{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VCJTYQJ6KZE6UAF3ZHXDV7MFSA","short_pith_number":"pith:VCJTYQJ6","canonical_record":{"source":{"id":"1606.06557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-06-21T13:23:26Z","cross_cats_sorted":[],"title_canon_sha256":"fa62b57a1172bfba0a95a9ec856b2b9ec7cb683f2f369891b075270ea3cc4902","abstract_canon_sha256":"1a658f69ec6f6a5ffc2cac05da7a4a25d892f9fde7ee6b2039265514da6225be"},"schema_version":"1.0"},"canonical_sha256":"a8933c413e5649ea00bbc9ee3afd85903f898c3f0e6eab2d2e02df8760c010a7","source":{"kind":"arxiv","id":"1606.06557","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VCJTYQJ6KZE6UAF3ZHXDV7MFSA","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-06-21T13:23:26Z","cross_cats_sorted":[],"title_canon_sha256":"fa62b57a1172bfba0a95a9ec856b2b9ec7cb683f2f369891b075270ea3cc4902","abstract_canon_sha256":"1a658f69ec6f6a5ffc2cac05da7a4a25d892f9fde7ee6b2039265514da6225be"},"schema_version":"1.0"},"canonical_sha256":"a8933c413e5649ea00bbc9ee3afd85903f898c3f0e6eab2d2e02df8760c010a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:09.254549Z","signature_b64":"z2aidAgxIej4BT33WfKzskd64uga6hngBGkjVjVUeiJxuUF9VaYlfqoHOv8GSe5a9Grxj+nLoOorPV8eHMxGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8933c413e5649ea00bbc9ee3afd85903f898c3f0e6eab2d2e02df8760c010a7","last_reissued_at":"2026-05-18T01:12:09.254040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:09.254040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06557","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kP5fhmrYDlEp/PZW3kYIWQEHmulavmZ7/Bgc85gQ2Ic4cN7VIPqbW5pbmkGKKqHYHpYN9kX+Dq4ZHO0j0fDpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:53:01.041095Z"},"content_sha256":"53b59519bad8bbb8fc403079ac7ce9fa5fff625f80e98e54c369e84835d18394","schema_version":"1.0","event_id":"sha256:53b59519bad8bbb8fc403079ac7ce9fa5fff625f80e98e54c369e84835d18394"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VCJTYQJ6KZE6UAF3ZHXDV7MFSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order Invariance on Decomposable Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Marlin Frickenschmidt, Martin Grohe, Michael Elberfeld","submitted_at":"2016-06-21T13:23:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcZZSij0gFBWWpGtyyW3uMRZdpEITvgNRQjDk8QTKIXoOjaWmd90tS3kC0gq52k3C9BVxycZY4p32eIiD5ksDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:53:01.041454Z"},"content_sha256":"595562c067785871178c386a82bf692db3c9cd3aee3b8934fa0a643a89d088fb","schema_version":"1.0","event_id":"sha256:595562c067785871178c386a82bf692db3c9cd3aee3b8934fa0a643a89d088fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/bundle.json","state_url":"https://pith.science/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T13:53:01Z","links":{"resolver":"https://pith.science/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA","bundle":"https://pith.science/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/bundle.json","state":"https://pith.science/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCJTYQJ6KZE6UAF3ZHXDV7MFSA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JyJ7q30lHeDTAS784QDTTOfkd1sQuVPh4Ktk8mql1g6zZbmcr8dDbxc2FKcozW7sLh2pKsqsD0HM1Ulnoav9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:53:01.043344Z","bundle_sha256":"cdb8d6e9c50860d143afc077fdf0c562ef44fdb30e1cd9e0bfe862fcffd61a7e"}}