{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GN7WR4UI3YXFQOLR4A3IHQSSAZ","short_pith_number":"pith:GN7WR4UI","schema_version":"1.0","canonical_sha256":"337f68f288de2e583971e03683c252064d3e4f7b5d8245d8638b4dd6d44e827a","source":{"kind":"arxiv","id":"1810.02389","version":1},"attestation_state":"computed","paper":{"title":"First-order interpretations of bounded expansion classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CO","math.LO"],"primary_cat":"cs.DM","authors_text":"Jakub Gajarsk\\'y, Jaroslav Ne\\v{s}et\\v{r}il, Micha{\\l} Pilipczuk, Patrice Ossona de Mendez, Sebastian Siebertz, Stephan Kreutzer, Szymon Toru\\'nczyk","submitted_at":"2018-10-04T18:40:46Z","abstract_excerpt":"The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.02389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-10-04T18:40:46Z","cross_cats_sorted":["cs.LO","math.CO","math.LO"],"title_canon_sha256":"8ae7505b3138d93508cf20770981cd9a0c5df2ba46bbe26df6abb70f39b99dfc","abstract_canon_sha256":"67c0129287b48eb6bf4e652f10ef8c57cc515d5f24e37d14550223841298a064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:02.028448Z","signature_b64":"6s5h8Dqr6E9hkzX/ukt4bREEK/1+zOc5IM+49Qh2gGCltSAtjJbrbmRrt0cX5Vu9lXVO5mS/f7CADTwqkReyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"337f68f288de2e583971e03683c252064d3e4f7b5d8245d8638b4dd6d44e827a","last_reissued_at":"2026-05-18T00:04:02.027835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:02.027835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First-order interpretations of bounded expansion classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CO","math.LO"],"primary_cat":"cs.DM","authors_text":"Jakub Gajarsk\\'y, Jaroslav Ne\\v{s}et\\v{r}il, Micha{\\l} Pilipczuk, Patrice Ossona de Mendez, Sebastian Siebertz, Stephan Kreutzer, Szymon Toru\\'nczyk","submitted_at":"2018-10-04T18:40:46Z","abstract_excerpt":"The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02389","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.02389","created_at":"2026-05-18T00:04:02.027930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02389v1","created_at":"2026-05-18T00:04:02.027930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02389","created_at":"2026-05-18T00:04:02.027930+00:00"},{"alias_kind":"pith_short_12","alias_value":"GN7WR4UI3YXF","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GN7WR4UI3YXFQOLR","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GN7WR4UI","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ","json":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ.json","graph_json":"https://pith.science/api/pith-number/GN7WR4UI3YXFQOLR4A3IHQSSAZ/graph.json","events_json":"https://pith.science/api/pith-number/GN7WR4UI3YXFQOLR4A3IHQSSAZ/events.json","paper":"https://pith.science/paper/GN7WR4UI"},"agent_actions":{"view_html":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ","download_json":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ.json","view_paper":"https://pith.science/paper/GN7WR4UI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02389&json=true","fetch_graph":"https://pith.science/api/pith-number/GN7WR4UI3YXFQOLR4A3IHQSSAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GN7WR4UI3YXFQOLR4A3IHQSSAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ/action/storage_attestation","attest_author":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ/action/author_attestation","sign_citation":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ/action/citation_signature","submit_replication":"https://pith.science/pith/GN7WR4UI3YXFQOLR4A3IHQSSAZ/action/replication_record"}},"created_at":"2026-05-18T00:04:02.027930+00:00","updated_at":"2026-05-18T00:04:02.027930+00:00"}