{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:63GW7PV5OOJYRPFAH6EWAKTVM7","short_pith_number":"pith:63GW7PV5","canonical_record":{"source":{"id":"2409.20505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T17:08:08Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a22ea7ce5e0750c720128aeb6979ef939d8d0e420e6eee098980f95b314c8a87","abstract_canon_sha256":"8d655aba3d69e8b8aca65afec395d3ad403032fd50d03ddee46315b4cf89bd8d"},"schema_version":"1.0"},"canonical_sha256":"f6cd6fbebd739388bca03f89602a7567cfe5f622586c662ac4067509ed78ebcc","source":{"kind":"arxiv","id":"2409.20505","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.20505","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"arxiv_version","alias_value":"2409.20505v2","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20505","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_12","alias_value":"63GW7PV5OOJY","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_16","alias_value":"63GW7PV5OOJYRPFA","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_8","alias_value":"63GW7PV5","created_at":"2026-07-05T10:29:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:63GW7PV5OOJYRPFAH6EWAKTVM7","target":"record","payload":{"canonical_record":{"source":{"id":"2409.20505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T17:08:08Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a22ea7ce5e0750c720128aeb6979ef939d8d0e420e6eee098980f95b314c8a87","abstract_canon_sha256":"8d655aba3d69e8b8aca65afec395d3ad403032fd50d03ddee46315b4cf89bd8d"},"schema_version":"1.0"},"canonical_sha256":"f6cd6fbebd739388bca03f89602a7567cfe5f622586c662ac4067509ed78ebcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:29:23.865732Z","signature_b64":"c/Atawuq1PR2TKT6LkllzjKeyI/AB6de8/T0gLUiXBjg6nGBTC1jjWd5KgHLwGGNhkJiddPLCpN9mouYwZ8eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6cd6fbebd739388bca03f89602a7567cfe5f622586c662ac4067509ed78ebcc","last_reissued_at":"2026-07-05T10:29:23.864884Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:29:23.864884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.20505","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:29:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k5p3mX99bGCyG2Ua7Kxt7OmNefCEtKAFiVIl7d/PjWFjOYCS24VtkeTLvAGHF/E3Mj7WyiDD8ffQ6MfILt58Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:51:22.637400Z"},"content_sha256":"5a83ac0dcc38a4ef79f50f85ed91728167b79d3cfed071b1de500f21759c607c","schema_version":"1.0","event_id":"sha256:5a83ac0dcc38a4ef79f50f85ed91728167b79d3cfed071b1de500f21759c607c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:63GW7PV5OOJYRPFAH6EWAKTVM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Closed Geodetic Game: algorithms and strategies","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Antoine Dailly, Harmender Gahlawat, Zin Mar Myint","submitted_at":"2024-09-30T17:08:08Z","abstract_excerpt":"The geodetic closure of a set S of vertices of a graph is the set of all vertices in shortest paths between pairs of vertices of S. A set S of vertices in a graph is geodetic if its geodetic closure contains all the vertices of the graph. Buckley introduced in 1984 the idea of a game where two players construct together a geodetic set by alternately selecting vertices, the game ending when all vertices are in the geodetic closure. The Geodetic Game was then studied in 1985 by Buckley and Harary, and allowed players to select vertices already in the geodetic closure of the current set. We study"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20505","kind":"arxiv","version":2},"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/2409.20505/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":"2026-07-05T10:29:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oz2+XEu/0kcby7tKq4BoAX6yfbpDEypvalFQW8Chx/FD8FqxEf8/gtOrZiIdpNDphPG1zg4hbKjicIWujjLUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:51:22.637966Z"},"content_sha256":"cd44eef5bce19afdb90b4a0fc6ca05e02917ce476b5eb044d03253e1666ae542","schema_version":"1.0","event_id":"sha256:cd44eef5bce19afdb90b4a0fc6ca05e02917ce476b5eb044d03253e1666ae542"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/bundle.json","state_url":"https://pith.science/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/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":"2026-08-15T10:51:22Z","links":{"resolver":"https://pith.science/pith/63GW7PV5OOJYRPFAH6EWAKTVM7","bundle":"https://pith.science/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/bundle.json","state":"https://pith.science/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63GW7PV5OOJYRPFAH6EWAKTVM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:63GW7PV5OOJYRPFAH6EWAKTVM7","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":"8d655aba3d69e8b8aca65afec395d3ad403032fd50d03ddee46315b4cf89bd8d","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T17:08:08Z","title_canon_sha256":"a22ea7ce5e0750c720128aeb6979ef939d8d0e420e6eee098980f95b314c8a87"},"schema_version":"1.0","source":{"id":"2409.20505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.20505","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"arxiv_version","alias_value":"2409.20505v2","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20505","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_12","alias_value":"63GW7PV5OOJY","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_16","alias_value":"63GW7PV5OOJYRPFA","created_at":"2026-07-05T10:29:23Z"},{"alias_kind":"pith_short_8","alias_value":"63GW7PV5","created_at":"2026-07-05T10:29:23Z"}],"graph_snapshots":[{"event_id":"sha256:cd44eef5bce19afdb90b4a0fc6ca05e02917ce476b5eb044d03253e1666ae542","target":"graph","created_at":"2026-07-05T10:29:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.20505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The geodetic closure of a set S of vertices of a graph is the set of all vertices in shortest paths between pairs of vertices of S. A set S of vertices in a graph is geodetic if its geodetic closure contains all the vertices of the graph. Buckley introduced in 1984 the idea of a game where two players construct together a geodetic set by alternately selecting vertices, the game ending when all vertices are in the geodetic closure. The Geodetic Game was then studied in 1985 by Buckley and Harary, and allowed players to select vertices already in the geodetic closure of the current set. We study","authors_text":"Antoine Dailly, Harmender Gahlawat, Zin Mar Myint","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T17:08:08Z","title":"The Closed Geodetic Game: algorithms and strategies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20505","kind":"arxiv","version":2},"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":"sha256:5a83ac0dcc38a4ef79f50f85ed91728167b79d3cfed071b1de500f21759c607c","target":"record","created_at":"2026-07-05T10:29:23Z","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":"8d655aba3d69e8b8aca65afec395d3ad403032fd50d03ddee46315b4cf89bd8d","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T17:08:08Z","title_canon_sha256":"a22ea7ce5e0750c720128aeb6979ef939d8d0e420e6eee098980f95b314c8a87"},"schema_version":"1.0","source":{"id":"2409.20505","kind":"arxiv","version":2}},"canonical_sha256":"f6cd6fbebd739388bca03f89602a7567cfe5f622586c662ac4067509ed78ebcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6cd6fbebd739388bca03f89602a7567cfe5f622586c662ac4067509ed78ebcc","first_computed_at":"2026-07-05T10:29:23.864884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:29:23.864884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/Atawuq1PR2TKT6LkllzjKeyI/AB6de8/T0gLUiXBjg6nGBTC1jjWd5KgHLwGGNhkJiddPLCpN9mouYwZ8eBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:29:23.865732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.20505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a83ac0dcc38a4ef79f50f85ed91728167b79d3cfed071b1de500f21759c607c","sha256:cd44eef5bce19afdb90b4a0fc6ca05e02917ce476b5eb044d03253e1666ae542"],"state_sha256":"0fd0db045f703e1d9cab34ca6d2e96404e48eb3a79a62a1d52164a870b351d5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHxntm4RKCpl43KF62PKdDNTsA++2UVzk35C75VsjZ/O7IusDKKyUO6RQeKkLtiTQINIcal0PESXe5KbhmV+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T10:51:22.641654Z","bundle_sha256":"9ea9463be6cda55803db8d720676ef2cb6815ef52bb15f6e209bfea1e82996b1"}}