{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A7OT5NYDRY7CZLOC7IIIAKANY6","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":"e59bc6b45fdbf5610a47e4dc65c3e4f4295208ac36e6fa2ecde634b2023b8cdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-05-26T00:09:16Z","title_canon_sha256":"22f337302683b4aca463eaa9394a00e3dfd1294d939b2aedbdfb4a3d1f3e7bf5"},"schema_version":"1.0","source":{"id":"1605.08106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08106","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08106v1","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08106","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"A7OT5NYDRY7C","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A7OT5NYDRY7CZLOC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A7OT5NYD","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:cb6cb0f4f4d5f69265efb9c8686bae5ac38912df6a15ad58398fdb2d6947b969","target":"graph","created_at":"2026-05-18T01:13:37Z","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"},"paper":{"abstract_excerpt":"This is a survey of {\\lambda}-calculi that, through the Curry-Howard isomorphism, correspond to constructive modal logics. We cover the prehistory of the subject and then concentrate on the developments that took place in the 1990s and early 2000s. We discuss logical aspects, modal {\\lambda}-calculi, and their categorical semantics. The logics underlying the calculi surveyed are constructive versions of K, K4, S4, and LTL.","authors_text":"G. A. Kavvos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-05-26T00:09:16Z","title":"The Many Worlds of Modal {\\lambda}-calculi: I. Curry-Howard for Necessity, Possibility and Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08106","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":"sha256:5804211ef3082063acb47b73a35dfd53f0dbf37cc9d7b120baeebb64c491c7df","target":"record","created_at":"2026-05-18T01:13:37Z","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":"e59bc6b45fdbf5610a47e4dc65c3e4f4295208ac36e6fa2ecde634b2023b8cdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-05-26T00:09:16Z","title_canon_sha256":"22f337302683b4aca463eaa9394a00e3dfd1294d939b2aedbdfb4a3d1f3e7bf5"},"schema_version":"1.0","source":{"id":"1605.08106","kind":"arxiv","version":1}},"canonical_sha256":"07dd3eb7038e3e2cadc2fa1080280dc786a1af8faa7e1047729e343429ffb917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07dd3eb7038e3e2cadc2fa1080280dc786a1af8faa7e1047729e343429ffb917","first_computed_at":"2026-05-18T01:13:37.098517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:37.098517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oe1Wfuun1Nrp0LtiGWXTzXgWdYJVhS81tJh51Rn2AU1pjmxZ/8SB9B1Ns/zCYkK4hTV3C14eFC1MPzVpIC6gDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:37.099019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5804211ef3082063acb47b73a35dfd53f0dbf37cc9d7b120baeebb64c491c7df","sha256:cb6cb0f4f4d5f69265efb9c8686bae5ac38912df6a15ad58398fdb2d6947b969"],"state_sha256":"8db0b0b98094e7c779ce2390dc39deef23edc48ba18b37520ba003cfc3b1a2c5"}