{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:MC3OTOPWK7KQ6CQRZIGWQMXT2R","short_pith_number":"pith:MC3OTOPW","canonical_record":{"source":{"id":"math/0605469","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2006-05-17T12:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"22f9c808bacaea1ea2f93cebab2387f6655576f579fdd70dd0a5811a67ff3098","abstract_canon_sha256":"a1b041548d879a290ad28bb47a2071653b2fe410a5ae06999bdc359a91db147f"},"schema_version":"1.0"},"canonical_sha256":"60b6e9b9f657d50f0a11ca0d6832f3d46a54b182e0ee3a1f5f27735fba2b4994","source":{"kind":"arxiv","id":"math/0605469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605469","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605469v1","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605469","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"MC3OTOPWK7KQ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MC3OTOPWK7KQ6CQR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MC3OTOPW","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:MC3OTOPWK7KQ6CQRZIGWQMXT2R","target":"record","payload":{"canonical_record":{"source":{"id":"math/0605469","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2006-05-17T12:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"22f9c808bacaea1ea2f93cebab2387f6655576f579fdd70dd0a5811a67ff3098","abstract_canon_sha256":"a1b041548d879a290ad28bb47a2071653b2fe410a5ae06999bdc359a91db147f"},"schema_version":"1.0"},"canonical_sha256":"60b6e9b9f657d50f0a11ca0d6832f3d46a54b182e0ee3a1f5f27735fba2b4994","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:45.945589Z","signature_b64":"jfLPb9mMTOo/nq+EDEmW0apGXEzZyBTIsnkaQs28BfUfu80bvbK9XIJAGo99lNgPvTCt19nRy2iNbhiFjJrrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b6e9b9f657d50f0a11ca0d6832f3d46a54b182e0ee3a1f5f27735fba2b4994","last_reissued_at":"2026-05-18T00:53:45.945236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:45.945236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0605469","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2gsyMVaO9pZjXb58DEsd201BVDfWQX513wI2Ebc6sUjYHskRwZNpP7xaO1023Rbz28dmW2oseRGoJD+lJEDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:53:50.243247Z"},"content_sha256":"5d349712db57ce5fcd543102116000363e9db545c86181ed09dc5b99b1b6e4f9","schema_version":"1.0","event_id":"sha256:5d349712db57ce5fcd543102116000363e9db545c86181ed09dc5b99b1b6e4f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:MC3OTOPWK7KQ6CQRZIGWQMXT2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Game Approach to Universally Kuratowski-Ulam Spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Kucharski, Sz. Plewik","submitted_at":"2006-05-17T12:25:05Z","abstract_excerpt":"We consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable, then the hyperspace exp(Y) with the Vietoris topology is I-favorable, and hence universally Kuratowski-Ulam, (Theorems 6 and 9). Notions of uK-U and uK-U* spaces are compared."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605469","kind":"arxiv","version":1},"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":"2026-05-18T00:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06J66znywipUCYOMWKUuzgh9TJ+P80gm0hcrjg5u4dwcFbqxEyhwUvWMytbc2JXbdDJqxZPM3VITLEbsdvQ3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:53:50.243620Z"},"content_sha256":"c0089e8d49bab59dd50d1c095cc944bd8dd9fd7282e46ea895b1d1663c760c59","schema_version":"1.0","event_id":"sha256:c0089e8d49bab59dd50d1c095cc944bd8dd9fd7282e46ea895b1d1663c760c59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/bundle.json","state_url":"https://pith.science/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/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":"2026-06-25T09:53:50Z","links":{"resolver":"https://pith.science/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R","bundle":"https://pith.science/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/bundle.json","state":"https://pith.science/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MC3OTOPWK7KQ6CQRZIGWQMXT2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MC3OTOPWK7KQ6CQRZIGWQMXT2R","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":"a1b041548d879a290ad28bb47a2071653b2fe410a5ae06999bdc359a91db147f","cross_cats_sorted":[],"license":"","primary_cat":"math.GN","submitted_at":"2006-05-17T12:25:05Z","title_canon_sha256":"22f9c808bacaea1ea2f93cebab2387f6655576f579fdd70dd0a5811a67ff3098"},"schema_version":"1.0","source":{"id":"math/0605469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605469","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605469v1","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605469","created_at":"2026-05-18T00:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"MC3OTOPWK7KQ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MC3OTOPWK7KQ6CQR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MC3OTOPW","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:c0089e8d49bab59dd50d1c095cc944bd8dd9fd7282e46ea895b1d1663c760c59","target":"graph","created_at":"2026-05-18T00:53:45Z","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 consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable, then the hyperspace exp(Y) with the Vietoris topology is I-favorable, and hence universally Kuratowski-Ulam, (Theorems 6 and 9). Notions of uK-U and uK-U* spaces are compared.","authors_text":"A. Kucharski, Sz. Plewik","cross_cats":[],"headline":"","license":"","primary_cat":"math.GN","submitted_at":"2006-05-17T12:25:05Z","title":"Game Approach to Universally Kuratowski-Ulam Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605469","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":"sha256:5d349712db57ce5fcd543102116000363e9db545c86181ed09dc5b99b1b6e4f9","target":"record","created_at":"2026-05-18T00:53:45Z","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":"a1b041548d879a290ad28bb47a2071653b2fe410a5ae06999bdc359a91db147f","cross_cats_sorted":[],"license":"","primary_cat":"math.GN","submitted_at":"2006-05-17T12:25:05Z","title_canon_sha256":"22f9c808bacaea1ea2f93cebab2387f6655576f579fdd70dd0a5811a67ff3098"},"schema_version":"1.0","source":{"id":"math/0605469","kind":"arxiv","version":1}},"canonical_sha256":"60b6e9b9f657d50f0a11ca0d6832f3d46a54b182e0ee3a1f5f27735fba2b4994","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60b6e9b9f657d50f0a11ca0d6832f3d46a54b182e0ee3a1f5f27735fba2b4994","first_computed_at":"2026-05-18T00:53:45.945236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:45.945236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jfLPb9mMTOo/nq+EDEmW0apGXEzZyBTIsnkaQs28BfUfu80bvbK9XIJAGo99lNgPvTCt19nRy2iNbhiFjJrrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:45.945589Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d349712db57ce5fcd543102116000363e9db545c86181ed09dc5b99b1b6e4f9","sha256:c0089e8d49bab59dd50d1c095cc944bd8dd9fd7282e46ea895b1d1663c760c59"],"state_sha256":"177c18a22ad9c9bf7abbb2dbd2252755a91ed5fa42dcf52c64316a3efb9367b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwOuVUv/hPdi+/r9ikP+vH9dxqE4vgl3QlwR9DnUOlzVOsiZYmUHhO3YYZZY4NgKh3CXG0ok/FbnUUywcMeSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:53:50.245557Z","bundle_sha256":"7fcd7595420e0f94982f610c5c404d90e59e5c57b4e3e19f88b1e972eb3f941f"}}