{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2BOZ5TEC5MPA5OMIZ2QAI3VEGK","short_pith_number":"pith:2BOZ5TEC","schema_version":"1.0","canonical_sha256":"d05d9ecc82eb1e0eb988cea0046ea432b5c723f602cb20cf4f40440a3f9bd50d","source":{"kind":"arxiv","id":"2502.17242","version":2},"attestation_state":"computed","paper":{"title":"An Intermediate Logic Contained in Medvedev's Logic with Disjunction Property","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zhicheng Chen","submitted_at":"2025-02-24T15:19:10Z","abstract_excerpt":"Let $\\textbf{SU}$ be the superintuitionistic logic defined by the axiom $\\boldsymbol{su} = ((\\neg p\\to q)\\land(\\neg q\\to p) \\rightarrow r \\vee s) \\to ( p \\rightarrow r) \\vee(q \\rightarrow s)$, or equivalently, by Andrew's axiom. It is easy to check that $\\textbf{SU}$ is contained in Medvedev's logic and contains both Kreisel-Putnam logic and Scott logic. We show that on \\textbf{S4} frames, $\\boldsymbol{su}$ corresponds to a certain first-order property, called the ``strong union'' property. The strong completeness of \\textbf{SU}, with respect to the class of \\textbf{S4} frames enjoying this pr"},"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":"2502.17242","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2025-02-24T15:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"4a0e89e1ce53699d6817169d3ea72d312ed718dc9c7d2133ccf5506750c4e20e","abstract_canon_sha256":"7e6e643b7d0f9f5d5d27dcc2d5a0990f38156d2faabf9faa3ef4fd98348fa193"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:33:08.614947Z","signature_b64":"NZUoVONxG69sMW/jvTlCQtEjMQY/mYGJ6fsvEfABrKrrRWa/t2U9n+sLpEG4cLqqYhg3ms80ShjZDl5aROxCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d05d9ecc82eb1e0eb988cea0046ea432b5c723f602cb20cf4f40440a3f9bd50d","last_reissued_at":"2026-07-05T10:33:08.613935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:33:08.613935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Intermediate Logic Contained in Medvedev's Logic with Disjunction Property","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zhicheng Chen","submitted_at":"2025-02-24T15:19:10Z","abstract_excerpt":"Let $\\textbf{SU}$ be the superintuitionistic logic defined by the axiom $\\boldsymbol{su} = ((\\neg p\\to q)\\land(\\neg q\\to p) \\rightarrow r \\vee s) \\to ( p \\rightarrow r) \\vee(q \\rightarrow s)$, or equivalently, by Andrew's axiom. It is easy to check that $\\textbf{SU}$ is contained in Medvedev's logic and contains both Kreisel-Putnam logic and Scott logic. We show that on \\textbf{S4} frames, $\\boldsymbol{su}$ corresponds to a certain first-order property, called the ``strong union'' property. The strong completeness of \\textbf{SU}, with respect to the class of \\textbf{S4} frames enjoying this pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17242","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/2502.17242/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":"2502.17242","created_at":"2026-07-05T10:33:08.614073+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.17242v2","created_at":"2026-07-05T10:33:08.614073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.17242","created_at":"2026-07-05T10:33:08.614073+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BOZ5TEC5MPA","created_at":"2026-07-05T10:33:08.614073+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BOZ5TEC5MPA5OMI","created_at":"2026-07-05T10:33:08.614073+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BOZ5TEC","created_at":"2026-07-05T10:33:08.614073+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/2BOZ5TEC5MPA5OMIZ2QAI3VEGK","json":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK.json","graph_json":"https://pith.science/api/pith-number/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/graph.json","events_json":"https://pith.science/api/pith-number/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/events.json","paper":"https://pith.science/paper/2BOZ5TEC"},"agent_actions":{"view_html":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK","download_json":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK.json","view_paper":"https://pith.science/paper/2BOZ5TEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.17242&json=true","fetch_graph":"https://pith.science/api/pith-number/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/graph.json","fetch_events":"https://pith.science/api/pith-number/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/action/storage_attestation","attest_author":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/action/author_attestation","sign_citation":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/action/citation_signature","submit_replication":"https://pith.science/pith/2BOZ5TEC5MPA5OMIZ2QAI3VEGK/action/replication_record"}},"created_at":"2026-07-05T10:33:08.614073+00:00","updated_at":"2026-07-05T10:33:08.614073+00:00"}