{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:27AK4NAHWIIIBXLCZDOOS43P2Z","short_pith_number":"pith:27AK4NAH","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"},"canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","source":{"kind":"arxiv","id":"2506.01323","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01323","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01323v3","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01323","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"27AK4NAHWIII","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"27AK4NAHWIIIBXLC","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"27AK4NAH","created_at":"2026-07-05T11:19:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:27AK4NAHWIIIBXLCZDOOS43P2Z","target":"record","payload":{"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"},"canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","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"},"source_kind":"arxiv","source_id":"2506.01323","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ELDqji0ODR9Gwa58u9h4vpmxKoYIuiweYClWuS2xkEdyTyJXNgSlg/gkfiRMNMTe71dToAeG/piYx0gC+FX1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:37:12.113099Z"},"content_sha256":"72edb34b2750d82c22d5fecc375b5727bfc8485d4a7c8835a0734f1565c52ca0","schema_version":"1.0","event_id":"sha256:72edb34b2750d82c22d5fecc375b5727bfc8485d4a7c8835a0734f1565c52ca0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:27AK4NAHWIIIBXLCZDOOS43P2Z","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQdmJ7uV7w3+q5PTG9GzJXErmAbHbWe2LlAAh6r1lAvgZgDllvQz0p0XeQjp7Bi+pEy65wNdU0WRXP7mZqe/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:37:12.114017Z"},"content_sha256":"382401c7c246856f31881ca81e07b33b9f462d938ece48ed4cd4b59134a776cf","schema_version":"1.0","event_id":"sha256:382401c7c246856f31881ca81e07b33b9f462d938ece48ed4cd4b59134a776cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/bundle.json","state_url":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T00:37:12Z","links":{"resolver":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z","bundle":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/bundle.json","state":"https://pith.science/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27AK4NAHWIIIBXLCZDOOS43P2Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:27AK4NAHWIIIBXLCZDOOS43P2Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9fa28cfff728be0a9aed23d69653de2d2432a9db20064e43d074b579027c5eb7","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-02T05:10:16Z","title_canon_sha256":"ec390a551aee0f8dd96ecb1bb306750068a57bdb6d5eb166f8bc867d01c7e8eb"},"schema_version":"1.0","source":{"id":"2506.01323","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01323","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01323v3","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01323","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"27AK4NAHWIII","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"27AK4NAHWIIIBXLC","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"27AK4NAH","created_at":"2026-07-05T11:19:07Z"}],"graph_snapshots":[{"event_id":"sha256:382401c7c246856f31881ca81e07b33b9f462d938ece48ed4cd4b59134a776cf","target":"graph","created_at":"2026-07-05T11:19:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.01323/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Arturo Merino, Gibeom Park, Mayank Goswami, Meng-Tsung Tsai, Waldo G\\'alvez","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-02T05:10:16Z","title":"Computing Diverse and Nice Triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01323","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:72edb34b2750d82c22d5fecc375b5727bfc8485d4a7c8835a0734f1565c52ca0","target":"record","created_at":"2026-07-05T11:19:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9fa28cfff728be0a9aed23d69653de2d2432a9db20064e43d074b579027c5eb7","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-06-02T05:10:16Z","title_canon_sha256":"ec390a551aee0f8dd96ecb1bb306750068a57bdb6d5eb166f8bc867d01c7e8eb"},"schema_version":"1.0","source":{"id":"2506.01323","kind":"arxiv","version":3}},"canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7c0ae3407b21080dd62c8dce9736fd647c657134cc844c2d0abc4654ec26660","first_computed_at":"2026-07-05T11:19:07.658780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:07.658780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iiOj7mOY6PboHfWfHV2yowO49nelM0+uP09VAUZVnF/sS5yRd2vtsBgUmCAhYfheMz5n4zehguAqjy+wepGmAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:07.659282Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01323","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72edb34b2750d82c22d5fecc375b5727bfc8485d4a7c8835a0734f1565c52ca0","sha256:382401c7c246856f31881ca81e07b33b9f462d938ece48ed4cd4b59134a776cf"],"state_sha256":"d02f2330cb17615bcb24d3a4b9e26241e3cc6dc19dd204009d89080f14468e86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpHleZdye/yuLfzO0F075ThHxjwKdXwERU4AE7MSrCJFa03I6WG1uPmqCfC0pCuDVL29gtIvj3iohRcYsQveDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T00:37:12.139249Z","bundle_sha256":"73e58088b39dcb5a8c21a5d5fb29856ccc6d06015ffa707dbfd8f1ec6231dbf7"}}