{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MEOUE3MS5CTPJOBF3GA3L5TUMG","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":"85c9af6f79a381a5ca398b27a8556a5366338c192e784a34e76d0d85f60f4534","cross_cats_sorted":["cs.LO","math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T17:25:08Z","title_canon_sha256":"38a4f15151cfcff09eb52fd4d6713f432f3f7b14809294547ff5f4b3b6978173"},"schema_version":"1.0","source":{"id":"2506.11118","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11118","created_at":"2026-06-02T02:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11118v2","created_at":"2026-06-02T02:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11118","created_at":"2026-06-02T02:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"MEOUE3MS5CTP","created_at":"2026-06-02T02:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"MEOUE3MS5CTPJOBF","created_at":"2026-06-02T02:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"MEOUE3MS","created_at":"2026-06-02T02:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:60e83006794d94f791542cb3f841e058508f27f50aa4390f28f4173f6959d125","target":"graph","created_at":"2026-06-02T02:04:47Z","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/2506.11118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem. Further, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the category version of Poincar\\'e Recurrence. The Poincar\\'e Recurrence Theorem for category states that for a homeomorphism without open wandering sets, the set of non recurrent points forms a first category (mea","authors_text":"Prajval Koul, Satyadev Nandakumar","cross_cats":["cs.LO","math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T17:25:08Z","title":"On Effective Banach-Mazur Games and an application to the Poincar\\'e Recurrence Theorem for Category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11118","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":"sha256:75c0d8b7ad6c72ee1906c2f30483288c6d8fa2edcb53e04c5c1b72d01739dfb3","target":"record","created_at":"2026-06-02T02:04:47Z","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":"85c9af6f79a381a5ca398b27a8556a5366338c192e784a34e76d0d85f60f4534","cross_cats_sorted":["cs.LO","math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-06-09T17:25:08Z","title_canon_sha256":"38a4f15151cfcff09eb52fd4d6713f432f3f7b14809294547ff5f4b3b6978173"},"schema_version":"1.0","source":{"id":"2506.11118","kind":"arxiv","version":2}},"canonical_sha256":"611d426d92e8a6f4b825d981b5f674619b4691056be7a010f7ac04ea6dbae6a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"611d426d92e8a6f4b825d981b5f674619b4691056be7a010f7ac04ea6dbae6a5","first_computed_at":"2026-06-02T02:04:47.203244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:47.203244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EPo9XUYUiKDKgk46LqTIcXuwd3/4A87eEnt9JlswHgVMfI78hegvshSV43WaJxSckw9TtYKQrejroRfKo2+0AQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:47.203818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11118","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75c0d8b7ad6c72ee1906c2f30483288c6d8fa2edcb53e04c5c1b72d01739dfb3","sha256:60e83006794d94f791542cb3f841e058508f27f50aa4390f28f4173f6959d125"],"state_sha256":"6a916f8d64e8c44616f6665998ecfeeb55895ce36939964ee9c5d1990bfbcd06"}