{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:W4EOL7S6ZWSCENCTOLB4YWPDYJ","short_pith_number":"pith:W4EOL7S6","schema_version":"1.0","canonical_sha256":"b708e5fe5ecda422345372c3cc59e3c26e92ac3a527b3f07d47dec7121669c6b","source":{"kind":"arxiv","id":"2201.07098","version":7},"attestation_state":"computed","paper":{"title":"Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Wesley H. Holliday","submitted_at":"2022-01-18T16:19:52Z","abstract_excerpt":"In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Plo\\v{s}\\v{c}ica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then extend each of the three representations to lattices with a "},"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":"2201.07098","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-01-18T16:19:52Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2be7e00f34df120987343d6819e1007c6bb4997d2731ec22c22f90faba4ce516","abstract_canon_sha256":"16228b5a23f5b2404a07f6e6ba22bf8e08abffd7dba634ca938df42815bff8c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:49:54.305939Z","signature_b64":"UPPoO9XJR7R2dqmbHW6w6UuaSs2yd+N3KCo0sPgpZqGNKyuCzNUynrC6jdCL6Yz+Qq8Zx1hAZRiDTE39uwReDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b708e5fe5ecda422345372c3cc59e3c26e92ac3a527b3f07d47dec7121669c6b","last_reissued_at":"2026-07-05T07:49:54.305423Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:49:54.305423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Wesley H. Holliday","submitted_at":"2022-01-18T16:19:52Z","abstract_excerpt":"In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Plo\\v{s}\\v{c}ica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then extend each of the three representations to lattices with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.07098","kind":"arxiv","version":7},"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/2201.07098/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":"2201.07098","created_at":"2026-07-05T07:49:54.305479+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.07098v7","created_at":"2026-07-05T07:49:54.305479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.07098","created_at":"2026-07-05T07:49:54.305479+00:00"},{"alias_kind":"pith_short_12","alias_value":"W4EOL7S6ZWSC","created_at":"2026-07-05T07:49:54.305479+00:00"},{"alias_kind":"pith_short_16","alias_value":"W4EOL7S6ZWSCENCT","created_at":"2026-07-05T07:49:54.305479+00:00"},{"alias_kind":"pith_short_8","alias_value":"W4EOL7S6","created_at":"2026-07-05T07:49:54.305479+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.29954","citing_title":"Fundamental Logic Through the Lens of Modality","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ","json":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ.json","graph_json":"https://pith.science/api/pith-number/W4EOL7S6ZWSCENCTOLB4YWPDYJ/graph.json","events_json":"https://pith.science/api/pith-number/W4EOL7S6ZWSCENCTOLB4YWPDYJ/events.json","paper":"https://pith.science/paper/W4EOL7S6"},"agent_actions":{"view_html":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ","download_json":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ.json","view_paper":"https://pith.science/paper/W4EOL7S6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.07098&json=true","fetch_graph":"https://pith.science/api/pith-number/W4EOL7S6ZWSCENCTOLB4YWPDYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/W4EOL7S6ZWSCENCTOLB4YWPDYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ/action/storage_attestation","attest_author":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ/action/author_attestation","sign_citation":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ/action/citation_signature","submit_replication":"https://pith.science/pith/W4EOL7S6ZWSCENCTOLB4YWPDYJ/action/replication_record"}},"created_at":"2026-07-05T07:49:54.305479+00:00","updated_at":"2026-07-05T07:49:54.305479+00:00"}