{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KLF3NK4WHMAPTW2BYYQ7CFCELI","short_pith_number":"pith:KLF3NK4W","schema_version":"1.0","canonical_sha256":"52cbb6ab963b00f9db41c621f114445a10d650b0f55dc2a6256b793b7352614c","source":{"kind":"arxiv","id":"2402.05990","version":2},"attestation_state":"computed","paper":{"title":"The Ginsburg--Sands theorem and computability theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrew De Lapo, Damir Dzhafarov, Heidi Benham, Java Darleen Villano, Reed Solomon","submitted_at":"2024-02-08T18:59:57Z","abstract_excerpt":"The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on $\\omega$: indiscrete, discrete, initial segment, final segment, and cofinite. The original proof is nonconstructive, and features an interesting application of Ramsey's theorem for pairs ($\\mathsf{RT}^2_2$). We analyze this principle in computability theory and reverse mathematics, using Dorais's formalization of CSC spaces. Among our results are that the Ginsburg-Sands theorem for CSC spaces is equivalent to $\\mathsf{AC"},"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":"2402.05990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-02-08T18:59:57Z","cross_cats_sorted":[],"title_canon_sha256":"5572e35d72ac4888cf32ba2a8a18d8e64b8e31d56e7d667f7389c54f32039809","abstract_canon_sha256":"2ef011ec16c767385f3de6f1a9ca486a0b4ba3721813767f8d5a07dc6d24e701"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:45.610667Z","signature_b64":"ULr7FJhAuZ9iAM1lV+cXyoRoaFCNGwoAO8YA/ZCwc42wzgaNUgfFhfJKSnoHcvoc3UxFsxN5Lst2m8fJPo5aDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52cbb6ab963b00f9db41c621f114445a10d650b0f55dc2a6256b793b7352614c","last_reissued_at":"2026-07-05T08:36:45.610161Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:45.610161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Ginsburg--Sands theorem and computability theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrew De Lapo, Damir Dzhafarov, Heidi Benham, Java Darleen Villano, Reed Solomon","submitted_at":"2024-02-08T18:59:57Z","abstract_excerpt":"The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on $\\omega$: indiscrete, discrete, initial segment, final segment, and cofinite. The original proof is nonconstructive, and features an interesting application of Ramsey's theorem for pairs ($\\mathsf{RT}^2_2$). We analyze this principle in computability theory and reverse mathematics, using Dorais's formalization of CSC spaces. Among our results are that the Ginsburg-Sands theorem for CSC spaces is equivalent to $\\mathsf{AC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.05990","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.05990/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2402.05990","created_at":"2026-07-05T08:36:45.610219+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.05990v2","created_at":"2026-07-05T08:36:45.610219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.05990","created_at":"2026-07-05T08:36:45.610219+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLF3NK4WHMAP","created_at":"2026-07-05T08:36:45.610219+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLF3NK4WHMAPTW2B","created_at":"2026-07-05T08:36:45.610219+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLF3NK4W","created_at":"2026-07-05T08:36:45.610219+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/KLF3NK4WHMAPTW2BYYQ7CFCELI","json":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI.json","graph_json":"https://pith.science/api/pith-number/KLF3NK4WHMAPTW2BYYQ7CFCELI/graph.json","events_json":"https://pith.science/api/pith-number/KLF3NK4WHMAPTW2BYYQ7CFCELI/events.json","paper":"https://pith.science/paper/KLF3NK4W"},"agent_actions":{"view_html":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI","download_json":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI.json","view_paper":"https://pith.science/paper/KLF3NK4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.05990&json=true","fetch_graph":"https://pith.science/api/pith-number/KLF3NK4WHMAPTW2BYYQ7CFCELI/graph.json","fetch_events":"https://pith.science/api/pith-number/KLF3NK4WHMAPTW2BYYQ7CFCELI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI/action/storage_attestation","attest_author":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI/action/author_attestation","sign_citation":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI/action/citation_signature","submit_replication":"https://pith.science/pith/KLF3NK4WHMAPTW2BYYQ7CFCELI/action/replication_record"}},"created_at":"2026-07-05T08:36:45.610219+00:00","updated_at":"2026-07-05T08:36:45.610219+00:00"}