{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TE4UBOS3P7ELBKYTOBVRMPQQYH","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":"5396379745e0e78a148bff168bfefd945f9d76d56867099cd4f8d72d2e83a5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-01T11:31:20Z","title_canon_sha256":"8760c66ddf7d31e85fc22357a77143eb38f17bc52941ca794727e1ba514587e8"},"schema_version":"1.0","source":{"id":"1308.0156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0156","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0156v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0156","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"TE4UBOS3P7EL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TE4UBOS3P7ELBKYT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TE4UBOS3","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:011686caa56799e9c901d07b4be56c5dee940f6cab2f0582c912adedaeb6417c","target":"graph","created_at":"2026-05-18T03:16:59Z","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 prove that it is relatively consistent with ZF + CH that there exist two models of cardinality \\aleph_2 such that the second player has a winning strategy in the Ehrenfeucht-Fra\\\"iss\\'e-game of length \\omega_1 but there is no \\sigma-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist.","authors_text":"Boban Velickovic, Jouko V\\\"a\\\"an\\\"anen, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-01T11:31:20Z","title":"Positional strategies in long Ehrenfeucht-Fraiss\\'e games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0156","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":"sha256:1c70c5a60fbd08b6ab993323dd9eeaf540e2b9de1f1d8c0d1a04446a56d88fdb","target":"record","created_at":"2026-05-18T03:16:59Z","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":"5396379745e0e78a148bff168bfefd945f9d76d56867099cd4f8d72d2e83a5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-01T11:31:20Z","title_canon_sha256":"8760c66ddf7d31e85fc22357a77143eb38f17bc52941ca794727e1ba514587e8"},"schema_version":"1.0","source":{"id":"1308.0156","kind":"arxiv","version":1}},"canonical_sha256":"993940ba5b7fc8b0ab13706b163e10c1dd6ef76995385389c5bb05a10a196599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"993940ba5b7fc8b0ab13706b163e10c1dd6ef76995385389c5bb05a10a196599","first_computed_at":"2026-05-18T03:16:59.681636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:59.681636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MaHB3+/bgFU031kK9cYjbwXkt+w2RBtsxsrbUUSyVc9nfGyNplBTgtIamcRv9CAVnEojMspTXa3WZdPqRX+LDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:59.682201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c70c5a60fbd08b6ab993323dd9eeaf540e2b9de1f1d8c0d1a04446a56d88fdb","sha256:011686caa56799e9c901d07b4be56c5dee940f6cab2f0582c912adedaeb6417c"],"state_sha256":"93a306a9739c1361fcff218be3f09c2507989efcdbaa20d655c2c7023f1d96f6"}