{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LACBWOOKVYL6EW6TGQC6U544VR","short_pith_number":"pith:LACBWOOK","canonical_record":{"source":{"id":"1212.5724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-12-22T20:57:41Z","cross_cats_sorted":[],"title_canon_sha256":"9abe814d150e08e6a6f47665e78b85b27b72552f6ecd62e51eb008aea126c84a","abstract_canon_sha256":"c09bbca65c22323f77f648faa37b57bfeb2b277143d3c8416c2f5510fed799bb"},"schema_version":"1.0"},"canonical_sha256":"58041b39caae17e25bd33405ea779cac684bd86848bb302494c97fa7b0e807ca","source":{"kind":"arxiv","id":"1212.5724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5724","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5724v2","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5724","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"pith_short_12","alias_value":"LACBWOOKVYL6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LACBWOOKVYL6EW6T","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LACBWOOK","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LACBWOOKVYL6EW6TGQC6U544VR","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-12-22T20:57:41Z","cross_cats_sorted":[],"title_canon_sha256":"9abe814d150e08e6a6f47665e78b85b27b72552f6ecd62e51eb008aea126c84a","abstract_canon_sha256":"c09bbca65c22323f77f648faa37b57bfeb2b277143d3c8416c2f5510fed799bb"},"schema_version":"1.0"},"canonical_sha256":"58041b39caae17e25bd33405ea779cac684bd86848bb302494c97fa7b0e807ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:58.476104Z","signature_b64":"rAoAQ7UJFsGdi98eZKUurduPjMYHBdQjoFoSDh3nCCTx4kkUpBz/C0eX0zOmYUkV5dwRUURWM6frFBPwYfaHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58041b39caae17e25bd33405ea779cac684bd86848bb302494c97fa7b0e807ca","last_reissued_at":"2026-05-18T03:32:58.475460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:58.475460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5724","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":"2026-05-18T03:32:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLg25VtJ3c4C1YetI9RE3CnwmTjwVWU1zLfofLxmdvHjfS9sJonrWBNjElQQ08yhiGs6Ir63ZspLD6B+xadwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:15:51.452552Z"},"content_sha256":"12198ccab025b3953d420f12a9e7deef530c11691e7713f5ef9d3c71766c2a3f","schema_version":"1.0","event_id":"sha256:12198ccab025b3953d420f12a9e7deef530c11691e7713f5ef9d3c71766c2a3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LACBWOOKVYL6EW6TGQC6U544VR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite games and cardinal properties of topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Angelo Bella, Santi Spadaro","submitted_at":"2012-12-22T20:57:41Z","abstract_excerpt":"Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindel\\\"of first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii's bound for the number of regular op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5724","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":"2026-05-18T03:32:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9QCPFJQ6cKzagPGaabpiLXhyX9KaU/x6MPO1UytZ7UHVaarWL5pG5g8cDAgjOUxBB1dAFHssnFA3OvaNii7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:15:51.452893Z"},"content_sha256":"8bd3b713dd2e7694df5ba1339d9737110c0b99752f4fe222289384565dee52e0","schema_version":"1.0","event_id":"sha256:8bd3b713dd2e7694df5ba1339d9737110c0b99752f4fe222289384565dee52e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LACBWOOKVYL6EW6TGQC6U544VR/bundle.json","state_url":"https://pith.science/pith/LACBWOOKVYL6EW6TGQC6U544VR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LACBWOOKVYL6EW6TGQC6U544VR/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":"2026-06-01T16:15:51Z","links":{"resolver":"https://pith.science/pith/LACBWOOKVYL6EW6TGQC6U544VR","bundle":"https://pith.science/pith/LACBWOOKVYL6EW6TGQC6U544VR/bundle.json","state":"https://pith.science/pith/LACBWOOKVYL6EW6TGQC6U544VR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LACBWOOKVYL6EW6TGQC6U544VR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LACBWOOKVYL6EW6TGQC6U544VR","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":"c09bbca65c22323f77f648faa37b57bfeb2b277143d3c8416c2f5510fed799bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-12-22T20:57:41Z","title_canon_sha256":"9abe814d150e08e6a6f47665e78b85b27b72552f6ecd62e51eb008aea126c84a"},"schema_version":"1.0","source":{"id":"1212.5724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5724","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5724v2","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5724","created_at":"2026-05-18T03:32:58Z"},{"alias_kind":"pith_short_12","alias_value":"LACBWOOKVYL6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LACBWOOKVYL6EW6T","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LACBWOOK","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:8bd3b713dd2e7694df5ba1339d9737110c0b99752f4fe222289384565dee52e0","target":"graph","created_at":"2026-05-18T03:32:58Z","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":"Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindel\\\"of first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii's bound for the number of regular op","authors_text":"Angelo Bella, Santi Spadaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-12-22T20:57:41Z","title":"Infinite games and cardinal properties of topological spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5724","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":"sha256:12198ccab025b3953d420f12a9e7deef530c11691e7713f5ef9d3c71766c2a3f","target":"record","created_at":"2026-05-18T03:32:58Z","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":"c09bbca65c22323f77f648faa37b57bfeb2b277143d3c8416c2f5510fed799bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-12-22T20:57:41Z","title_canon_sha256":"9abe814d150e08e6a6f47665e78b85b27b72552f6ecd62e51eb008aea126c84a"},"schema_version":"1.0","source":{"id":"1212.5724","kind":"arxiv","version":2}},"canonical_sha256":"58041b39caae17e25bd33405ea779cac684bd86848bb302494c97fa7b0e807ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58041b39caae17e25bd33405ea779cac684bd86848bb302494c97fa7b0e807ca","first_computed_at":"2026-05-18T03:32:58.475460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:58.475460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rAoAQ7UJFsGdi98eZKUurduPjMYHBdQjoFoSDh3nCCTx4kkUpBz/C0eX0zOmYUkV5dwRUURWM6frFBPwYfaHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:58.476104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12198ccab025b3953d420f12a9e7deef530c11691e7713f5ef9d3c71766c2a3f","sha256:8bd3b713dd2e7694df5ba1339d9737110c0b99752f4fe222289384565dee52e0"],"state_sha256":"efffafb7f4a54702801ab830814a025df0ea24474aed4c6b605cbc6663db2795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OBklR0gRcQlOvsRnOBDM48Hd4yO7EosBOL8/hogiwhvjSekAx6bt0XdqvScUza5Tw/xbeY9+mvpHW8HmZVqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:15:51.454811Z","bundle_sha256":"67d0cc97378f609f6202e5c00a08867406726e8aa3924a29662ef0afb14c14f5"}}