{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:O3N7ZQQ6GIZ55AT25NWFDPX6QS","short_pith_number":"pith:O3N7ZQQ6","schema_version":"1.0","canonical_sha256":"76dbfcc21e3233de827aeb6c51befe8483e48471b495cf10cf26e04930cc1d6c","source":{"kind":"arxiv","id":"2209.11229","version":3},"attestation_state":"computed","paper":{"title":"Decomposition horizons and a characterization of stable hereditary classes of graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LO","math.CO","math.LO"],"primary_cat":"cs.DM","authors_text":"Jaroslav Ne\\v{s}et\\v{r}il, Patrice Ossona de Mendez, Samuel Braunfeld, Sebastian Siebertz","submitted_at":"2022-09-15T16:29:03Z","abstract_excerpt":"The notions of bounded-size and quasibounded-size decompositions with bounded treedepth base classes are central to the structural theory of graph sparsity introduced by two of the authors years ago, and provide a characterization of both classes with bounded expansions and nowhere dense classes. Strong connections of this theory with model theory led to considering first-order transductions, which are logically defined graph transformations, and to initiate a comparative study of combinatorial and model theoretical properties of graph classes, with an emphasis on the model theoretical notions"},"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":"2209.11229","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2022-09-15T16:29:03Z","cross_cats_sorted":["cs.LO","math.CO","math.LO"],"title_canon_sha256":"8170e11cf384d6b71653de0c02f869379bea630226cad7e48960dcf518d4bef2","abstract_canon_sha256":"dc980ae90418def9228503ffcede93768063acc8bd753ddb34f6a5b85fde8c7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:55.756862Z","signature_b64":"yuizVyEL2n/e89bevkd7ICPf7wUQojRhZXDUor5GIF8ke9QGm/qPHGd4HHAjzXCuZn18CQg/bP5aEv0UDB0NDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76dbfcc21e3233de827aeb6c51befe8483e48471b495cf10cf26e04930cc1d6c","last_reissued_at":"2026-07-05T09:52:55.756366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:55.756366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition horizons and a characterization of stable hereditary classes of graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LO","math.CO","math.LO"],"primary_cat":"cs.DM","authors_text":"Jaroslav Ne\\v{s}et\\v{r}il, Patrice Ossona de Mendez, Samuel Braunfeld, Sebastian Siebertz","submitted_at":"2022-09-15T16:29:03Z","abstract_excerpt":"The notions of bounded-size and quasibounded-size decompositions with bounded treedepth base classes are central to the structural theory of graph sparsity introduced by two of the authors years ago, and provide a characterization of both classes with bounded expansions and nowhere dense classes. Strong connections of this theory with model theory led to considering first-order transductions, which are logically defined graph transformations, and to initiate a comparative study of combinatorial and model theoretical properties of graph classes, with an emphasis on the model theoretical notions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.11229","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.11229/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2209.11229","created_at":"2026-07-05T09:52:55.756426+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.11229v3","created_at":"2026-07-05T09:52:55.756426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.11229","created_at":"2026-07-05T09:52:55.756426+00:00"},{"alias_kind":"pith_short_12","alias_value":"O3N7ZQQ6GIZ5","created_at":"2026-07-05T09:52:55.756426+00:00"},{"alias_kind":"pith_short_16","alias_value":"O3N7ZQQ6GIZ55AT2","created_at":"2026-07-05T09:52:55.756426+00:00"},{"alias_kind":"pith_short_8","alias_value":"O3N7ZQQ6","created_at":"2026-07-05T09:52:55.756426+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.04166","citing_title":"Graph classes through the lens of logic","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS","json":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS.json","graph_json":"https://pith.science/api/pith-number/O3N7ZQQ6GIZ55AT25NWFDPX6QS/graph.json","events_json":"https://pith.science/api/pith-number/O3N7ZQQ6GIZ55AT25NWFDPX6QS/events.json","paper":"https://pith.science/paper/O3N7ZQQ6"},"agent_actions":{"view_html":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS","download_json":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS.json","view_paper":"https://pith.science/paper/O3N7ZQQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.11229&json=true","fetch_graph":"https://pith.science/api/pith-number/O3N7ZQQ6GIZ55AT25NWFDPX6QS/graph.json","fetch_events":"https://pith.science/api/pith-number/O3N7ZQQ6GIZ55AT25NWFDPX6QS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS/action/storage_attestation","attest_author":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS/action/author_attestation","sign_citation":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS/action/citation_signature","submit_replication":"https://pith.science/pith/O3N7ZQQ6GIZ55AT25NWFDPX6QS/action/replication_record"}},"created_at":"2026-07-05T09:52:55.756426+00:00","updated_at":"2026-07-05T09:52:55.756426+00:00"}