{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2NQUYRAARMOMM23C2NRTWDCSIA","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":"9107c3b4ac1885455be558c522b00f88e38ac0e18b43eece8566f3cca3482a17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-19T04:37:26Z","title_canon_sha256":"d9f78060c0b776553bcc888a81f92d131b1b6799334808dcc9fe590cb2f41c18"},"schema_version":"1.0","source":{"id":"2605.19349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19349","created_at":"2026-05-20T01:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19349v1","created_at":"2026-05-20T01:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19349","created_at":"2026-05-20T01:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"2NQUYRAARMOM","created_at":"2026-05-20T01:05:40Z"},{"alias_kind":"pith_short_16","alias_value":"2NQUYRAARMOMM23C","created_at":"2026-05-20T01:05:40Z"},{"alias_kind":"pith_short_8","alias_value":"2NQUYRAA","created_at":"2026-05-20T01:05:40Z"}],"graph_snapshots":[{"event_id":"sha256:8e44c1ed71040177413752400418b98d6f6853f722b4d5ef0e35549eaa5291b8","target":"graph","created_at":"2026-05-20T01:05:40Z","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":[],"endpoint":"/pith/2605.19349/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a proof system $\\mathsf{GL}_{+}^{\\top\\bot}$, which is based on a sequent system $\\mathsf{K}_{+}^{\\top\\bot}$ given by Dunn, for the positive fragment of $\\mathsf{GL}$. Positive modal formulas are modal formulas that contain neither negation symbols nor implication symbols. More precisely, they are modal formulas constructed from the connectives $\\lor$, $\\land$, $\\Diamond$, $\\Box$, $\\bot$, $\\top$, and propositional variables. The logic $\\mathsf{GL}$ is the least normal modal logic that contains $\\mathsf{K}$ and the L\\\"{o}b formula $\\Box(\\Box p\\supset p)\\supset\\Box p$. F","authors_text":"Yoshihito Tanaka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-19T04:37:26Z","title":"A proof system for the positive fragment of GL"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19349","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:c07941e31c141df1c502901a68d6d49b470bcf9e980dd7d0f953714a82541915","target":"record","created_at":"2026-05-20T01:05:40Z","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":"9107c3b4ac1885455be558c522b00f88e38ac0e18b43eece8566f3cca3482a17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-19T04:37:26Z","title_canon_sha256":"d9f78060c0b776553bcc888a81f92d131b1b6799334808dcc9fe590cb2f41c18"},"schema_version":"1.0","source":{"id":"2605.19349","kind":"arxiv","version":1}},"canonical_sha256":"d3614c44008b1cc66b62d3633b0c524022b03b2861fd6a5e96a470cb52b223a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3614c44008b1cc66b62d3633b0c524022b03b2861fd6a5e96a470cb52b223a2","first_computed_at":"2026-05-20T01:05:40.858497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:40.858497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y26iK22bCsF2hP9jXsm51VY2gjE79XSd7I4VtZjhq4X8SYOyWKZ5pU0y9SaeVgHP0ND0g1J6rDjc4+8Hem1+AQ==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:40.859810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c07941e31c141df1c502901a68d6d49b470bcf9e980dd7d0f953714a82541915","sha256:8e44c1ed71040177413752400418b98d6f6853f722b4d5ef0e35549eaa5291b8"],"state_sha256":"d8253bad442c82c34945e9ab6e1817478aabc58a65967bd204179857305f409f"}