{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:27AK4NAHWIIIBXLCZDOOS43P2Z","short_pith_number":"pith:27AK4NAH","schema_version":"1.0","canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","source":{"kind":"arxiv","id":"2506.01323","version":3},"attestation_state":"computed","paper":{"title":"Computing Diverse and Nice Triangulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Arturo Merino, Gibeom Park, Mayank Goswami, Meng-Tsung Tsai, Waldo G\\'alvez","submitted_at":"2025-06-02T05:10:16Z","abstract_excerpt":"We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \\geq 2 $, a quality measure $\\sigma$ on the set of triangulations of $P$ and a factor $ \\alpha \\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \\emph{distinct} triangulations $T_1,\\dots,T_k$ of $P$ such that a) their diversity, $\\sum_{i < j} d(T_i,T_j) $, is as large as possible \\emph{and} b) they are nice, i.e., $\\sigma(T_i) \\leq \\alpha \\sigma^* $ for all $1\\leq i \\leq k$. Here, $d$ denotes the symmetric difference of edge se"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.01323","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-02T05:10:16Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"ec390a551aee0f8dd96ecb1bb306750068a57bdb6d5eb166f8bc867d01c7e8eb","abstract_canon_sha256":"9fa28cfff728be0a9aed23d69653de2d2432a9db20064e43d074b579027c5eb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:07.659282Z","signature_b64":"iiOj7mOY6PboHfWfHV2yowO49nelM0+uP09VAUZVnF/sS5yRd2vtsBgUmCAhYfheMz5n4zehguAqjy+wepGmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","last_reissued_at":"2026-07-05T11:19:07.658780Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:07.658780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Diverse and Nice Triangulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Arturo Merino, Gibeom Park, Mayank Goswami, Meng-Tsung Tsai, Waldo G\\'alvez","submitted_at":"2025-06-02T05:10:16Z","abstract_excerpt":"We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \\geq 2 $, a quality measure $\\sigma$ on the set of triangulations of $P$ and a factor $ \\alpha \\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \\emph{distinct} triangulations $T_1,\\dots,T_k$ of $P$ such that a) their diversity, $\\sum_{i < j} d(T_i,T_j) $, is as large as possible \\emph{and} b) they are nice, i.e., $\\sigma(T_i) \\leq \\alpha \\sigma^* $ for all $1\\leq i \\leq k$. Here, $d$ denotes the symmetric difference of edge se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01323","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01323/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.01323","created_at":"2026-07-05T11:19:07.658837+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.01323v3","created_at":"2026-07-05T11:19:07.658837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01323","created_at":"2026-07-05T11:19:07.658837+00:00"},{"alias_kind":"pith_short_12","alias_value":"27AK4NAHWIII","created_at":"2026-07-05T11:19:07.658837+00:00"},{"alias_kind":"pith_short_16","alias_value":"27AK4NAHWIIIBXLC","created_at":"2026-07-05T11:19:07.658837+00:00"},{"alias_kind":"pith_short_8","alias_value":"27AK4NAH","created_at":"2026-07-05T11:19:07.658837+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z","json":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z.json","graph_json":"https://pith.science/api/pith-number/27AK4NAHWIIIBXLCZDOOS43P2Z/graph.json","events_json":"https://pith.science/api/pith-number/27AK4NAHWIIIBXLCZDOOS43P2Z/events.json","paper":"https://pith.science/paper/27AK4NAH"},"agent_actions":{"view_html":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z","download_json":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z.json","view_paper":"https://pith.science/paper/27AK4NAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.01323&json=true","fetch_graph":"https://pith.science/api/pith-number/27AK4NAHWIIIBXLCZDOOS43P2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/27AK4NAHWIIIBXLCZDOOS43P2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/action/storage_attestation","attest_author":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/action/author_attestation","sign_citation":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/action/citation_signature","submit_replication":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/action/replication_record"}},"created_at":"2026-07-05T11:19:07.658837+00:00","updated_at":"2026-07-05T11:19:07.658837+00:00"}