{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2SXC5WKH2FBYN6D27M4SN3P2KE","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":"ad3439828114c032d8897fac9e94090fe43b5e3e8dfac9e7fea4eba8e21b59c3","cross_cats_sorted":["cs.CC","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-18T14:41:26Z","title_canon_sha256":"f43cdffacc151f6874e3414667376f52a452557dc31a31564b54d77b69e7476b"},"schema_version":"1.0","source":{"id":"2210.09899","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.09899","created_at":"2026-06-11T02:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"2210.09899v5","created_at":"2026-06-11T02:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.09899","created_at":"2026-06-11T02:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"2SXC5WKH2FBY","created_at":"2026-06-11T02:09:21Z"},{"alias_kind":"pith_short_16","alias_value":"2SXC5WKH2FBYN6D2","created_at":"2026-06-11T02:09:21Z"},{"alias_kind":"pith_short_8","alias_value":"2SXC5WKH","created_at":"2026-06-11T02:09:21Z"}],"graph_snapshots":[{"event_id":"sha256:458e4398e2df1647bd55fce2b30c7646d4b2a83efdd7b307092a693974d25a53","target":"graph","created_at":"2026-06-11T02:09:21Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth)"},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The graphs under consideration have bounded pathwidth (as opposed to merely bounded treewidth), which is the structural restriction that permits the elementary dependence; this premise is invoked in the statement of the main meta-theorem."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"FO-expressible properties on bounded-pathwidth graphs admit elementary dependence on the formula, unlike the non-elementary case for treewidth."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"All first-order expressible properties on bounded-pathwidth graphs can be decided with elementary dependence on the formula."}],"snapshot_sha256":"7dc8e041c07d676d7eece00b516054f3e31da4d0bcdc11b3df50b69db67be180"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.09899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Courcelle's celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height increases with each quantifier alternation in the formula. More devastatingly, this cannot be improved, under standard assumptions, even if we consider the much more restricted problem of deciding FO-expressible properties on trees.\n  In this paper we revisit this well-studied topic and identify a natural special case where the dependence of Courcelle's theorem c","authors_text":"Michael Lampis","cross_cats":["cs.CC","cs.LO"],"headline":"All first-order expressible properties on bounded-pathwidth graphs can be decided with elementary dependence on the formula.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-18T14:41:26Z","title":"First Order Logic on Pathwidth Revisited Again"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09899","kind":"arxiv","version":5},"verdict":{"created_at":"2026-05-24T10:53:57.120757Z","id":"91728761-efba-424d-b9f6-86688467a12c","model_set":{"reader":"grok-4.3"},"one_line_summary":"FO-expressible properties on bounded-pathwidth graphs admit elementary dependence on the formula, unlike the non-elementary case for treewidth.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"All first-order expressible properties on bounded-pathwidth graphs can be decided with elementary dependence on the formula.","strongest_claim":"all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth)","weakest_assumption":"The graphs under consideration have bounded pathwidth (as opposed to merely bounded treewidth), which is the structural restriction that permits the elementary dependence; this premise is invoked in the statement of the main meta-theorem."}},"verdict_id":"91728761-efba-424d-b9f6-86688467a12c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:298956575b9ec7d65d2a262ea290972b45923e7ab2779fcbaa684297bc470fde","target":"record","created_at":"2026-06-11T02:09:21Z","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":"ad3439828114c032d8897fac9e94090fe43b5e3e8dfac9e7fea4eba8e21b59c3","cross_cats_sorted":["cs.CC","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-18T14:41:26Z","title_canon_sha256":"f43cdffacc151f6874e3414667376f52a452557dc31a31564b54d77b69e7476b"},"schema_version":"1.0","source":{"id":"2210.09899","kind":"arxiv","version":5}},"canonical_sha256":"d4ae2ed947d14386f87afb3926edfa510615be06c7f91ae7f650a49c49483b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4ae2ed947d14386f87afb3926edfa510615be06c7f91ae7f650a49c49483b2f","first_computed_at":"2026-06-11T02:09:21.451622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T02:09:21.451622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cx4fgS7MvuieCqNGiS2iYm8zLxlt8Fxyz7IDzFYgvYQ39oVe2pAFN/1TEWQ7WCWYT5MHKdJnuEelcsabg9wzCw==","signature_status":"signed_v1","signed_at":"2026-06-11T02:09:21.454200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.09899","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:298956575b9ec7d65d2a262ea290972b45923e7ab2779fcbaa684297bc470fde","sha256:458e4398e2df1647bd55fce2b30c7646d4b2a83efdd7b307092a693974d25a53"],"state_sha256":"b1c19b9afc3310594c5a7788184bca76c0fa6a93f070ce635e9138dbb28aacd3"}