{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RAXZ4JO72ZLNAMHS2DMCHPB7QR","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":"1df7b2e87ab437007c43862204bccc2e7816efa17e412d22870d2beaa1064112","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-05-13T09:01:50Z","title_canon_sha256":"1fe3a5061b454ebbd241d965c66b67574dd6e3ad0edd02d7467747f64ec3d933"},"schema_version":"1.0","source":{"id":"1605.04087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04087","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04087v1","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04087","created_at":"2026-05-18T01:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"RAXZ4JO72ZLN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RAXZ4JO72ZLNAMHS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RAXZ4JO7","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:2d6833778a73d5446957cb4a86d180c0f0b1901d56e2bff6f22638ff051b058c","target":"graph","created_at":"2026-05-18T01:14:54Z","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 show that every filter $\\mathcal{F}$ on $\\omega$, viewed as a subspace of $2^\\omega$, is homeomorphic to $\\mathcal{F}^2$. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.","authors_text":"Andrea Medini, Lyubomyr Zdomskyy","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-05-13T09:01:50Z","title":"Every filter is homeomorphic to its square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04087","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":"sha256:33ab154fe73cedbb3dec581c0272c245a42aa3b1f9d89d707de38bcd5e52689d","target":"record","created_at":"2026-05-18T01:14:54Z","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":"1df7b2e87ab437007c43862204bccc2e7816efa17e412d22870d2beaa1064112","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-05-13T09:01:50Z","title_canon_sha256":"1fe3a5061b454ebbd241d965c66b67574dd6e3ad0edd02d7467747f64ec3d933"},"schema_version":"1.0","source":{"id":"1605.04087","kind":"arxiv","version":1}},"canonical_sha256":"882f9e25dfd656d030f2d0d823bc3f844155a9ed8777146559aa8b7ce56a192d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"882f9e25dfd656d030f2d0d823bc3f844155a9ed8777146559aa8b7ce56a192d","first_computed_at":"2026-05-18T01:14:54.380160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:54.380160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"13dw4DviF6Chrzz6bnGrvLhJtzBB84HWXg6cJ+Wd0UqG0Fa1qKg+xU3Y5VU3IGU/KGmATssm1iELOTTv737OBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:54.380711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ab154fe73cedbb3dec581c0272c245a42aa3b1f9d89d707de38bcd5e52689d","sha256:2d6833778a73d5446957cb4a86d180c0f0b1901d56e2bff6f22638ff051b058c"],"state_sha256":"e760294c73dc20ed50339ec509bab32f897999413b52c77169c09c7319d45f5a"}