{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FW5FVDN3EB3Q3TLAVASE44WBWK","short_pith_number":"pith:FW5FVDN3","canonical_record":{"source":{"id":"1411.1303","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-04T18:05:26Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"a708fda7150538e84651acb1ec2541baf2302e4b51e461ede60252bcf4b2ae2c","abstract_canon_sha256":"f2eb066b5abdcb0676a9f9510ffa67147b1b5a1db459955deb6ba9338df8026f"},"schema_version":"1.0"},"canonical_sha256":"2dba5a8dbb20770dcd60a8244e72c1b29790f7fc1b7788d50d52077ebd0c5efa","source":{"kind":"arxiv","id":"1411.1303","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1303","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1303v3","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1303","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"FW5FVDN3EB3Q","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FW5FVDN3EB3Q3TLA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FW5FVDN3","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FW5FVDN3EB3Q3TLAVASE44WBWK","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1303","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-04T18:05:26Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"a708fda7150538e84651acb1ec2541baf2302e4b51e461ede60252bcf4b2ae2c","abstract_canon_sha256":"f2eb066b5abdcb0676a9f9510ffa67147b1b5a1db459955deb6ba9338df8026f"},"schema_version":"1.0"},"canonical_sha256":"2dba5a8dbb20770dcd60a8244e72c1b29790f7fc1b7788d50d52077ebd0c5efa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:23.732269Z","signature_b64":"K3dPYby8U4iFgCRExg5+tDfSfQWxhNB4LetvcIrklqeL9WpDrJAqjmUzjXcxHLOxF1AkAhNnu6hj3ngJ9hKOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dba5a8dbb20770dcd60a8244e72c1b29790f7fc1b7788d50d52077ebd0c5efa","last_reissued_at":"2026-05-18T00:38:23.731480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:23.731480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1303","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":"2026-05-18T00:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Peel0nKR1WRR0eLyK2v2erkdMKAqIGYBwKJu6U+nf8SziRnRF4L6gVSeQq0+UY93WhHSvLjkArBu4UmE/jY5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:40:10.392542Z"},"content_sha256":"d25e130e0cd13e86a5e619977709a5317723e40e2e46139a293387f63e273053","schema_version":"1.0","event_id":"sha256:d25e130e0cd13e86a5e619977709a5317723e40e2e46139a293387f63e273053"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FW5FVDN3EB3Q3TLAVASE44WBWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex polygons in geometric triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","submitted_at":"2014-11-04T18:05:26Z","abstract_excerpt":"We show that the maximum number of convex polygons in a triangulation of $n$ points in the plane is $O(1.5029^n)$. This improves an earlier bound of $O(1.6181^n)$ established by van Kreveld, L\\\"offler, and Pach (2012) and almost matches the current best lower bound of $\\Omega(1.5028^n)$ due to the same authors. Given a planar straight-line graph $G$ with $n$ vertices, we show how to compute efficiently the number of convex polygons in $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1303","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":""},"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":"2026-05-18T00:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nxw3QlSE/HQnYMThFuseaati/xBe7p+iSEged/djO/v3gVFfEEm5MgtcbqA2yuN2rtZl6vofwjiFwhZJQuouBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:40:10.393437Z"},"content_sha256":"341f72a0989d60eccc2a0a31538475b8e8581b26f98a1e41bc5e89d53746e375","schema_version":"1.0","event_id":"sha256:341f72a0989d60eccc2a0a31538475b8e8581b26f98a1e41bc5e89d53746e375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/bundle.json","state_url":"https://pith.science/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/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":"2026-05-30T17:40:10Z","links":{"resolver":"https://pith.science/pith/FW5FVDN3EB3Q3TLAVASE44WBWK","bundle":"https://pith.science/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/bundle.json","state":"https://pith.science/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FW5FVDN3EB3Q3TLAVASE44WBWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FW5FVDN3EB3Q3TLAVASE44WBWK","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":"f2eb066b5abdcb0676a9f9510ffa67147b1b5a1db459955deb6ba9338df8026f","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-04T18:05:26Z","title_canon_sha256":"a708fda7150538e84651acb1ec2541baf2302e4b51e461ede60252bcf4b2ae2c"},"schema_version":"1.0","source":{"id":"1411.1303","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1303","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1303v3","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1303","created_at":"2026-05-18T00:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"FW5FVDN3EB3Q","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FW5FVDN3EB3Q3TLA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FW5FVDN3","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:341f72a0989d60eccc2a0a31538475b8e8581b26f98a1e41bc5e89d53746e375","target":"graph","created_at":"2026-05-18T00:38:23Z","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"},"paper":{"abstract_excerpt":"We show that the maximum number of convex polygons in a triangulation of $n$ points in the plane is $O(1.5029^n)$. This improves an earlier bound of $O(1.6181^n)$ established by van Kreveld, L\\\"offler, and Pach (2012) and almost matches the current best lower bound of $\\Omega(1.5028^n)$ due to the same authors. Given a planar straight-line graph $G$ with $n$ vertices, we show how to compute efficiently the number of convex polygons in $G$.","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-04T18:05:26Z","title":"Convex polygons in geometric triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1303","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:d25e130e0cd13e86a5e619977709a5317723e40e2e46139a293387f63e273053","target":"record","created_at":"2026-05-18T00:38:23Z","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":"f2eb066b5abdcb0676a9f9510ffa67147b1b5a1db459955deb6ba9338df8026f","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-04T18:05:26Z","title_canon_sha256":"a708fda7150538e84651acb1ec2541baf2302e4b51e461ede60252bcf4b2ae2c"},"schema_version":"1.0","source":{"id":"1411.1303","kind":"arxiv","version":3}},"canonical_sha256":"2dba5a8dbb20770dcd60a8244e72c1b29790f7fc1b7788d50d52077ebd0c5efa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dba5a8dbb20770dcd60a8244e72c1b29790f7fc1b7788d50d52077ebd0c5efa","first_computed_at":"2026-05-18T00:38:23.731480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:23.731480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3dPYby8U4iFgCRExg5+tDfSfQWxhNB4LetvcIrklqeL9WpDrJAqjmUzjXcxHLOxF1AkAhNnu6hj3ngJ9hKOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:23.732269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1303","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d25e130e0cd13e86a5e619977709a5317723e40e2e46139a293387f63e273053","sha256:341f72a0989d60eccc2a0a31538475b8e8581b26f98a1e41bc5e89d53746e375"],"state_sha256":"216bb0a49669dc3f8d01544d4f06cf7e0fc63b62478949e8437c6465739a72f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XREFg4C5ZDHqZMTOIdwLFSO6TN28AZQ0QfrKfTIOJ+6Mdbm9/1M4G8qS13OQuS3iKE7Qd9+SEz9JOUFJBUcoBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:40:10.403667Z","bundle_sha256":"6840cfc25d872db00389e63c69d80473f6762efabc1e192ea4b45c3c4609688d"}}