{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VCJTYQJ6KZE6UAF3ZHXDV7MFSA","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":"1a658f69ec6f6a5ffc2cac05da7a4a25d892f9fde7ee6b2039265514da6225be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-06-21T13:23:26Z","title_canon_sha256":"fa62b57a1172bfba0a95a9ec856b2b9ec7cb683f2f369891b075270ea3cc4902"},"schema_version":"1.0","source":{"id":"1606.06557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06557","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06557v1","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06557","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCJTYQJ6KZE6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VCJTYQJ6KZE6UAF3","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VCJTYQJ6","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:595562c067785871178c386a82bf692db3c9cd3aee3b8934fa0a643a89d088fb","target":"graph","created_at":"2026-05-18T01:12:09Z","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":"Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas capture unordered problems of complexity classes and they model the independence of the answer to a database query from low-level aspects of databases. We study the expressive power of order-invariant monadic second-order (MSO) and first-order (FO) logic on restricted classes of structures that admit certain forms of tree decompositions (not necessarily of b","authors_text":"Marlin Frickenschmidt, Martin Grohe, Michael Elberfeld","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-06-21T13:23:26Z","title":"Order Invariance on Decomposable Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06557","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":"sha256:53b59519bad8bbb8fc403079ac7ce9fa5fff625f80e98e54c369e84835d18394","target":"record","created_at":"2026-05-18T01:12:09Z","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":"1a658f69ec6f6a5ffc2cac05da7a4a25d892f9fde7ee6b2039265514da6225be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-06-21T13:23:26Z","title_canon_sha256":"fa62b57a1172bfba0a95a9ec856b2b9ec7cb683f2f369891b075270ea3cc4902"},"schema_version":"1.0","source":{"id":"1606.06557","kind":"arxiv","version":1}},"canonical_sha256":"a8933c413e5649ea00bbc9ee3afd85903f898c3f0e6eab2d2e02df8760c010a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8933c413e5649ea00bbc9ee3afd85903f898c3f0e6eab2d2e02df8760c010a7","first_computed_at":"2026-05-18T01:12:09.254040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:09.254040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2aidAgxIej4BT33WfKzskd64uga6hngBGkjVjVUeiJxuUF9VaYlfqoHOv8GSe5a9Grxj+nLoOorPV8eHMxGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:09.254549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53b59519bad8bbb8fc403079ac7ce9fa5fff625f80e98e54c369e84835d18394","sha256:595562c067785871178c386a82bf692db3c9cd3aee3b8934fa0a643a89d088fb"],"state_sha256":"b2e3f5626a787d91d3c940196dcf868ca4362038a8bea6ab4df4c6fe688f8ed5"}