cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.30082039.v4
title: [2025-10-13v3]A Unified Proof of the Collatz Conjecture The Invariant Structure of the $3n+1$ Problem: Generalization to All Integers via Phase Expression Theory and Universal Structural Limits.pdf

description: This paper presents a \textbf{unified and constructive framework} that resolves the long-standing open problem, the \textbf{Collatz Conjecture} ($3n+1$), over all non-zero integers (positive and negative). We introduce the \textbf{Collatz Phase Expression (CPE)}, which models the Collatz map as deterministic geometric transformations. The CPE utilizes the \textbf{Alternating Binary Notation (ABN)}, a method that encodes integers as alternating-sign powers of 2, and decomposes this into structural units: Chain ($\mathbf{R}$), Single ($\mathbf{T}$), and Node ($\mathbf{K}$). Using the CPE's characteristic quantities ($\mu$: unit count, $H_{RT}$: complexity, $B$: bit-length), we establish two \textbf{Universal Structural Limits}. These constraints imply that infinite divergence and non-trivial cycles are structurally impossible: \begin{enumerate} \item A strict linear bound on the total bit-length, $B(F^m (n)) \le B(n) + m$, prevents exponential growth. \item A deterministic, self-regulating trade-off for the local complexity $H_{RT}$ is enforced by the **Fundamental Inequality**, ensuring complexity cannot increase unboundedly. \end{enumerate} These structural constraints demonstrate that every positive sequence converges to the minimal complexity state ($\mathbf{H_{K}=0}$), leading exclusively to the trivial loop $\{1\}$. Furthermore, the same formalism resolves the negative Collatz conjecture by establishing a universal structural upper bound ($\mathbf{H_{RT} &lt; 6}$), which guarantees convergence to the known finite loops (including $\{-1, -3, -11\}$ cycles). The CPE framework provides a deterministic lens for analyzing discrete dynamical systems.
DOI: 10.15468/dl.su4amv
title: Occurrence Download

description: A dataset containing 2592259 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON((46.62162 13.91571,40.36111 31.41662,28.97838 29.45394,36.37716 9.45823,46.62162 13.91571))",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present"
 ]
}

 The dataset includes 2592259 records from 920 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0023628-251009101135966/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.tn289q
title: Occurrence Download

description: A dataset containing 136 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Specimen",
 "Country is one of (Haiti, Dominican Republic)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present",
 "TaxonKey is Testudines"
 ]
}

 The dataset includes 136 records from 8 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0003361-250525065834625/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.zzwuhy
title: Occurrence Download

description: A dataset containing 14 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Polygala parrasana Brandegee"
 ]
}

 The dataset includes 14 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0091468-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.am88uw
title: Occurrence Download

description: A dataset containing 37 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Strobilurus torquatus Wiegmann, 1834)",
 "BasisOfRecord is one of (Specimen, Human Observation, Observation, Machine Observation)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 37 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0050541-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.has9zf
title: Occurrence Download

description: A dataset containing 9 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Arrhenechthites haplogynus (F.Muell.) Mattf."
 ]
}

 The dataset includes 9 records from 4 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0052727-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.9ypkzj
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is incertae sedis",
 "Year is greater than 2013",
 "Geometry MULTIPOLYGON (((8.444386 40.022099,8.444795 40.02137,8.445594 40.020232,8.446104 40.019262,8.446142 40.018873,8.446748 40.017652,8.44754 40.016437,8.44825 40.015325,8.447998 40.014569,8.447671 40.014005,8.447426 40.013555,8.446922 40.012969,8.446174 40.012125,8.445269 40.011318,8.444409 40.010378,8.443267 40.009355,8.442081 40.008239,8.440866 40.007279,8.43956 40.006165,8.438405 40.005447,8.437004 40.004396,8.4359 40.003608,8.434565 40.002655,8.433299 40.001773,8.432069 40.000965,8.431128 40.000322,8.430342 39.999733,8.429527 39.999376,8.42923 39.999287,8.428705 39.999195,8.428061 39.999324,8.427615 39.999614,8.427216 39.999915,8.426431 39.999731,8.426098 39.999586,8.42572 39.999376,8.425549 39.999249,8.425223 39.999113,8.424749 39.999149,8.424282 39.999127,8.423794 39.999207,8.423357 39.999376,8.422816 39.99984,8.422357 40.000151,8.421972 40.000377,8.421869 40.000663,8.421831 40.000954,8.42192 40.000972,8.42192 40.00108,8.421987 40.001674,8.422291 40.002271,8.422558 40.002786,8.422818 40.003606,8.422796 40.004037,8.422633 40.004657,8.42256 40.005324,8.422663 40.006234,8.422915 40.006914,8.42319 40.007789,8.423478 40.008485,8.423938 40.009353,8.424591 40.010272,8.42534 40.011268,8.426073 40.012174,8.42683 40.012788,8.427541 40.013288,8.428467 40.013696,8.429386 40.01391,8.430209 40.013885,8.431009 40.01353,8.431527 40.013218,8.432031 40.013022,8.432549 40.01279,8.433031 40.012853,8.433394 40.012973,8.433564 40.013136,8.433742 40.013425,8.433794 40.013662,8.433809 40.014041,8.433795 40.014382,8.433854 40.014786,8.433758 40.015181,8.433736 40.015337,8.433692 40.015721,8.433558 40.016092,8.433462 40.016388,8.433344 40.016714,8.433159 40.017054,8.432996 40.017306,8.432737 40.017638,8.432515 40.018026,8.432418 40.018169,8.432249 40.018276,8.432026 40.018632,8.431908 40.018896,8.431998 40.01922,8.432301 40.019615,8.432768 40.020186,8.432916 40.02064,8.433162 40.021262,8.433414 40.021938,8.433443 40.022083,8.433592 40.022587,8.433637 40.023165,8.433801 40.023795,8.43392 40.024167,8.433919 40.024574,8.434189 40.024749,8.434573 40.024714,8.435436 40.024719,8.436157 40.024464,8.436784 40.023988,8.437984 40.023846,8.439376 40.023558,8.440962 40.023161,8.442548 40.022652,8.444133 40.022291,8.444386 40.022099)))"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0028042-230530130749713/datasets/export for details.
DOI: 10.15468/dl.jq9mpt
title: Occurrence Download

description: A dataset containing 17 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Polygala perrieri Paiva"
 ]
}

 The dataset includes 17 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0091481-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.fzztv5
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Cercosaura quadrilineata Boettger, 1876)",
 "BasisOfRecord is one of (Specimen, Human Observation, Observation, Machine Observation)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0050547-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.pnggpt
title: Occurrence Download

description: A dataset containing 73 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Ballistura albertinae (Ellis, 1976)"
 ]
}

 The dataset includes 73 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0052729-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.bvw3uh
title: Occurrence Download

description: A dataset containing 7 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Sedum batallae Barocio"
 ]
}

 The dataset includes 7 records from 4 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0122301-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.g9extf
title: Occurrence Download

description: A dataset containing 2893 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Specimen",
 "Country is Mexico",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "TaxonKey is Bipes biporus (Cope, 1894)"
 ]
}

 The dataset includes 2893 records from 20 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0016492-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.7t4vm5
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Lepanthes rosoria Luer & Hirtz"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0007167-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.zbgfnz
title: Occurrence Download

description: A dataset containing 6 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Arrhenechthites hydrangeoides C.Jeffrey"
 ]
}

 The dataset includes 6 records from 6 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0052731-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.ahdb29
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is incertae sedis",
 "Year is greater than 2013",
 "Geometry MULTIPOLYGON (((12.947524 41.363681,12.947341 41.363802,12.946924 41.364132,12.946618 41.364363,12.946231 41.364669,12.945003 41.365589,12.944474 41.365985,12.943767 41.366469,12.942635 41.367201,12.941341 41.368137,12.939809 41.369121,12.939479 41.36934,12.938189 41.370199,12.937034 41.370959,12.936151 41.371561,12.935578 41.371914,12.935113 41.372231,12.934555 41.372656,12.933388 41.373439,12.932941 41.373724,12.932468 41.374006,12.932191 41.374169,12.931524 41.374561,12.931211 41.374742,12.930172 41.375372,12.92911 41.376007,12.928633 41.376334,12.928049 41.376715,12.927743 41.376896,12.927287 41.377137,12.926443 41.377625,12.924944 41.378554,12.924449 41.3789,12.92406 41.379111,12.923723 41.379285,12.923391 41.379449,12.923084 41.379622,12.922718 41.379855,12.921953 41.380363,12.921422 41.380705,12.921139 41.380877,12.920304 41.381301,12.919944 41.381485,12.918959 41.382108,12.917656 41.38295,12.917149 41.383282,12.916723 41.383495,12.916432 41.383638,12.916353 41.383701,12.91779 41.385081,12.918719 41.385833,12.919685 41.386329,12.921106 41.386594,12.930786 41.386694,12.933518 41.386815,12.933534 41.386797,12.936313 41.387153,12.936314 41.387148,12.93644 41.387161,12.93646 41.387142,12.936524 41.387145,12.940219 41.38446,12.942677 41.382758,12.951876 41.378298,12.952051 41.378204,12.954568 41.377312,12.955406 41.376615,12.958689 41.373214,12.959004 41.37286,12.958878 41.372758,12.95869 41.372608,12.956715 41.371019,12.947727 41.363791,12.947578 41.36367,12.947566 41.363661,12.947561 41.363657,12.947524 41.363681)))"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0028048-230530130749713/datasets/export for details.
DOI: 10.15468/dl.x5t6ss
title: Occurrence Download

description: A dataset containing 3 species occurrences available in GBIF matching the query:
{
 "and" : [
 "InstitutionCode is us",
 "TaxonKey is Zehneria emirnensis (Baker) Keraudren"
 ]
}

 The dataset includes 3 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0128225-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.89cac4
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Lepidium botschantzevii (R.Vinograd.) Al-Shehbaz & Mummenhoff"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0007642-230530130749713/datasets/export for details.
DOI: 10.15468/dl.q3z29f
title: Occurrence Download

description: A dataset listing the 117 species recorded in GBIF matching the query:
{
 "DatasetKey" : [
 "is The Freshwater Biodiversity Information System (FBIS) Fish Data"
 ]
}

 The dataset's 117 records were derived from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0007166-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.e9ctuu
title: Occurrence Download

description: A dataset containing 418392 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Solanum dulcamara L.",
 "HasCoordinate is true",
 "Year is greater than or equal to 1900",
 "BasisOfRecord is one of (Human Observation, Specimen, Unknown evidence)"
 ]
}

 The dataset includes 418392 records from 1504 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0052718-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.2z65wd
title: Occurrence Download

description: A dataset containing 3701 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Germany",
 "TaxonKey is Procyon lotor (Linnaeus, 1758)"
 ]
}

 The dataset includes 3701 records from 26 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0091478-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.f3t3ur
title: Occurrence Download

description: A dataset containing 119 species occurrences available in GBIF matching the query:
{
 "and" : [
 "GadmGid is CHN.30_1",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present",
 "TaxonKey is Ternstroemia gymnanthera (Wight & Arn.) Sprague"
 ]
}

 The dataset includes 119 records from 14 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0028046-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.mqekx8
title: Occurrence Download

description: A dataset containing 4 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Dryadosaura nordestina Rodrigues, Xavier Freire, Machado Pellegrino & Sites, 2005)",
 "BasisOfRecord is one of (Specimen, Human Observation, Observation, Machine Observation)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 4 records from 2 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0050549-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.dk2626
title: Occurrence Download

description: A dataset containing 965726 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Culicidae",
 "Country is United States of America"
 ]
}

 The dataset includes 965726 records from 107 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0028045-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15156/bio/sh1392420.10fu
title: SH1392420.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.
DOI: 10.15156/bio/sh1392424.10fu
title: SH1392424.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.
DOI: 10.15156/bio/sh1392427.10fu
title: SH1392427.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.
DOI: 10.15156/bio/sh1392428.10fu
title: SH1392428.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.
DOI: 10.15156/bio/sh1392429.10fu
title: SH1392429.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.
DOI: 10.15156/bio/sh1392431.10fu
title: SH1392431.10FU

description: UNITE provides a unified way for delimiting, identifying, communicating, and working with DNA-based Species Hypotheses (SH). All fungal ITS sequences in the international nucleotide sequence databases are clustered to approximately the species level by applying a set of dynamic distance values (<0.5 - 3.0%). All species hypotheses are given a unique, stable name in the form of a DOI, and their taxonomic and ecological annotations are verified through distributed, web-based third-party annotation efforts. SHs are connected to a taxon name and its classification as far as possible (phylum, class, order, etc.) by taking into account identifications for all sequences in the SH. An automatically or manually designated sequence is chosen to represent each such SH. These sequences are released (https://unite.ut.ee/repository.php) for use by the scientific community in, for example, local sequence similarity searches and next-generation sequencing analysis pipelines. The system and the data are updated automatically as the number of public fungal ITS sequences grows.