{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4U6BXAVFUHVVJYKN4EFNW2D2KO","short_pith_number":"pith:4U6BXAVF","schema_version":"1.0","canonical_sha256":"e53c1b82a5a1eb54e14de10adb687a53bcc0f73ebdd19b17f49353430240319e","source":{"kind":"arxiv","id":"1608.07144","version":2},"attestation_state":"computed","paper":{"title":"The existence of continuous weak selections and orderability-type properties in products and filter spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dmitri Shakhmatov, Koichi Motooka, Takamitsu Yamauchi","submitted_at":"2016-08-25T13:48:42Z","abstract_excerpt":"Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable space must be hereditarily paracompact provided that its product X\\times Y with some non-discrete space Y has a separately continuous weak selection."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.07144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-08-25T13:48:42Z","cross_cats_sorted":[],"title_canon_sha256":"326c28d6f9e79d9c7e225514d51913b4949ad570f7496223e327e6320faa9afd","abstract_canon_sha256":"cdc9a018dd89a592233c51f6928b097a3a1a07a131d18c6cbea6f0bb0f32dc4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:36.441905Z","signature_b64":"Fi16rrygN0goJei/R7PEYPu6AB8YRG/K0xkoSxD4LfmI1bmiCT/tiBZhMdM3pgqraS85oRXC9lqq8HQB282yBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e53c1b82a5a1eb54e14de10adb687a53bcc0f73ebdd19b17f49353430240319e","last_reissued_at":"2026-05-18T00:32:36.441184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:36.441184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of continuous weak selections and orderability-type properties in products and filter spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dmitri Shakhmatov, Koichi Motooka, Takamitsu Yamauchi","submitted_at":"2016-08-25T13:48:42Z","abstract_excerpt":"Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable space must be hereditarily paracompact provided that its product X\\times Y with some non-discrete space Y has a separately continuous weak selection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07144","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.07144","created_at":"2026-05-18T00:32:36.441308+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07144v2","created_at":"2026-05-18T00:32:36.441308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07144","created_at":"2026-05-18T00:32:36.441308+00:00"},{"alias_kind":"pith_short_12","alias_value":"4U6BXAVFUHVV","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4U6BXAVFUHVVJYKN","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4U6BXAVF","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO","json":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO.json","graph_json":"https://pith.science/api/pith-number/4U6BXAVFUHVVJYKN4EFNW2D2KO/graph.json","events_json":"https://pith.science/api/pith-number/4U6BXAVFUHVVJYKN4EFNW2D2KO/events.json","paper":"https://pith.science/paper/4U6BXAVF"},"agent_actions":{"view_html":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO","download_json":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO.json","view_paper":"https://pith.science/paper/4U6BXAVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07144&json=true","fetch_graph":"https://pith.science/api/pith-number/4U6BXAVFUHVVJYKN4EFNW2D2KO/graph.json","fetch_events":"https://pith.science/api/pith-number/4U6BXAVFUHVVJYKN4EFNW2D2KO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO/action/storage_attestation","attest_author":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO/action/author_attestation","sign_citation":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO/action/citation_signature","submit_replication":"https://pith.science/pith/4U6BXAVFUHVVJYKN4EFNW2D2KO/action/replication_record"}},"created_at":"2026-05-18T00:32:36.441308+00:00","updated_at":"2026-05-18T00:32:36.441308+00:00"}