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Dunyo bo'ylab millionlab insonlar ingliz tilini o'rganishga intilmoqda, biroq tilni mukammal o'zlashtirish jarayonida ko'plab o'quvchilar bir xil xatolarga yo'l qo'yishadi. Ushbu xatolarni o'z vaqtida aniqlab, ularni bartaraf etish til o'rganish jarayonini sezilarli darajada yengillashtiradi. Mazkur maqolada ingliz tilini o'rganishda ko'p uchraydigan keng tarqalgan xatolar va ularning sabablari tahlil qilinadi."},{"descriptionType":"Other","description":"English abstract\nIn today's context of globalization, knowing English has become an integral part of modern education, professional development, and international communication. Millions of people around the world strive to learn English, yet many learners make similar mistakes in the process of mastering the language. Identifying these mistakes in a timely manner and correcting them significantly facilitates the language learning process. 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В данной статье анализируются наиболее распространённые ошибки при изучении английского языка и их причины."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21744203","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-08-01T17:17:04Z","registered":"2026-08-01T17:17:04Z","published":null,"updated":"2026-08-01T17:17:04Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21743982","type":"dois","attributes":{"doi":"10.5281/zenodo.21743982","identifiers":[],"creators":[{"nameType":"Personal","affiliation":["Universitat Politècnica de València"],"givenName":"Santiago","familyName":"Moll Lopez","name":"Moll Lopez, Santiago","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0003-3388-5135"}]},{"nameType":"Personal","affiliation":["Universitat Politècnica de València"],"givenName":"Sara","familyName":"Sánchez López","name":"Sánchez López, Sara","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0001-7680-023X"}]},{"nameType":"Personal","affiliation":["Universitat Politècnica de València"],"givenName":"Carlos","familyName":"Delgado Caro","name":"Delgado Caro, Carlos","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0000-0001-9109-8485"}]}],"titles":[{"title":"Dataset and analysis code for AI sycophancy, epistemic calibration, and verification in university students' evaluation of research proposals"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"generative artificial intelligence"},{"subject":"sycophancy"},{"subject":"epistemic calibration"},{"subject":"verification"},{"subject":"critical thinking"}],"contributors":[],"dates":[{"date":"2026-08-01","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"Dataset","resourceTypeGeneral":"Dataset","citeproc":"dataset","bibtex":"misc","ris":"DATA","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21743982","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"1.0","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"}],"descriptions":[{"descriptionType":"Abstract","description":"De-identified quantitative dataset and reproducible Python code for a balanced 2×2 between-participants experiment with 120 first-year Aerospace Engineering students, crossing conversational tone (praising vs. neutral) with epistemic stance (validation vs. calibrated assessment). 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07]"},{"titleType":"TranslatedTitle","lang":"ita","title":"Riformulazione informazionale-geometrica della congettura di Poincaré 3D tramite il teorema di unicità n=2 e il flusso di Ricci di Perelman — Imposizione sferica su 3-varietà semplicemente connesse e isomorfismo al funzionale W-entropia di Perelman — [Articolo 07]"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-08-01","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21404387","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"Copyright (C) 2026 Yuuki YAMAGISHI / 山岸勇輝"}],"descriptions":[{"descriptionType":"Abstract","description":"We present an information-geometric reformulation of the 3D Poincaré Conjecture (Perelman's Theorem). The argument proceeds in three stages. Stage 1: We formulate the Triple Enforcement Principle (Analytic, Dynamical, Topological), showing that n=2 uniqueness drives local curvature uniformization. Stage 2: We prove a quantitative isomorphism between Perelman's W-entropy functional W(g, f, τ) monotonicity (dWdt ≥ 0) and Universe OS memory compression optimization (avoiding n ≠ 2 system crash). Stage 3: We demonstrate that Ricci flow ∂_t g_(ij) = -2 R_(ij) with surgery re-formats spatial rendering using m=4π units, proving why any simply connected closed 3-manifold converges structurally to the round 3-sphere S³.\n\n(scope note) Positioning of this paper: This paper offers a structural interpretation of established physical laws and mathematical theorems. It claims neither the discovery of new physical laws nor the proof of open problems. The 3D Poincaré Conjecture was completely proved by Perelman (2002--2003); this paper proposes an information-geometric rereading of that proof. It contributes nothing to the proof and proposes no alternative to it.\n\nA note on the aim of this work. This is a structural reinterpretation of well-established physics, not a proposal for a new physical law. Every relation shown is a substitution into, or a geometric re-reading of, equations that are already known and that remain unchanged. The aim is a modest one: to make a few recurring geometric structures — in particular the solid angle 4π and the exponent n = 2 — easier to see within a single picture. Where a particular unit convention is adopted (for example G = 4π), this is a choice of notation, not a claim about nature. Nothing here is intended to contradict existing results.\n\nOn the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated.\n\n-----\n\n「単連結な3次元閉多様体は3次元球面 S³ に同相である」という3次元ポアンカレ予想(ペレルマンの定理)に対し、n=2 唯一性定理(dm/dr = 4π)に基づく情報幾何学的再定式化を提示する。本稿の論証は3段階からなる。第一段階:解析的・動力学的・位相的の「三重強制原理(Triple Enforcement)」を定式化し、n=2 唯一性条件が多様体の局所曲率を一様化させる幾何学的ドライバであることを明示する。第二段階:ペレルマンの W エントロピー汎関数 W(g, f, τ) の単調増加性が、宇宙OSにおける空間メモリ圧縮率の最適化(n ≠ 2 でのクラッシュ回避)と定量的同型であることを証明する(エントロピー構造同型定理)。第三段階:リッチフロー ∂_t g_(ij) = -2 R_(ij) と特異点手術が山岸パッチ m=4π を単位とする空間一様化プロセスであることを示し、単連結3次元閉多様体が最終的に丸い S³ へ収束する構造的根拠を解明する。\n\n(射程注記) 本稿の位置づけ:本稿は既存の物理法則・数学的定理に対する構造的解釈を提示するものであり、新たな物理法則の発見や未解決問題の証明を主張しない。3次元ポアンカレ予想はペレルマン(2002--2003)により完全に証明されており、本稿はその証明に対する情報幾何学的な読み替えを提案するものである。本稿は当該証明に何ら寄与せず、また代替を提案するものでもない。\n\n本稿の位置づけ。本稿は確立した物理法則に対する構造的解釈であり、新たな物理法則を提案するものではありません。示される関係はいずれも既知の式への代入、またはその幾何学的な読み替えであり、元の式は変わりません。目的はささやかで、繰り返し現れる幾何構造——とくに立体角 4π と指数 n = 2——を一つの描像の中で見やすくすることにあります。特定の単位系(例:G = 4π)を採る箇所は記法上の約束であって、自然についての主張ではありません。既存の結果と矛盾する意図はありません。\n\n作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。\n\n-----\n\nWir stellen eine informationsgeometrische Neuformulierung der 3D-Poincaré-Vermutung (Perelmans Satz) vor. Die Argumentation verläuft in drei Stufen. Stufe 1: Wir formulieren das Prinzip der dreifachen Erzwingung (analytisch, dynamisch, topologisch) und zeigen, dass die Eindeutigkeit von n = 2 die lokale Krümmungsvereinheitlichung antreibt. Stufe 2: Wir beweisen eine quantitative Isomorphie zwischen der Monotonie von Perelmans W-Entropie-Funktional W(g, f, τ) (dW/dt ≥ 0) und der Optimierung der Speicherkompression im Universum-OS (Vermeidung eines Systemabsturzes bei n ≠ 2). Stufe 3: Wir zeigen, dass der Ricci-Fluss ∂ₜg_ij = −2R_ij mit Chirurgie das räumliche Rendering mit m = 4π-Einheiten neu formatiert und beweisen, warum jede einfach zusammenhängende geschlossene 3-Mannigfaltigkeit strukturell zur runden 3-Sphäre S³ konvergiert.\n\n-----\n\nNous présentons une reformulation informationnelle-géométrique de la conjecture de Poincaré 3D (théorème de Perelman). L'argument procède en trois étapes. Étape 1 : nous formulons le principe de triple imposition (analytique, dynamique, topologique), montrant que l'unicité de n = 2 pilote l'uniformisation locale de la courbure. Étape 2 : nous démontrons un isomorphisme quantitatif entre la monotonie de la fonctionnelle W-entropie de Perelman W(g, f, τ) (dW/dt ≥ 0) et l'optimisation de la compression mémoire de l'OS de l'Univers (évitant un plantage système pour n ≠ 2). Étape 3 : nous montrons que le flot de Ricci ∂ₜg_ij = −2R_ij avec chirurgie reformate le rendu spatial en utilisant des unités m = 4π, prouvant pourquoi toute 3-variété fermée simplement connexe converge structurellement vers la 3-sphère ronde S³.\n\n-----\n\nPresentiamo una riformulazione informazionale-geometrica della congettura di Poincaré 3D (teorema di Perelman). L'argomentazione procede in tre fasi. Fase 1: formuliamo il principio di tripla imposizione (analitico, dinamico, topologico), mostrando che l'unicità di n = 2 guida l'uniformizzazione locale della curvatura. Fase 2: dimostriamo un isomorfismo quantitativo tra la monotonia del funzionale W-entropia di Perelman W(g, f, τ) (dW/dt ≥ 0) e l'ottimizzazione della compressione di memoria nell'OS dell'Universo (evitando un crash di sistema per n ≠ 2). Fase 3: mostriamo che il flusso di Ricci ∂ₜg_ij = −2R_ij con chirurgia riformatta il rendering spaziale usando unità m = 4π, dimostrando perché ogni 3-varietà chiusa semplicemente connessa converge strutturalmente alla 3-sfera rotonda S³.\n\n-----"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21744112","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-08-01T17:13:40Z","registered":"2026-08-01T17:13:40Z","published":null,"updated":"2026-08-01T17:15:38Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21404387","type":"dois","attributes":{"doi":"10.5281/zenodo.21404387","identifiers":[],"creators":[{"nameType":"Personal","familyName":"Yuuki Yamagishi","name":"Yuuki Yamagishi","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"Information-Geometric Reformulation of the 3D Poincaré Conjecture via the n=2 Uniqueness Theorem and Perelman's Ricci Flow ── Spherical Enforcement on Simply Connected 3-Manifolds and Isomorphism to Perelman's W-Entropy Functional ── [Paper 07]"},{"titleType":"TranslatedTitle","lang":"jpn","title":"n=2唯一性定理とペレルマン・リッチフローに基づく 3次元ポアンカレ予想の情報幾何学的再定式化 ── 3次元単連結閉多様体における球面強制性とペレルマンWエントロピー汎関数との構造的同型 ── [論文07]"},{"titleType":"TranslatedTitle","lang":"deu","title":"Informationsgeometrische Neuformulierung der 3D-Poincaré-Vermutung mittels des Eindeutigkeitssatzes n=2 und Perelmans Ricci-Fluss — Sphärische Erzwingung auf einfach zusammenhängenden 3-Mannigfaltigkeiten und Isomorphie zu Perelmans W-Entropie-Funktional — [Aufsatz 07]"},{"titleType":"TranslatedTitle","lang":"fra","title":"Reformulation informationnelle-géométrique de la conjecture de Poincaré 3D via le théorème d'unicité n=2 et le flot de Ricci de Perelman — Imposition sphérique sur les 3-variétés simplement connexes et isomorphisme à la fonctionnelle W-entropie de Perelman — [Article 07]"},{"titleType":"TranslatedTitle","lang":"ita","title":"Riformulazione informazionale-geometrica della congettura di Poincaré 3D tramite il teorema di unicità n=2 e il flusso di Ricci di Perelman — Imposizione sferica su 3-varietà semplicemente connesse e isomorfismo al funzionale W-entropia di Perelman — [Articolo 07]"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[],"contributors":[],"dates":[{"date":"2026-08-01","dateType":"Issued"}],"language":null,"types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21404387","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"Copyright (C) 2026 Yuuki YAMAGISHI / 山岸勇輝"}],"descriptions":[{"descriptionType":"Abstract","description":"We present an information-geometric reformulation of the 3D Poincaré Conjecture (Perelman's Theorem). The argument proceeds in three stages. Stage 1: We formulate the Triple Enforcement Principle (Analytic, Dynamical, Topological), showing that n=2 uniqueness drives local curvature uniformization. Stage 2: We prove a quantitative isomorphism between Perelman's W-entropy functional W(g, f, τ) monotonicity (dWdt ≥ 0) and Universe OS memory compression optimization (avoiding n ≠ 2 system crash). Stage 3: We demonstrate that Ricci flow ∂_t g_(ij) = -2 R_(ij) with surgery re-formats spatial rendering using m=4π units, proving why any simply connected closed 3-manifold converges structurally to the round 3-sphere S³.\n\n(scope note) Positioning of this paper: This paper offers a structural interpretation of established physical laws and mathematical theorems. It claims neither the discovery of new physical laws nor the proof of open problems. The 3D Poincaré Conjecture was completely proved by Perelman (2002--2003); this paper proposes an information-geometric rereading of that proof. It contributes nothing to the proof and proposes no alternative to it.\n\nA note on the aim of this work. This is a structural reinterpretation of well-established physics, not a proposal for a new physical law. Every relation shown is a substitution into, or a geometric re-reading of, equations that are already known and that remain unchanged. The aim is a modest one: to make a few recurring geometric structures — in particular the solid angle 4π and the exponent n = 2 — easier to see within a single picture. Where a particular unit convention is adopted (for example G = 4π), this is a choice of notation, not a claim about nature. Nothing here is intended to contradict existing results.\n\nOn the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated.\n\n-----\n\n「単連結な3次元閉多様体は3次元球面 S³ に同相である」という3次元ポアンカレ予想(ペレルマンの定理)に対し、n=2 唯一性定理(dm/dr = 4π)に基づく情報幾何学的再定式化を提示する。本稿の論証は3段階からなる。第一段階:解析的・動力学的・位相的の「三重強制原理(Triple Enforcement)」を定式化し、n=2 唯一性条件が多様体の局所曲率を一様化させる幾何学的ドライバであることを明示する。第二段階:ペレルマンの W エントロピー汎関数 W(g, f, τ) の単調増加性が、宇宙OSにおける空間メモリ圧縮率の最適化(n ≠ 2 でのクラッシュ回避)と定量的同型であることを証明する(エントロピー構造同型定理)。第三段階:リッチフロー ∂_t g_(ij) = -2 R_(ij) と特異点手術が山岸パッチ m=4π を単位とする空間一様化プロセスであることを示し、単連結3次元閉多様体が最終的に丸い S³ へ収束する構造的根拠を解明する。\n\n(射程注記) 本稿の位置づけ:本稿は既存の物理法則・数学的定理に対する構造的解釈を提示するものであり、新たな物理法則の発見や未解決問題の証明を主張しない。3次元ポアンカレ予想はペレルマン(2002--2003)により完全に証明されており、本稿はその証明に対する情報幾何学的な読み替えを提案するものである。本稿は当該証明に何ら寄与せず、また代替を提案するものでもない。\n\n本稿の位置づけ。本稿は確立した物理法則に対する構造的解釈であり、新たな物理法則を提案するものではありません。示される関係はいずれも既知の式への代入、またはその幾何学的な読み替えであり、元の式は変わりません。目的はささやかで、繰り返し現れる幾何構造——とくに立体角 4π と指数 n = 2——を一つの描像の中で見やすくすることにあります。特定の単位系(例:G = 4π)を採る箇所は記法上の約束であって、自然についての主張ではありません。既存の結果と矛盾する意図はありません。\n\n作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。\n\n-----\n\nWir stellen eine informationsgeometrische Neuformulierung der 3D-Poincaré-Vermutung (Perelmans Satz) vor. Die Argumentation verläuft in drei Stufen. Stufe 1: Wir formulieren das Prinzip der dreifachen Erzwingung (analytisch, dynamisch, topologisch) und zeigen, dass die Eindeutigkeit von n = 2 die lokale Krümmungsvereinheitlichung antreibt. Stufe 2: Wir beweisen eine quantitative Isomorphie zwischen der Monotonie von Perelmans W-Entropie-Funktional W(g, f, τ) (dW/dt ≥ 0) und der Optimierung der Speicherkompression im Universum-OS (Vermeidung eines Systemabsturzes bei n ≠ 2). Stufe 3: Wir zeigen, dass der Ricci-Fluss ∂ₜg_ij = −2R_ij mit Chirurgie das räumliche Rendering mit m = 4π-Einheiten neu formatiert und beweisen, warum jede einfach zusammenhängende geschlossene 3-Mannigfaltigkeit strukturell zur runden 3-Sphäre S³ konvergiert.\n\n-----\n\nNous présentons une reformulation informationnelle-géométrique de la conjecture de Poincaré 3D (théorème de Perelman). L'argument procède en trois étapes. Étape 1 : nous formulons le principe de triple imposition (analytique, dynamique, topologique), montrant que l'unicité de n = 2 pilote l'uniformisation locale de la courbure. Étape 2 : nous démontrons un isomorphisme quantitatif entre la monotonie de la fonctionnelle W-entropie de Perelman W(g, f, τ) (dW/dt ≥ 0) et l'optimisation de la compression mémoire de l'OS de l'Univers (évitant un plantage système pour n ≠ 2). Étape 3 : nous montrons que le flot de Ricci ∂ₜg_ij = −2R_ij avec chirurgie reformate le rendu spatial en utilisant des unités m = 4π, prouvant pourquoi toute 3-variété fermée simplement connexe converge structurellement vers la 3-sphère ronde S³.\n\n-----\n\nPresentiamo una riformulazione informazionale-geometrica della congettura di Poincaré 3D (teorema di Perelman). L'argomentazione procede in tre fasi. Fase 1: formuliamo il principio di tripla imposizione (analitico, dinamico, topologico), mostrando che l'unicità di n = 2 guida l'uniformizzazione locale della curvatura. Fase 2: dimostriamo un isomorfismo quantitativo tra la monotonia del funzionale W-entropia di Perelman W(g, f, τ) (dW/dt ≥ 0) e l'ottimizzazione della compressione di memoria nell'OS dell'Universo (evitando un crash di sistema per n ≠ 2). Fase 3: mostriamo che il flusso di Ricci ∂ₜg_ij = −2R_ij con chirurgia riformatta il rendering spaziale usando unità m = 4π, dimostrando perché ogni 3-varietà chiusa semplicemente connessa converge strutturalmente alla 3-sfera rotonda S³.\n\n-----"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21404387","contentUrl":null,"metadataVersion":4,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":5,"versionOfCount":1,"created":"2026-07-17T03:23:22Z","registered":"2026-07-17T03:23:22Z","published":null,"updated":"2026-08-01T17:15:38Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21742382","type":"dois","attributes":{"doi":"10.5281/zenodo.21742382","identifiers":[{"identifier":"oai:zenodo.org:21742382","identifierType":"oai"}],"creators":[{"nameType":"Personal","familyName":"叶兴阳双语音标有声读物","name":"叶兴阳双语音标有声读物","nameIdentifiers":[],"affiliation":[]}],"titles":[{"title":"电脑版动物会说话的地方:西非民间传说(Where Animals Talk West African Folk Lore 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Tool"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21742381","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":2,"versionOfCount":1,"created":"2026-08-01T17:15:35Z","registered":"2026-08-01T17:15:35Z","published":null,"updated":"2026-08-01T17:15:35Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.21744051","type":"dois","attributes":{"doi":"10.5281/zenodo.21744051","identifiers":[{"identifier":"oai:zenodo.org:21744051","identifierType":"oai"}],"creators":[{"nameType":"Personal","givenName":"Andrea","familyName":"Paone","name":"Paone, Andrea","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0003-6194-948X"}],"affiliation":[]},{"nameType":"Personal","givenName":"Marco","familyName":"Paone","name":"Paone, Marco","nameIdentifiers":[{"nameIdentifierScheme":"ORCID","nameIdentifier":"0009-0001-6792-879X"}],"affiliation":[]}],"titles":[{"title":"Line-graph inertia of roses and generalized theta graphs"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"rose graph"},{"subject":"generalized theta graph"},{"subject":"line graph"},{"subject":"adjacency inertia"},{"subject":"graph signature"},{"subject":"signless Laplacian"},{"subject":"generalized Schur complement"},{"subject":"spectral graph theory"},{"subject":"2020 MSC 05C50"},{"subject":"2020 MSC 15A18"}],"contributors":[],"dates":[{"date":"2026-08-01","dateType":"Issued"}],"language":"en","types":{"schemaOrg":"CreativeWork","resourceTypeGeneral":"Preprint","citeproc":"article","bibtex":"misc","ris":"GEN","resourceType":""},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.21744050","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"1.0","rightsList":[{"rightsIdentifierScheme":"SPDX","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rights":"Creative Commons Attribution 4.0 International","rightsIdentifier":"cc-by-4.0"},{"rightsUri":"http://rightsstatements.org/vocab/InC/1.0/","rights":"Copyright (C) 2026 The Authors."}],"descriptions":[{"descriptionType":"Abstract","description":"For a graph G, the adjacency inertia of the line graph L(G) is determined by the number of eigenvalues of the signless Laplacian Q(G) above, equal to, and below 2. We compute the inertia of Q(G) - 2I, and hence the inertia of the adjacency matrix of L(G), exactly, including every singular case, for rose graphs and generalized theta graphs.\n\nBoth computations follow from a common reduction. Deleting the common vertices leaves disjoint paths. Range-kernel elimination then leaves their singular kernel directions and a residual scalar for a rose graph, or a 2 x 2 matrix for a generalized theta graph. Terminal exchange determines the eigenvectors of the latter. The resulting formulas depend only on the path lengths modulo 4.\n\nWe obtain closed expressions for the full inertia, the signature, and the multiplicity of the signless Laplacian eigenvalue 2. One theta mode is the rose scalar shifted by the contribution of the second terminal, while the other has no rose analogue.\n\nFurther consequences include the bound m_Q(G,2) \u003c= c(G) for generalized theta graphs with at least three paths, and an exact comparison with the conjectured bound 2s(L(G)) \u003c= c(G) + 1. Its slack grows linearly with the cyclomatic number on both graph classes, with equality only for cycles whose length is congruent to 1 modulo 4. The general conjecture is not proved.\n\nWe also give a partial extension to bridgeless cacti. Exact finite computations check every formula branch, and the accompanying archive provides the source files, verification scripts, frozen outputs, and build information."}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.21744051","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-08-01T17:14:04Z","registered":"2026-08-01T17:14:04Z","published":null,"updated":"2026-08-01T17:15:34Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}}],"meta":{"total":12586380,"totalPages":400,"page":1},"links":{"self":"https://api.datacite.org/dois?provider-id=cern","next":"https://api.datacite.org/dois?page%5Bnumber%5D=2\u0026page%5Bsize%5D=25\u0026provider-id=cern"}}