{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MPWTKNCNU4LU4MMKBER4VFGTQR","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":"b5a2f42ec4377bc4304ca293e4326d7fb1eb77db95baf75e1af95e137b559dfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-11-16T05:56:56Z","title_canon_sha256":"c57951d1123c9b15b9e784760eb2925d9f9333de5516e846330463eb589ea431"},"schema_version":"1.0","source":{"id":"1011.3586","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3586","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3586v1","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3586","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"MPWTKNCNU4LU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MPWTKNCNU4LU4MMK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MPWTKNCN","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:3671c23b407a800b814cdddb81b2614178f6d7dc254a6bfb19e6cb829d7468d5","target":"graph","created_at":"2026-05-18T04:35:48Z","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 a Hausdorff space $X$ is very $\\mathrm I$-favorable if and only if $X$ is the almost limit space of a $\\sigma$-complete inverse system consisting of (not necessarily Hausdorff) second countable spaces and surjective d-open bonding maps. It is also shown that the class of Tychonoff very $\\mathrm I$-favorable spaces with respect to the co-zero sets coincides with the d-openly generated spaces.","authors_text":"A. Kucharski, Sz. Plewik, V. Valov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-11-16T05:56:56Z","title":"Very I-favorable spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3586","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:a8f93c3bb43405f7e2ae651e1d62f4b2dada8efff13d743f52404779a7d61215","target":"record","created_at":"2026-05-18T04:35:48Z","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":"b5a2f42ec4377bc4304ca293e4326d7fb1eb77db95baf75e1af95e137b559dfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-11-16T05:56:56Z","title_canon_sha256":"c57951d1123c9b15b9e784760eb2925d9f9333de5516e846330463eb589ea431"},"schema_version":"1.0","source":{"id":"1011.3586","kind":"arxiv","version":1}},"canonical_sha256":"63ed35344da7174e318a0923ca94d384725b9b94d5628ccfb168ddc042a249bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63ed35344da7174e318a0923ca94d384725b9b94d5628ccfb168ddc042a249bf","first_computed_at":"2026-05-18T04:35:48.518511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:48.518511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HtWNNIrLMthbc09OVuiA865+PFHT4/ip9b0My8QHMIJRn1y0PNHrgwPpgRIpSFoY4zSHv8ubRHwi81Puu9evAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:48.519084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3586","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8f93c3bb43405f7e2ae651e1d62f4b2dada8efff13d743f52404779a7d61215","sha256:3671c23b407a800b814cdddb81b2614178f6d7dc254a6bfb19e6cb829d7468d5"],"state_sha256":"f4385177930b0fda790abc93bee8f09bfdc22ae697f08fe4d66793a30d33a593"}