{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5FP2M6GGWA4YUX5WCVA7BALGWZ","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":"011cfb01fbf3b4b54546b96b5c2516ff8b27834cbb8a999be432240d258356b9","cross_cats_sorted":["cs.FL","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-02-29T14:16:31Z","title_canon_sha256":"c450fb7e7cb3959437837a2cb61d64bbf7daff91fce4e3bcaf549c4544bcd293"},"schema_version":"1.0","source":{"id":"1602.08971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08971","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08971v1","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08971","created_at":"2026-05-18T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"5FP2M6GGWA4Y","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5FP2M6GGWA4YUX5W","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5FP2M6GG","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:f4518b2fb7df441ac1945c6b08b4b37bb85b1959f9ca466848b95b9a5983a7ee","target":"graph","created_at":"2026-05-18T01:19:51Z","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 establish the strictness of several set quantifier alternation hierarchies that are based on modal logic, evaluated on various classes of finite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict.\n  Thereby, the present paper settles a question raised by van Benthem (1983), revived by ten Cate (2006), and partially answered by Kuusisto (2008, 2015).","authors_text":"Fabian Reiter","cross_cats":["cs.FL","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-02-29T14:16:31Z","title":"Alternating Set Quantifiers in Modal Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08971","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":"sha256:41dd518bab172e75ae0e8c4f4eb5a6ce39d9c97c883647236e8171bf7fcacfe5","target":"record","created_at":"2026-05-18T01:19:51Z","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":"011cfb01fbf3b4b54546b96b5c2516ff8b27834cbb8a999be432240d258356b9","cross_cats_sorted":["cs.FL","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-02-29T14:16:31Z","title_canon_sha256":"c450fb7e7cb3959437837a2cb61d64bbf7daff91fce4e3bcaf549c4544bcd293"},"schema_version":"1.0","source":{"id":"1602.08971","kind":"arxiv","version":1}},"canonical_sha256":"e95fa678c6b0398a5fb61541f08166b662ab0d12d6ef67f13f9cd5b7e3ee62ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e95fa678c6b0398a5fb61541f08166b662ab0d12d6ef67f13f9cd5b7e3ee62ee","first_computed_at":"2026-05-18T01:19:51.578993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:51.578993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nH476FBXXIPrT/4MugPe9Dvsb54WDQWGCc2ny9vV1hL3beaEa3Kx0dg/Rd5j9/Fi5oigHgWzoCkykmYi+JAmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:51.579616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41dd518bab172e75ae0e8c4f4eb5a6ce39d9c97c883647236e8171bf7fcacfe5","sha256:f4518b2fb7df441ac1945c6b08b4b37bb85b1959f9ca466848b95b9a5983a7ee"],"state_sha256":"f75201418f9d6b9f44845b369cb27e735b43c7de58928619a267efd4bda79d2f"}