{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5GBHF2GHGK7H626WD6EYAREMEO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"35d11ed3d706663b588b076cd4360d0e3813a8c60e31dcc9337e23e9d3693611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-05-18T08:34:48Z","title_canon_sha256":"20b615b5eabac4de71c77f058e955de7565874e556eee31d9c4441715fdde5eb"},"schema_version":"1.0","source":{"id":"2605.18043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18043","created_at":"2026-05-20T00:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18043v1","created_at":"2026-05-20T00:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18043","created_at":"2026-05-20T00:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"5GBHF2GHGK7H","created_at":"2026-05-20T00:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"5GBHF2GHGK7H626W","created_at":"2026-05-20T00:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"5GBHF2GH","created_at":"2026-05-20T00:05:12Z"}],"graph_snapshots":[{"event_id":"sha256:b4910a667bb3d63eab7301ad92229196794a3a0eeb594f313080c9e7be0098b6","target":"graph","created_at":"2026-05-20T00:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"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"}],"endpoint":"/pith/2605.18043/integrity.json","findings":[],"snapshot_sha256":"3f1dad8ff568be0af04a86c47954180336f8cd24b98cf406ada305a3189c86f4","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Hirohiko Kushida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-05-18T08:34:48Z","title":"A Proof-Theoretic Study of Modal Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18043","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ca0982a6f7db6ffea9ff00dc9b1525a87def90734203040e81f801a185d81ba4","target":"record","created_at":"2026-05-20T00:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"35d11ed3d706663b588b076cd4360d0e3813a8c60e31dcc9337e23e9d3693611","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-05-18T08:34:48Z","title_canon_sha256":"20b615b5eabac4de71c77f058e955de7565874e556eee31d9c4441715fdde5eb"},"schema_version":"1.0","source":{"id":"2605.18043","kind":"arxiv","version":1}},"canonical_sha256":"e98272e8c732be7f6bd61f8980448c23af9913eaeeb2f5e8ec30fe7f220df30a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e98272e8c732be7f6bd61f8980448c23af9913eaeeb2f5e8ec30fe7f220df30a","first_computed_at":"2026-05-20T00:05:12.888394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:12.888394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xl/3BorE2K2vHSNTAtz0zrvigKKWz5BNKOvpHWvj5jpYJ+7OWKNzS+/xQuRBdRgUJg93aZ5emKNbfy7B9tlyBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:12.889245Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0982a6f7db6ffea9ff00dc9b1525a87def90734203040e81f801a185d81ba4","sha256:b4910a667bb3d63eab7301ad92229196794a3a0eeb594f313080c9e7be0098b6"],"state_sha256":"4a3228b8bc7d3481ca437aa89318b038d41face7d20d02ca0a8d8e08ac72856a"}