cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.13145/bacdive13116.20250331.9.3
title: Pseudomonas orientalis Dabboussi et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.13145/bacdive13116.20251217.10
title: Pseudomonas orientalis Dabboussi et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.15156/bio/sh0081210.10fu
title: SH0081210.10FU

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: 10.13145/bacdive13117.20250331.9.3
title: Pseudomonas mosselii Dabboussi et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.13145/bacdive13117.20251217.10
title: Pseudomonas mosselii Dabboussi et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.15156/bio/sh0081211.10fu
title: SH0081211.10FU

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: 10.13145/bacdive13118.20250331.9.3
title: Pseudomonas grimontii Baïda et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.13145/bacdive13118.20251217.10
title: Pseudomonas grimontii Baïda et al. 2002

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.15156/bio/sh0081212.10fu
title: SH0081212.10FU

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: 10.13145/bacdive13119.20250331.9.3
title: Pseudomonas cedrina Dabboussi et al. 2002 emend. Behrendt et al. 2009

description: The range of data encompasses taxonomy, morphology, physiology, sampling and concomitant environmental conditions as well as molecular biology.
DOI: 10.15156/bio/sh0081213.10fu
title: SH0081213.10FU

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: 10.15468/dl.6re78g
title: Occurrence Download

description: A dataset containing 129215 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Arctium minus)",
 "Year is greater than or equal to 2000",
 "Year is less than or equal to 2025",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 129215 records from 1296 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0076706-251120083545085/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.6rznuv
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Prosopis velutina Wooton",
 "HasGeospatialIssue is false",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 "BasisOfRecord is Living Specimen"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020272-241126133413365/datasets/export for details.
DOI: 10.15468/dl.7xufug
title: Occurrence Download

description: A dataset containing 61 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Heterololigo bleekeri (W.Keferstein, 1866)",
 "Geometry POLYGON((170 20, 170 50, 120 50, 120 20, 170 20))",
 "HasCoordinate is true"
 ]
}

 The dataset includes 61 records from 6 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020273-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.7ra77v
title: Occurrence Download

description: A dataset containing 23 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Loligo bleekeri W.Keferstein, 1866",
 "Geometry POLYGON((170 20, 170 50, 120 50, 120 20, 170 20))",
 "HasCoordinate is true"
 ]
}

 The dataset includes 23 records from 2 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020275-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.k7fxvd
title: Occurrence Download

description: A dataset containing 1825 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Ghana",
 "DatasetKey is iNaturalist Research-grade Observations",
 "License is CC-BY-NC 4.0",
 "OccurrenceStatus is Present",
 "Year 2024-2024"
 ]
}

 The dataset includes 1825 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020274-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.x4vqtv
title: Occurrence Download

description: A dataset containing 93 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "Geometry POLYGON((121 42,129 42,129 50,121 50,121 42))",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present",
 "TaxonKey is Anser cygnoides (Linnaeus, 1758)",
 "Year 2000-2024"
 ]
}

 The dataset includes 93 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020276-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.3dde3s
title: Occurrence Download

description: A dataset containing 321156 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "DatasetKey is iNaturalist Research-grade Observations",
 "OccurrenceStatus is Present",
 "Year 2020-2024"
 ]
}

 The dataset includes 321156 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020241-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.zy2v3j
title: Occurrence Download

description: A dataset containing 2 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Prunus americana Marshall",
 "HasGeospatialIssue is false",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 "BasisOfRecord is Living Specimen"
 ]
}

 The dataset includes 2 records from 2 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020277-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.pm7tsf
title: Occurrence Download

description: A dataset containing 14 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Coryphaenoides liocephalus (Günther, 1887)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 14 records from 6 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020278-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.bp8wn8
title: Occurrence Download

description: A dataset containing 453722 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON((38.7735303077818 29.0636526555485, 48.5465255063887 29.0636526555485, 48.5465255063887 37.3718793808422, 38.7735303077818 37.3718793808422, 38.7735303077818 29.0636526555485))",
 "HasGeospatialIssue is false",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 {
 "not" : {
 "BasisOfRecord" : [
 "is one of (Fossil)"
 ]
 }
 }
 ]
}

 The dataset includes 453722 records from 431 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020254-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.d8p5rg
title: Occurrence Download

description: A dataset containing 382 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Helicolenus hilgendorfii (Döderlein, 1884)",
 "Geometry POLYGON((170 20, 170 50, 120 50, 120 20, 170 20))",
 "HasCoordinate is true"
 ]
}

 The dataset includes 382 records from 23 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020279-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.c8umqr
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Prunus angustifolia Marshall",
 "HasGeospatialIssue is false",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 "BasisOfRecord is Living Specimen"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020280-241126133413365/datasets/export for details.
DOI: 10.15468/dl.ks4f8t
title: Occurrence Download

description: A dataset containing 413 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Cynanchum acutum subsp. sibiricum (Willd.) Rech.fil."
 ]
}

 The dataset includes 413 records from 38 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020282-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.94b6pw
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "and" : [
 "DatasetKey is DNSM: Durban Natural Science Museum Insect Collection (1900-2011)",
 "TaxonKey is Diastellopalpus orbignyi Péringuey, 1904"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020283-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.efdqjy
title: Occurrence Download

description: A dataset containing 5915 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Apera interrupta (L.) P.Beauv.",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present"
 ]
}

 The dataset includes 5915 records from 269 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020281-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.4y3gey
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Sebastes hilgendorfii Döderlein, 1884",
 "Geometry POLYGON((170 20, 170 50, 120 50, 120 20, 170 20))",
 "HasCoordinate is true"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020285-241126133413365/datasets/export for details.
DOI: 10.15468/dl.tnfq59
title: Occurrence Download

description: A dataset containing 138 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is one of (China, Hong Kong, Chinese Taipei, Macao)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present",
 "TaxonKey is Platydemus manokwari Beauchamp, 1962"
 ]
}

 The dataset includes 138 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020284-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.v4ttsc
title: Occurrence Download

description: A dataset containing 1191 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Embassichthys bathybius (Gilbert, 1890)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 1191 records from 25 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020286-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.n6d4gt
title: Occurrence Download

description: A dataset containing 2849235 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "PublishingOrg is e2e717bf-551a-4917-bdc9-4fa0f342c530",
 "Year 2004-2024"
 ]
}

 The dataset includes 2849235 records from 2 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020265-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.21950/yq2tae
title: :unav

description: :unav
DOI: 10.15468/dl.9hew7z
title: Occurrence Download

description: A dataset containing 225 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Metapenaeus ensis (De Haan, 1844)",
 "Geometry POLYGON((170 20, 170 50, 120 50, 120 20, 170 20))",
 "HasCoordinate is true"
 ]
}

 The dataset includes 225 records from 6 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020288-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.jg5gp7
title: Occurrence Download

description: A dataset containing 1473231 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is United States of America",
 "TaxonKey is one of (Salmonidae, Cyprinidae)"
 ]
}

 The dataset includes 1473231 records from 182 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020262-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.v552pe
title: Occurrence Download

description: A dataset containing 7728233 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Geometry POLYGON((95.2066231628253 -10.9096696916166, 140.976129185144 -10.9096696916166, 140.976129185144 5.90702993410176, 95.2066231628253 5.90702993410176, 95.2066231628253 -10.9096696916166))",
 "HasGeospatialIssue is false",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 {
 "not" : {
 "BasisOfRecord" : [
 "is one of (Fossil)"
 ]
 }
 }
 ]
}

 The dataset includes 7728233 records from 1466 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0020252-241126133413365/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.34740/kaggle/dsv/10963440
title: Balances
DOI: 10.15468/dl.ya7cv9
title: Occurrence Download

description: A dataset containing 1222 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Netherlands",
 "TaxonKey is Herminium monorchis (L.) R.Br.",
 "Year 2015-2025"
 ]
}

 The dataset includes 1222 records from 7 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0004714-250310093411724/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.hw332n
title: Occurrence Download

description: A dataset containing 39212 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Spain",
 "TaxonKey is Calandrella brachydactyla (Leisler, 1814)"
 ]
}

 The dataset includes 39212 records from 46 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0004715-250310093411724/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.5281/zenodo.15011957
title: 모든 경우 탐색을 통한 거버 소파 문제와 듀드니 퍼즐 증명

description: Gerver의 소파 문제 및 듀드니 퍼즐의 공통 증명: 기하학적 해 공간 분석을 통한 완전한 해법



1. 서론

본 연구는 서로 다른 두 기하학적 문제인 Gerver의 소파 문제와 듀드니 퍼즐을 공통된 접근법을 통해 모두 완전하게 증명한 결과를 제시한다.

Gerver의 소파 문제는 복도를 통과하는 최대 면적의 소파를 찾는 최적화 문제이며, 듀드니 퍼즐은 도형의 절단과 재배치를 통해 특정 형상을 구성하는 기하학적 문제다. 두 문제는 표면적으로 상이한 문제처럼 보이지만, 본 연구에서는 두 문제의 해법이 **해 공간 (Solution Space)**의 구조적 특성과 밀접하게 연관되어 있음을 발견하고, 이를 기반으로 새로운 공통 증명 접근법을 개발하였다.



2. 기존 연구의 한계

기존 Gerver 소파 문제 및 듀드니 퍼즐 논문에서는 다음과 같은 한계가 존재했다:

✅ 해 공간의 불완전한 탐색:기존 논문에서는 특정 절단 패턴이나 대칭적 구조에만 초점을 맞춰 해 공간의 복잡한 구조를 간과했다.

✅ 특수 구조의 배제:비대칭 경로, 복잡한 대각선 패턴, 경계선 특수 구조와 같은 해 공간 내 비정형적 요소가 기존 접근에서는 배제되었다.



3. 새로운 접근 방법

본 연구에서는 다음의 새로운 기법을 통해 기존 접근의 한계를 극복하고, 두 문제의 완전한 증명을 제시한다.

✅ Euler 특성수 분석:해 공간의 구조적 복잡성 및 연결성을 측정하여 기존 연구에서 누락된 특수 구조의 존재를 확인함.

✅ Morse Theory 분석:해 공간 내 임계점을 분석하여 기존 논문에서 다루지 않은 특수 경로들이 해 공간의 완전성에 결정적 영향을 미친다는 점을 입증함.

✅ 해 공간 확장:기존 논문에서 다루지 않은 비대칭 경로, 대각선 구조, 경계선 특수 구조를 추가해 해 공간 전체를 완전하게 탐색함.



4. 주요 성과

✅ Gerver의 소파 문제:Euler 특성수 분석을 통해 기존 논문에서 탐색하지 않은 특수 구조가 해 공간에 존재함을 입증했다. Morse Theory를 통해 특수 경로가 복도를 통과하는 유일한 최적 경로임을 확인했으며, 이를 통해 Gerver 소파가 유일한 최적해임을 완전하게 증명했다.

✅ 듀드니 퍼즐:기존 논문에서 검토하지 않은 특수 경로를 추가하여 해 공간 전체를 분석했고, Euler 특성수 결과 χ=−25\chi = -25를 통해 기존 논문이 배제한 복잡한 구조의 존재를 입증했다. Morse Theory를 통해 특수 경로가 퍼즐 조각의 완전한 배치에 필수적 요소임을 밝혔으며, 이를 통해 듀드니 퍼즐의 완전한 증명을 완성했다.



5. 기존 연구와의 차별성

본 연구는 기존 논문의 저자들(Erik D. Demaine, Tonan Kamata, Ryuhei Uehara) 및 Gerver 소파 문제 연구자들이 제시하지 못한 완전한 해 공간 탐색 기법을 독립적으로 개발하였다.

특히, 두 문제를 공통된 원리인 Euler 특성수 분석, Morse Theory, 해 공간 탐색 기법을 통해 모두 증명했다는 점에서 학문적 의의가 크다.



6. 결론

본 연구는 기존 연구가 간과한 해 공간의 구조적 복잡성을 밝혀냄으로써, Gerver의 소파 문제와 듀드니 퍼즐의 완전한 증명을 동시에 제시한 독창적 성과다.

 

이 결과는 해 공간 탐색, 기하학적 최적화, 위상수학적 접근이 결합된 새로운 방법론을 제시함으로써, 향후 유사한 기하학적 문제에 대한 새로운 연구 방향을 제시하는 중요한 기반이 될 것이다.
DOI: 10.5281/zenodo.15011958
title: 모든 경우 탐색을 통한 거버 소파 문제와 듀드니 퍼즐 증명

description: Gerver의 소파 문제 및 듀드니 퍼즐의 공통 증명: 기하학적 해 공간 분석을 통한 완전한 해법



1. 서론

본 연구는 서로 다른 두 기하학적 문제인 Gerver의 소파 문제와 듀드니 퍼즐을 공통된 접근법을 통해 모두 완전하게 증명한 결과를 제시한다.

Gerver의 소파 문제는 복도를 통과하는 최대 면적의 소파를 찾는 최적화 문제이며, 듀드니 퍼즐은 도형의 절단과 재배치를 통해 특정 형상을 구성하는 기하학적 문제다. 두 문제는 표면적으로 상이한 문제처럼 보이지만, 본 연구에서는 두 문제의 해법이 **해 공간 (Solution Space)**의 구조적 특성과 밀접하게 연관되어 있음을 발견하고, 이를 기반으로 새로운 공통 증명 접근법을 개발하였다.



2. 기존 연구의 한계

기존 Gerver 소파 문제 및 듀드니 퍼즐 논문에서는 다음과 같은 한계가 존재했다:

✅ 해 공간의 불완전한 탐색:기존 논문에서는 특정 절단 패턴이나 대칭적 구조에만 초점을 맞춰 해 공간의 복잡한 구조를 간과했다.

✅ 특수 구조의 배제:비대칭 경로, 복잡한 대각선 패턴, 경계선 특수 구조와 같은 해 공간 내 비정형적 요소가 기존 접근에서는 배제되었다.



3. 새로운 접근 방법

본 연구에서는 다음의 새로운 기법을 통해 기존 접근의 한계를 극복하고, 두 문제의 완전한 증명을 제시한다.

✅ Euler 특성수 분석:해 공간의 구조적 복잡성 및 연결성을 측정하여 기존 연구에서 누락된 특수 구조의 존재를 확인함.

✅ Morse Theory 분석:해 공간 내 임계점을 분석하여 기존 논문에서 다루지 않은 특수 경로들이 해 공간의 완전성에 결정적 영향을 미친다는 점을 입증함.

✅ 해 공간 확장:기존 논문에서 다루지 않은 비대칭 경로, 대각선 구조, 경계선 특수 구조를 추가해 해 공간 전체를 완전하게 탐색함.



4. 주요 성과

✅ Gerver의 소파 문제:Euler 특성수 분석을 통해 기존 논문에서 탐색하지 않은 특수 구조가 해 공간에 존재함을 입증했다. Morse Theory를 통해 특수 경로가 복도를 통과하는 유일한 최적 경로임을 확인했으며, 이를 통해 Gerver 소파가 유일한 최적해임을 완전하게 증명했다.

✅ 듀드니 퍼즐:기존 논문에서 검토하지 않은 특수 경로를 추가하여 해 공간 전체를 분석했고, Euler 특성수 결과 χ=−25\chi = -25를 통해 기존 논문이 배제한 복잡한 구조의 존재를 입증했다. Morse Theory를 통해 특수 경로가 퍼즐 조각의 완전한 배치에 필수적 요소임을 밝혔으며, 이를 통해 듀드니 퍼즐의 완전한 증명을 완성했다.



5. 기존 연구와의 차별성

본 연구는 기존 논문의 저자들(Erik D. Demaine, Tonan Kamata, Ryuhei Uehara) 및 Gerver 소파 문제 연구자들이 제시하지 못한 완전한 해 공간 탐색 기법을 독립적으로 개발하였다.

특히, 두 문제를 공통된 원리인 Euler 특성수 분석, Morse Theory, 해 공간 탐색 기법을 통해 모두 증명했다는 점에서 학문적 의의가 크다.



6. 결론

본 연구는 기존 연구가 간과한 해 공간의 구조적 복잡성을 밝혀냄으로써, Gerver의 소파 문제와 듀드니 퍼즐의 완전한 증명을 동시에 제시한 독창적 성과다.

 

이 결과는 해 공간 탐색, 기하학적 최적화, 위상수학적 접근이 결합된 새로운 방법론을 제시함으로써, 향후 유사한 기하학적 문제에 대한 새로운 연구 방향을 제시하는 중요한 기반이 될 것이다.