{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EGOIVHHOMNNVI3JKTJP2RXIQZW","short_pith_number":"pith:EGOIVHHO","canonical_record":{"source":{"id":"1709.01354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-05T12:40:10Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4d74d0306db7dcf9004d6d42b22ee2b53cb11e2737ab3b87672495c4ed3e5be4","abstract_canon_sha256":"e98a62571ddf1476438a11789d85abe298197428dc27526a1474d623f5322cb6"},"schema_version":"1.0"},"canonical_sha256":"219c8a9cee635b546d2a9a5fa8dd10cd8b63f3210b270090cce20c1eb11e0765","source":{"kind":"arxiv","id":"1709.01354","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01354","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01354v2","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01354","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"EGOIVHHOMNNV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGOIVHHOMNNVI3JK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGOIVHHO","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EGOIVHHOMNNVI3JKTJP2RXIQZW","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-05T12:40:10Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4d74d0306db7dcf9004d6d42b22ee2b53cb11e2737ab3b87672495c4ed3e5be4","abstract_canon_sha256":"e98a62571ddf1476438a11789d85abe298197428dc27526a1474d623f5322cb6"},"schema_version":"1.0"},"canonical_sha256":"219c8a9cee635b546d2a9a5fa8dd10cd8b63f3210b270090cce20c1eb11e0765","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:45.616266Z","signature_b64":"4TCAeGUseYsB5UaSBL3IAW6NeAKthSJJOP9lxIhCTOQUuMohj5braJijMWjGwGy3J1fT/kU6NT+WxEWnqJCACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"219c8a9cee635b546d2a9a5fa8dd10cd8b63f3210b270090cce20c1eb11e0765","last_reissued_at":"2026-05-18T00:02:45.615788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:45.615788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01354","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":"2026-05-18T00:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgJ8uBxpDVmbcmlXJhw2nV7fP+IiFU934aY3bVHkbJcKpQh6NQJHpZkd+uUVbquO+WWcBfPvFefcoBEhNdZbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:11:31.338073Z"},"content_sha256":"3105e03d207520921ac1b320f91194c0742647a3db4945b240f70fdc1b62feea","schema_version":"1.0","event_id":"sha256:3105e03d207520921ac1b320f91194c0742647a3db4945b240f70fdc1b62feea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EGOIVHHOMNNVI3JKTJP2RXIQZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A vertex and edge deletion game on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Cormac O'Sullivan","submitted_at":"2017-09-05T12:40:10Z","abstract_excerpt":"Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of nim-values to new families of graphs. A conjecture of Khandhawit and Ye on the nim-values of graphs with one odd cycle is proved. We also see that, for wheels and their subgraphs, this game exhibits a surprising amount of unexplained regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01354","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":""},"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":"2026-05-18T00:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zF/L2Jq8dd4Y2HWpIW6uF0TY9KyzxvZoj9jECqymwMLgZBUILqHjwtGCkPcFmx0JBh3MwV8+XPq1j5g17P1VBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:11:31.338748Z"},"content_sha256":"7a8db9e7833b8c32f4c3c140644ecf0fe5a261c660f984edfda0e41fee74fd9a","schema_version":"1.0","event_id":"sha256:7a8db9e7833b8c32f4c3c140644ecf0fe5a261c660f984edfda0e41fee74fd9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/bundle.json","state_url":"https://pith.science/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/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":"2026-06-23T06:11:31Z","links":{"resolver":"https://pith.science/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW","bundle":"https://pith.science/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/bundle.json","state":"https://pith.science/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGOIVHHOMNNVI3JKTJP2RXIQZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EGOIVHHOMNNVI3JKTJP2RXIQZW","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":"e98a62571ddf1476438a11789d85abe298197428dc27526a1474d623f5322cb6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-05T12:40:10Z","title_canon_sha256":"4d74d0306db7dcf9004d6d42b22ee2b53cb11e2737ab3b87672495c4ed3e5be4"},"schema_version":"1.0","source":{"id":"1709.01354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01354","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01354v2","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01354","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"EGOIVHHOMNNV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGOIVHHOMNNVI3JK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGOIVHHO","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:7a8db9e7833b8c32f4c3c140644ecf0fe5a261c660f984edfda0e41fee74fd9a","target":"graph","created_at":"2026-05-18T00:02:45Z","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":"Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of nim-values to new families of graphs. A conjecture of Khandhawit and Ye on the nim-values of graphs with one odd cycle is proved. We also see that, for wheels and their subgraphs, this game exhibits a surprising amount of unexplained regularity.","authors_text":"Cormac O'Sullivan","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-05T12:40:10Z","title":"A vertex and edge deletion game on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01354","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":"sha256:3105e03d207520921ac1b320f91194c0742647a3db4945b240f70fdc1b62feea","target":"record","created_at":"2026-05-18T00:02:45Z","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":"e98a62571ddf1476438a11789d85abe298197428dc27526a1474d623f5322cb6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-05T12:40:10Z","title_canon_sha256":"4d74d0306db7dcf9004d6d42b22ee2b53cb11e2737ab3b87672495c4ed3e5be4"},"schema_version":"1.0","source":{"id":"1709.01354","kind":"arxiv","version":2}},"canonical_sha256":"219c8a9cee635b546d2a9a5fa8dd10cd8b63f3210b270090cce20c1eb11e0765","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"219c8a9cee635b546d2a9a5fa8dd10cd8b63f3210b270090cce20c1eb11e0765","first_computed_at":"2026-05-18T00:02:45.615788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:45.615788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TCAeGUseYsB5UaSBL3IAW6NeAKthSJJOP9lxIhCTOQUuMohj5braJijMWjGwGy3J1fT/kU6NT+WxEWnqJCACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:45.616266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3105e03d207520921ac1b320f91194c0742647a3db4945b240f70fdc1b62feea","sha256:7a8db9e7833b8c32f4c3c140644ecf0fe5a261c660f984edfda0e41fee74fd9a"],"state_sha256":"7b2613efd16bbee733dbbe4503bdb5c2c731874d2d53990c34a9de31523a28c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/Zge8R2r5jbOGJ95nf7KWvoCKwNDBdl2yQdUvrfNugjzzUwGlmauZAQTG2F7HTYXm+0/l/1y2D8mIgRb2hSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:11:31.341977Z","bundle_sha256":"29814653eedfc918b46beb88de860b49e22a1cd50801fce1b6dd1c91ec648a67"}}