{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7DPG6YASG4PNC6FG5CCENNYC54","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":"3f495e39a91936fb30528fb2f9f0dc1728b24f1cc78f74bc23f3249bd3ae54b9","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T11:00:35Z","title_canon_sha256":"bdf98a64598fb979c7ee22e9b33655155904ca8c68f8968423378babe88ca56a"},"schema_version":"1.0","source":{"id":"2607.02033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02033","created_at":"2026-07-03T01:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02033v1","created_at":"2026-07-03T01:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02033","created_at":"2026-07-03T01:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"7DPG6YASG4PN","created_at":"2026-07-03T01:17:37Z"},{"alias_kind":"pith_short_16","alias_value":"7DPG6YASG4PNC6FG","created_at":"2026-07-03T01:17:37Z"},{"alias_kind":"pith_short_8","alias_value":"7DPG6YAS","created_at":"2026-07-03T01:17:37Z"}],"graph_snapshots":[{"event_id":"sha256:a1a289af70b5427d6ad800e499c0620dba4bbe38d47f76dfe0a17ec5e40acc12","target":"graph","created_at":"2026-07-03T01:17:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.02033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Courcelle's theorem states that there exists an algorithm that takes as input a graph $G$ of treewidth at most $t$ and a MSO formula $\\phi$, and determines whether $G$ satisfies $\\phi$ in time $f(\\phi,t) \\cdot n$. It is folklore that the the function $f$ contains a tower of exponentials whose height depends as a linear function of the number of quantifier alternations of the input formula $\\phi$. A classic reduction of Frick and Grohe shows that, assuming the Exponential Time Hypothesis (ETH), the linear growth of the height of the tower is unavoidable. Nevertheless, there is still a huge gap ","authors_text":"Daniel Lokshtanov, Fahad Panolan, Jie Xue, Meirav Zehavi, Saket Saurabh","cross_cats":["cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T11:00:35Z","title":"Fine-Grained Bounds for Courcelle's Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02033","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":"sha256:2697296cb42dbe02280034c8aaa6e4c31d1dbc94c46c7b3d2a1ff4d6687817c6","target":"record","created_at":"2026-07-03T01:17:37Z","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":"3f495e39a91936fb30528fb2f9f0dc1728b24f1cc78f74bc23f3249bd3ae54b9","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T11:00:35Z","title_canon_sha256":"bdf98a64598fb979c7ee22e9b33655155904ca8c68f8968423378babe88ca56a"},"schema_version":"1.0","source":{"id":"2607.02033","kind":"arxiv","version":1}},"canonical_sha256":"f8de6f6012371ed178a6e88446b702ef0aee9148ac84d51da783a072c6d8437d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8de6f6012371ed178a6e88446b702ef0aee9148ac84d51da783a072c6d8437d","first_computed_at":"2026-07-03T01:17:37.633606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:37.633606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H51ssBOBxCGexZ7Xagqz2lehlL85AZcjmjMv300/9/MpvtdJ+pUaSiem+zsdyjRhhqKoJ+XZKkMrOATc1PRmAw==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:37.633997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2697296cb42dbe02280034c8aaa6e4c31d1dbc94c46c7b3d2a1ff4d6687817c6","sha256:a1a289af70b5427d6ad800e499c0620dba4bbe38d47f76dfe0a17ec5e40acc12"],"state_sha256":"fcfa5f16162d126c524a80514916946d25ff1b604aebfa06afb5b1f815d45764"}