{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5GBHF2GHGK7H626WD6EYAREMEO","short_pith_number":"pith:5GBHF2GH","schema_version":"1.0","canonical_sha256":"e98272e8c732be7f6bd61f8980448c23af9913eaeeb2f5e8ec30fe7f220df30a","source":{"kind":"arxiv","id":"2605.18043","version":1},"attestation_state":"computed","paper":{"title":"A Proof-Theoretic Study of Modal Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Hirohiko Kushida","submitted_at":"2026-05-18T08:34:48Z","abstract_excerpt":"This paper proposes a basic proof theoretic framework for major modal logics: {\\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\\sf K} and its standard extensions with combinations of axioms: $T, D, 4, B, 5$. First we propose a reasonable explanation of how the standard sequent and hypersequent calculi for some of those modal logics such as {\\sf K, T, D, S4, S5} emerge on the basis of the framework. Then, by a syntactic method, we prove the cut-elimination theorem for the modal logics ex"},"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":"2605.18043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-05-18T08:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"20b615b5eabac4de71c77f058e955de7565874e556eee31d9c4441715fdde5eb","abstract_canon_sha256":"35d11ed3d706663b588b076cd4360d0e3813a8c60e31dcc9337e23e9d3693611"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:12.889245Z","signature_b64":"Xl/3BorE2K2vHSNTAtz0zrvigKKWz5BNKOvpHWvj5jpYJ+7OWKNzS+/xQuRBdRgUJg93aZ5emKNbfy7B9tlyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e98272e8c732be7f6bd61f8980448c23af9913eaeeb2f5e8ec30fe7f220df30a","last_reissued_at":"2026-05-20T00:05:12.888394Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:12.888394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Proof-Theoretic Study of Modal Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Hirohiko Kushida","submitted_at":"2026-05-18T08:34:48Z","abstract_excerpt":"This paper proposes a basic proof theoretic framework for major modal logics: {\\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\\sf K} and its standard extensions with combinations of axioms: $T, D, 4, B, 5$. First we propose a reasonable explanation of how the standard sequent and hypersequent calculi for some of those modal logics such as {\\sf K, T, D, S4, S5} emerge on the basis of the framework. Then, by a syntactic method, we prove the cut-elimination theorem for the modal logics ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18043","kind":"arxiv","version":1},"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/2605.18043/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:59.302734Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.494160Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3f1dad8ff568be0af04a86c47954180336f8cd24b98cf406ada305a3189c86f4"},"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":"2605.18043","created_at":"2026-05-20T00:05:12.888537+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18043v1","created_at":"2026-05-20T00:05:12.888537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18043","created_at":"2026-05-20T00:05:12.888537+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GBHF2GHGK7H","created_at":"2026-05-20T00:05:12.888537+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GBHF2GHGK7H626W","created_at":"2026-05-20T00:05:12.888537+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GBHF2GH","created_at":"2026-05-20T00:05:12.888537+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/5GBHF2GHGK7H626WD6EYAREMEO","json":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO.json","graph_json":"https://pith.science/api/pith-number/5GBHF2GHGK7H626WD6EYAREMEO/graph.json","events_json":"https://pith.science/api/pith-number/5GBHF2GHGK7H626WD6EYAREMEO/events.json","paper":"https://pith.science/paper/5GBHF2GH"},"agent_actions":{"view_html":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO","download_json":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO.json","view_paper":"https://pith.science/paper/5GBHF2GH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18043&json=true","fetch_graph":"https://pith.science/api/pith-number/5GBHF2GHGK7H626WD6EYAREMEO/graph.json","fetch_events":"https://pith.science/api/pith-number/5GBHF2GHGK7H626WD6EYAREMEO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO/action/storage_attestation","attest_author":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO/action/author_attestation","sign_citation":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO/action/citation_signature","submit_replication":"https://pith.science/pith/5GBHF2GHGK7H626WD6EYAREMEO/action/replication_record"}},"created_at":"2026-05-20T00:05:12.888537+00:00","updated_at":"2026-05-20T00:05:12.888537+00:00"}