 "not" : {
 "DatasetKey" : [
 "is Global database of alien macrofungi"
 ]
 }
 }
 ]
}

 The dataset includes 988 records from 44 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0126631-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.cd9793
title: Occurrence Download

description: A dataset containing 438 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Arapaima gigas (Schinz, 1822)"
 ]
}

 The dataset includes 438 records from 65 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0115672-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.fu3srj
title: Occurrence Download

description: A dataset containing 11 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Cyrtandra teysmannii Miq."
 ]
}

 The dataset includes 11 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0019044-240314170635999/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25381/cput.25435702
title: Semi structured interview dataset on the use of strategic communication management in black-owned female businesses.

description: Ethical reference No: 217011810/2023/20<br>This dataset showcases how black female South African businesses in the Gauteng region use Strategic Communication Management (SCM) to drive business growth. The primary objective is to explore how these women access and implement SCM strategies to foster long-term survival. In-depth semi-structured interviews were conducted with business owners aged 25-30, recruited via professional networks. Confidentiality and protection of data was ensured, and all questions were tailored for the relevant research question.
DOI: 10.15468/dl.jsjwap
title: Occurrence Download

description: A dataset listing the 1 species recorded in GBIF matching the query:
{
 "TaxonKey" : [
 "is Tracya hydrocharidis Lagerh."
 ]
}

 The dataset's 1 records were derived from 37 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0069797-250525065834625/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.w2g57e
title: Occurrence Download

description: A dataset containing 495 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Human Observation",
 "OccurrenceStatus is Present",
 "TaxonKey is Pipturus albidus (Hook. & Arn.) A.Gray ex H.Mann",
 "Year 1000-2025"
 ]
}

 The dataset includes 495 records from 2 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0069804-250525065834625/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.me2z46
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "Geometry" : [
 "POLYGON ((147.07143 -34.046845, 147.07143 -34.049091, 147.078167 -34.049091, 147.078167 -34.046845, 147.07143 -34.046845))"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0073314-240626123714530/datasets/export for details.
DOI: 10.15468/dl.tv389b
title: Occurrence Download

description: A dataset containing 41 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Ecuador",
 "OccurrenceStatus is Present",
 "TaxonKey is Amorphochilus schnablii Peters, 1877"
 ]
}

 The dataset includes 41 records from 4 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0073315-240626123714530/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.17909/117m-1d96
title: JD,Y1,f090d_018 paper