{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5SWT75JHYXBGBYCWFBYOU27DFF","short_pith_number":"pith:5SWT75JH","schema_version":"1.0","canonical_sha256":"ecad3ff527c5c260e0562870ea6be3294914a63575b4209fccac71fbb3dd43b5","source":{"kind":"arxiv","id":"1804.05758","version":2},"attestation_state":"computed","paper":{"title":"Partial strong compactness and squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yair Hayut","submitted_at":"2018-04-16T15:58:08Z","abstract_excerpt":"In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\\mathcal{L}_{\\kappa,\\kappa}$. Using this equivalence we show that if any $\\kappa$-complete filter on $\\lambda$ can be extended to a $\\kappa$-complete ultrafilter and $\\lambda^{<\\kappa} = \\lambda$ then $\\square(\\mu)$ fails for all regular $\\mu\\in[\\kappa,2^\\lambda]$. As an application, we improve the lower bound for the consistency strength of $\\kappa$-compactness, a case which was explicitly considered by Mitchell"},"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":"1804.05758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-16T15:58:08Z","cross_cats_sorted":[],"title_canon_sha256":"9b4e514daac4b6ef442b27ecb1b79570da5f1a2bf68ac624fedf02af700e0075","abstract_canon_sha256":"678a6faa2b529afa973e45dc6fed4710ac51e778f63d4449263e00b94e399a1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:39.130555Z","signature_b64":"XlbaFp0eeaAEHEfX1vU8ehFQDTEFCdalu6IMEWT8cJA2bMCX/+mnbnzoP/KR9MrrCpwtOYZhA/h7abUHK0ZfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecad3ff527c5c260e0562870ea6be3294914a63575b4209fccac71fbb3dd43b5","last_reissued_at":"2026-05-18T00:05:39.129848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:39.129848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial strong compactness and squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yair Hayut","submitted_at":"2018-04-16T15:58:08Z","abstract_excerpt":"In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\\mathcal{L}_{\\kappa,\\kappa}$. Using this equivalence we show that if any $\\kappa$-complete filter on $\\lambda$ can be extended to a $\\kappa$-complete ultrafilter and $\\lambda^{<\\kappa} = \\lambda$ then $\\square(\\mu)$ fails for all regular $\\mu\\in[\\kappa,2^\\lambda]$. As an application, we improve the lower bound for the consistency strength of $\\kappa$-compactness, a case which was explicitly considered by Mitchell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05758","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":"1804.05758","created_at":"2026-05-18T00:05:39.129951+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.05758v2","created_at":"2026-05-18T00:05:39.129951+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05758","created_at":"2026-05-18T00:05:39.129951+00:00"},{"alias_kind":"pith_short_12","alias_value":"5SWT75JHYXBG","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5SWT75JHYXBGBYCW","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5SWT75JH","created_at":"2026-05-18T12:32:08.215937+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/5SWT75JHYXBGBYCWFBYOU27DFF","json":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF.json","graph_json":"https://pith.science/api/pith-number/5SWT75JHYXBGBYCWFBYOU27DFF/graph.json","events_json":"https://pith.science/api/pith-number/5SWT75JHYXBGBYCWFBYOU27DFF/events.json","paper":"https://pith.science/paper/5SWT75JH"},"agent_actions":{"view_html":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF","download_json":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF.json","view_paper":"https://pith.science/paper/5SWT75JH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.05758&json=true","fetch_graph":"https://pith.science/api/pith-number/5SWT75JHYXBGBYCWFBYOU27DFF/graph.json","fetch_events":"https://pith.science/api/pith-number/5SWT75JHYXBGBYCWFBYOU27DFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF/action/storage_attestation","attest_author":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF/action/author_attestation","sign_citation":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF/action/citation_signature","submit_replication":"https://pith.science/pith/5SWT75JHYXBGBYCWFBYOU27DFF/action/replication_record"}},"created_at":"2026-05-18T00:05:39.129951+00:00","updated_at":"2026-05-18T00:05:39.129951+00:00"}