{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YW32SSDTMV3RQVANZAD6VCXSNH","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":"614931dd1953a1db98a9080560490c42c2d3d6787a3647d332ba615af06dec3f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-02-27T12:59:50Z","title_canon_sha256":"9cd40de7d65c81013cd71cdf48e2fa6a3b82c79cf99f26f2757f7a67370ae987"},"schema_version":"1.0","source":{"id":"1502.07884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07884","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07884v2","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07884","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"YW32SSDTMV3R","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YW32SSDTMV3RQVAN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YW32SSDT","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:394bd4be292483fa2cf4b02f18352c19839bd63492548b06f117eeee924cebca","target":"graph","created_at":"2026-05-17T23:58:19Z","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":"We study model and frame definability of various modal logics. Let ML(A+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models is definable in ML(A+) if and only if the class is elementary and closed under disjoint unions and surjective bisimulations. We also characterise the definability of ML(A+) in the spirit of the well-known Goldblatt--Thomason theorem. We show that an elementary class F of Kripke frames is definable in ML(A+) if and only if F is closed under taking generated s","authors_text":"Jonni Virtema, Katsuhiko Sano","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-02-27T12:59:50Z","title":"Characterising Modal Definability of Team-Based Logics via the Universal Modality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07884","kind":"arxiv","version":2},"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:e3ec68594901f80680cb61126de02ce764d812f552935648de593cfebcb4d216","target":"record","created_at":"2026-05-17T23:58:19Z","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":"614931dd1953a1db98a9080560490c42c2d3d6787a3647d332ba615af06dec3f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-02-27T12:59:50Z","title_canon_sha256":"9cd40de7d65c81013cd71cdf48e2fa6a3b82c79cf99f26f2757f7a67370ae987"},"schema_version":"1.0","source":{"id":"1502.07884","kind":"arxiv","version":2}},"canonical_sha256":"c5b7a94873657718540dc807ea8af269f1b403ac2dbff091adca270a7d90e972","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5b7a94873657718540dc807ea8af269f1b403ac2dbff091adca270a7d90e972","first_computed_at":"2026-05-17T23:58:19.857796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.857796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9JlgdPotaGUP8ZfbL297DpXsic+vPucWpdfcE/eTnDBPURNICPRIQaaHCnSePy/vHaKGyh6UbHyU9t+JS5UCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.858202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ec68594901f80680cb61126de02ce764d812f552935648de593cfebcb4d216","sha256:394bd4be292483fa2cf4b02f18352c19839bd63492548b06f117eeee924cebca"],"state_sha256":"0b83665f2b825dc8b4c5cdc0f87eec73abe4632e7e1b9795becf4093c298e048"}