{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IAML623IPRNTR6T77XQ2O7P4P2","short_pith_number":"pith:IAML623I","schema_version":"1.0","canonical_sha256":"4018bf6b687c5b38fa7ffde1a77dfc7e9f29e0a737c5b9f90d404695d9c894ae","source":{"kind":"arxiv","id":"1606.06493","version":2},"attestation_state":"computed","paper":{"title":"Tukey Order, Calibres and the Rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ana Mamatelashvili, Paul Gartside","submitted_at":"2016-06-21T09:25:58Z","abstract_excerpt":"One partially ordered set, $Q$, is a Tukey quotient of another, $P$, denoted $P \\geq_T Q$, if there is a map $\\phi : P \\to Q$ carrying cofinal sets of $P$ to cofinal sets of $Q$. Let $X$ be a space and denote by $\\mathcal{K}(X)$ the set of compact subsets of $X$, ordered by inclusion. For certain separable metrizable spaces $M$, Tukey upper and lower bounds of $\\mathcal{K}(M)$ are calculated. Results on invariants of $\\mathcal{K}(M)$'s are deduced. The structure of all $\\mathcal{K}(M)$'s under $\\le_T$ is investigated. Particular emphasis is placed on the position of $\\mathcal{K}(M)$ when $M$ i"},"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":"1606.06493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-06-21T09:25:58Z","cross_cats_sorted":[],"title_canon_sha256":"36831675afeefafeffd45cd734b774abfaa3b0a5925115e7d1bfb1aaee36cb48","abstract_canon_sha256":"59072858387e2f40af0d0b7d61f5455f6ef2a574a6492c361be876216ff19dcc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:04.254122Z","signature_b64":"NPvZqf5fOGXTDDPi+CB0Dt4UYJle8dV5HruEeApifyc0iv3SU8VpMTMKaojfPceuIRssRyGncqfrILPiDIVXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4018bf6b687c5b38fa7ffde1a77dfc7e9f29e0a737c5b9f90d404695d9c894ae","last_reissued_at":"2026-05-18T00:56:04.253553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:04.253553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tukey Order, Calibres and the Rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ana Mamatelashvili, Paul Gartside","submitted_at":"2016-06-21T09:25:58Z","abstract_excerpt":"One partially ordered set, $Q$, is a Tukey quotient of another, $P$, denoted $P \\geq_T Q$, if there is a map $\\phi : P \\to Q$ carrying cofinal sets of $P$ to cofinal sets of $Q$. Let $X$ be a space and denote by $\\mathcal{K}(X)$ the set of compact subsets of $X$, ordered by inclusion. For certain separable metrizable spaces $M$, Tukey upper and lower bounds of $\\mathcal{K}(M)$ are calculated. Results on invariants of $\\mathcal{K}(M)$'s are deduced. The structure of all $\\mathcal{K}(M)$'s under $\\le_T$ is investigated. Particular emphasis is placed on the position of $\\mathcal{K}(M)$ when $M$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06493","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":"1606.06493","created_at":"2026-05-18T00:56:04.253639+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.06493v2","created_at":"2026-05-18T00:56:04.253639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06493","created_at":"2026-05-18T00:56:04.253639+00:00"},{"alias_kind":"pith_short_12","alias_value":"IAML623IPRNT","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IAML623IPRNTR6T7","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IAML623I","created_at":"2026-05-18T12:30:22.444734+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/IAML623IPRNTR6T77XQ2O7P4P2","json":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2.json","graph_json":"https://pith.science/api/pith-number/IAML623IPRNTR6T77XQ2O7P4P2/graph.json","events_json":"https://pith.science/api/pith-number/IAML623IPRNTR6T77XQ2O7P4P2/events.json","paper":"https://pith.science/paper/IAML623I"},"agent_actions":{"view_html":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2","download_json":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2.json","view_paper":"https://pith.science/paper/IAML623I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.06493&json=true","fetch_graph":"https://pith.science/api/pith-number/IAML623IPRNTR6T77XQ2O7P4P2/graph.json","fetch_events":"https://pith.science/api/pith-number/IAML623IPRNTR6T77XQ2O7P4P2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2/action/storage_attestation","attest_author":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2/action/author_attestation","sign_citation":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2/action/citation_signature","submit_replication":"https://pith.science/pith/IAML623IPRNTR6T77XQ2O7P4P2/action/replication_record"}},"created_at":"2026-05-18T00:56:04.253639+00:00","updated_at":"2026-05-18T00:56:04.253639+00:00"}