{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4IGIZFRQELYPOZCISX3G3BCN57","short_pith_number":"pith:4IGIZFRQ","canonical_record":{"source":{"id":"2508.12789","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-18T10:05:47Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"90d86e49a9685363bb10e64e7da5c2a62544799f64ef8c94eb31605228fbb787","abstract_canon_sha256":"03f0161b0366795d21e238c3039056373d0042d965909f0a99cf346791459724"},"schema_version":"1.0"},"canonical_sha256":"e20c8c963022f0f7644895f66d844defc7bceb95168e82968c79787e149797bc","source":{"kind":"arxiv","id":"2508.12789","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.12789","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.12789v1","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.12789","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"4IGIZFRQELYP","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_16","alias_value":"4IGIZFRQELYPOZCI","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_8","alias_value":"4IGIZFRQ","created_at":"2026-07-05T11:55:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4IGIZFRQELYPOZCISX3G3BCN57","target":"record","payload":{"canonical_record":{"source":{"id":"2508.12789","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-18T10:05:47Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"90d86e49a9685363bb10e64e7da5c2a62544799f64ef8c94eb31605228fbb787","abstract_canon_sha256":"03f0161b0366795d21e238c3039056373d0042d965909f0a99cf346791459724"},"schema_version":"1.0"},"canonical_sha256":"e20c8c963022f0f7644895f66d844defc7bceb95168e82968c79787e149797bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:27.183451Z","signature_b64":"AAHwSGsya/Vi9SO17OzrzUefNkases9X/OlgW0mug0GGwJY1c9OgiM9r/kpyOYCCN3qMLiEWkJYIPa4UzXCWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e20c8c963022f0f7644895f66d844defc7bceb95168e82968c79787e149797bc","last_reissued_at":"2026-07-05T11:55:27.182966Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:27.182966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.12789","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZSE+ZmfDfhCfX6NVd79/rVaCoh8gRvSBZX9VkEsL0ro9IDt26e1I6O1nSdoojv+yihAE+FRDaj9vYv+QZMnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:42:36.055957Z"},"content_sha256":"a9f2a744c96a7eaa4d6025b84d953ccc874588e9f0fbb1c2f3b3c4fa606ca6a6","schema_version":"1.0","event_id":"sha256:a9f2a744c96a7eaa4d6025b84d953ccc874588e9f0fbb1c2f3b3c4fa606ca6a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4IGIZFRQELYPOZCISX3G3BCN57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On saturated triangulation-free convex geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Chaya Keller, David Garber, Olga Nissenbaum, Shimon Aviram","submitted_at":"2025-08-18T10:05:47Z","abstract_excerpt":"A convex geometric graph is a graph whose vertices are the corners of a convex polygon P in the plane and whose edges are boundary edges and diagonals of the polygon. It is called triangulation-free if its non-boundary edges do not contain the set of diagonals of some triangulation of P. Aichholzer et al. (2010) showed that the maximum number of edges in a triangulation-free convex geometric graph on n vertices is ${{n}\\choose{2}}-(n-2)$, and subsequently, Keller and Stein (2020) and (independently) Ali et al. (2022) characterized the triangulation-free graphs with this maximum number of edges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12789","kind":"arxiv","version":1},"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/2508.12789/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":"2026-07-05T11:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJYGvRzl7G2ZbKqWu5/IPuRuATHZ1GSzXtP5/7N49rEcLM7yIB2LDlW4zSfw3gBXp2OHgW2UgFQzuOQE9qZ9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T15:42:36.056870Z"},"content_sha256":"a9514e06f13f8a3d5741c9fe24e524fc987cd10022d8afb913aefcd39b90810e","schema_version":"1.0","event_id":"sha256:a9514e06f13f8a3d5741c9fe24e524fc987cd10022d8afb913aefcd39b90810e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IGIZFRQELYPOZCISX3G3BCN57/bundle.json","state_url":"https://pith.science/pith/4IGIZFRQELYPOZCISX3G3BCN57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IGIZFRQELYPOZCISX3G3BCN57/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":"2026-08-19T15:42:36Z","links":{"resolver":"https://pith.science/pith/4IGIZFRQELYPOZCISX3G3BCN57","bundle":"https://pith.science/pith/4IGIZFRQELYPOZCISX3G3BCN57/bundle.json","state":"https://pith.science/pith/4IGIZFRQELYPOZCISX3G3BCN57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IGIZFRQELYPOZCISX3G3BCN57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4IGIZFRQELYPOZCISX3G3BCN57","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":"03f0161b0366795d21e238c3039056373d0042d965909f0a99cf346791459724","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-18T10:05:47Z","title_canon_sha256":"90d86e49a9685363bb10e64e7da5c2a62544799f64ef8c94eb31605228fbb787"},"schema_version":"1.0","source":{"id":"2508.12789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.12789","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.12789v1","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.12789","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"4IGIZFRQELYP","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_16","alias_value":"4IGIZFRQELYPOZCI","created_at":"2026-07-05T11:55:27Z"},{"alias_kind":"pith_short_8","alias_value":"4IGIZFRQ","created_at":"2026-07-05T11:55:27Z"}],"graph_snapshots":[{"event_id":"sha256:a9514e06f13f8a3d5741c9fe24e524fc987cd10022d8afb913aefcd39b90810e","target":"graph","created_at":"2026-07-05T11:55:27Z","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/2508.12789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A convex geometric graph is a graph whose vertices are the corners of a convex polygon P in the plane and whose edges are boundary edges and diagonals of the polygon. It is called triangulation-free if its non-boundary edges do not contain the set of diagonals of some triangulation of P. Aichholzer et al. (2010) showed that the maximum number of edges in a triangulation-free convex geometric graph on n vertices is ${{n}\\choose{2}}-(n-2)$, and subsequently, Keller and Stein (2020) and (independently) Ali et al. (2022) characterized the triangulation-free graphs with this maximum number of edges","authors_text":"Chaya Keller, David Garber, Olga Nissenbaum, Shimon Aviram","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-18T10:05:47Z","title":"On saturated triangulation-free convex geometric graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12789","kind":"arxiv","version":1},"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:a9f2a744c96a7eaa4d6025b84d953ccc874588e9f0fbb1c2f3b3c4fa606ca6a6","target":"record","created_at":"2026-07-05T11:55:27Z","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":"03f0161b0366795d21e238c3039056373d0042d965909f0a99cf346791459724","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-18T10:05:47Z","title_canon_sha256":"90d86e49a9685363bb10e64e7da5c2a62544799f64ef8c94eb31605228fbb787"},"schema_version":"1.0","source":{"id":"2508.12789","kind":"arxiv","version":1}},"canonical_sha256":"e20c8c963022f0f7644895f66d844defc7bceb95168e82968c79787e149797bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e20c8c963022f0f7644895f66d844defc7bceb95168e82968c79787e149797bc","first_computed_at":"2026-07-05T11:55:27.182966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:27.182966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAHwSGsya/Vi9SO17OzrzUefNkases9X/OlgW0mug0GGwJY1c9OgiM9r/kpyOYCCN3qMLiEWkJYIPa4UzXCWBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:27.183451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.12789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9f2a744c96a7eaa4d6025b84d953ccc874588e9f0fbb1c2f3b3c4fa606ca6a6","sha256:a9514e06f13f8a3d5741c9fe24e524fc987cd10022d8afb913aefcd39b90810e"],"state_sha256":"223c83aabea126e3a3abd779bc37110d2334bd6891951781455dff85635d38c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGe4HPAe25QJKY0pelI1bL/ROLLDjFfsiNfgw3yUOSChEarvsL385Rn8XjLx/YNZwXilQhW21aFtXqpXWwZPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T15:42:36.063883Z","bundle_sha256":"8f23c341a27c77dd2b6c15bb4527e5eba4526a90b626012bdb7df0c19489c330"}}