{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W5NFS67CT3ESH6SMBGJYUHYA4R","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":"0e1c0248e0dd8f5bbb622bb764e0136c2ec18207aa769242812742b19838de3e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T00:13:38Z","title_canon_sha256":"97a4103fb223f5b87a28d55d59d0e2d98ae5d1df3647f86c0db023322e5cc5e0"},"schema_version":"1.0","source":{"id":"1202.0847","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0847","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0847v2","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0847","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"W5NFS67CT3ES","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W5NFS67CT3ESH6SM","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W5NFS67C","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:653e90ee62e0eaf108d07a30ab4b1b28c6b9710d80c36e7c8a91b49fbedfc6de","target":"graph","created_at":"2026-05-18T03:16:40Z","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 study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the players alternately take one vertex of G in each turn. The first turn is Alice's. The vertices are to be taken according to one (or both) of the following two rules: (T) the subgraph of G induced by the taken vertices is connected during the whole game, (R) the subgraph of G induced by the remaining vertices is connected during the whole game. We show that if rul","authors_text":"Jan Kyn\\v{c}l, Josef Cibulka, Pavel Valtr, Rudolf Stola\\v{r}, Viola M\\'esz\\'aros","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T00:13:38Z","title":"Graph sharing games: complexity and connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0847","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":"sha256:3385ed78c0ebc4a540e3cb7882ff83986bf813e918a57e04a10c533ae606d324","target":"record","created_at":"2026-05-18T03:16:40Z","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":"0e1c0248e0dd8f5bbb622bb764e0136c2ec18207aa769242812742b19838de3e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-04T00:13:38Z","title_canon_sha256":"97a4103fb223f5b87a28d55d59d0e2d98ae5d1df3647f86c0db023322e5cc5e0"},"schema_version":"1.0","source":{"id":"1202.0847","kind":"arxiv","version":2}},"canonical_sha256":"b75a597be29ec923fa4c09938a1f00e456c7b21a99c67b24d2862c69aef0ed7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b75a597be29ec923fa4c09938a1f00e456c7b21a99c67b24d2862c69aef0ed7f","first_computed_at":"2026-05-18T03:16:40.593580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:40.593580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l46+gKw9+4ACwxp/FR6nhrlfdJYvA7E5A7azxeN2GH4m5pw5XKluEdVoRQyyhXZPTzgDnGor8PAB1+M5+tHeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:40.594682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0847","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3385ed78c0ebc4a540e3cb7882ff83986bf813e918a57e04a10c533ae606d324","sha256:653e90ee62e0eaf108d07a30ab4b1b28c6b9710d80c36e7c8a91b49fbedfc6de"],"state_sha256":"a158bc3968c9b85667dbb557fb4994bd63239af400e0e5e9b75ef78f06132caa"}