{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JN6PQXP2VX7YCVBP3SPKC2WDDA","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":"67c94a8b11e48d1aef62fa301d19bf1f94cd2f0e2957244554fa1f8421b49f9e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-11T20:48:36Z","title_canon_sha256":"ff5e3b1c6bbfd970a1cff4040595529f56c9ae6550010d4aff2ed244e88556f6"},"schema_version":"1.0","source":{"id":"1208.2384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2384","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2384v1","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2384","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"JN6PQXP2VX7Y","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JN6PQXP2VX7YCVBP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JN6PQXP2","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e548434b0a548938cb05d1562f91c5767ad62eb132360c661e008ed77b4dd471","target":"graph","created_at":"2026-05-18T03:48:58Z","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 a game theoretic dichotomy for $G_{\\delta\\sigma}$ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis' proof of $G_{\\delta\\sigma}$ determinacy.","authors_text":"Christian Rosendal","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-11T20:48:36Z","title":"Determinacy of adversarial Gowers games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2384","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:ee59a770ec0ba276f6c50d8c66ab5ee523e233cfd9e1bccc1ef00e96110720d1","target":"record","created_at":"2026-05-18T03:48:58Z","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":"67c94a8b11e48d1aef62fa301d19bf1f94cd2f0e2957244554fa1f8421b49f9e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-11T20:48:36Z","title_canon_sha256":"ff5e3b1c6bbfd970a1cff4040595529f56c9ae6550010d4aff2ed244e88556f6"},"schema_version":"1.0","source":{"id":"1208.2384","kind":"arxiv","version":1}},"canonical_sha256":"4b7cf85dfaadff81542fdc9ea16ac31818c2a2d69b0ef24bede0acaf2da59d13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7cf85dfaadff81542fdc9ea16ac31818c2a2d69b0ef24bede0acaf2da59d13","first_computed_at":"2026-05-18T03:48:58.028697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:58.028697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RV+TuN4q70S9uJpa1nMnuM6zPGUmbqW87SBiz8dMrENQ2Ud95MP8ex/izoMPc7xAeUu1xXpA0iqCq6aEpxWPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:58.029488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee59a770ec0ba276f6c50d8c66ab5ee523e233cfd9e1bccc1ef00e96110720d1","sha256:e548434b0a548938cb05d1562f91c5767ad62eb132360c661e008ed77b4dd471"],"state_sha256":"b6ba87dcad21572a33efcab2ef59b350435739a89635acdaf87d96161bfcb0e1"}