{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2IZW7WPIOMYJ4VH2UMDTEROMP7","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":"ff780301e70f2f8ef621cc6511541bbc8f826aeed3594196cf9d65fe689e007c","cross_cats_sorted":["cs.CC","cs.LO","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-15T17:49:07Z","title_canon_sha256":"fca11e830d4ca1f19fa79e9b98a2f40d4d199b9686caa2b86f763c14cda59d20"},"schema_version":"1.0","source":{"id":"1904.07216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07216","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07216v1","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07216","created_at":"2026-05-17T23:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"2IZW7WPIOMYJ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2IZW7WPIOMYJ4VH2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2IZW7WPI","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:ab4edd5af11dee8c238681348076801fb331d768f48c692212935c16e5139c04","target":"graph","created_at":"2026-05-17T23:48:34Z","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":"The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be characterised in terms of the number of variables that is required to describe the graph up to isomorphism in first-order logic with counting quantifiers.\n  It is known that the WL dimension is upper-bounded for all graphs that exclude some fixed graph as a minor (Grohe, JACM 2012). However, the bounds that can be derived from this general result ","authors_text":"Martin Grohe, Sandra Kiefer","cross_cats":["cs.CC","cs.LO","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-15T17:49:07Z","title":"A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded Genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07216","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:a4927372076e2760315202b233d404825e291d343833478c1b8e3869c5fade4a","target":"record","created_at":"2026-05-17T23:48:34Z","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":"ff780301e70f2f8ef621cc6511541bbc8f826aeed3594196cf9d65fe689e007c","cross_cats_sorted":["cs.CC","cs.LO","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-15T17:49:07Z","title_canon_sha256":"fca11e830d4ca1f19fa79e9b98a2f40d4d199b9686caa2b86f763c14cda59d20"},"schema_version":"1.0","source":{"id":"1904.07216","kind":"arxiv","version":1}},"canonical_sha256":"d2336fd9e873309e54faa3073245cc7ff7e0e2a7ac3408e5118d30fb05c9cb9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2336fd9e873309e54faa3073245cc7ff7e0e2a7ac3408e5118d30fb05c9cb9f","first_computed_at":"2026-05-17T23:48:34.897606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:34.897606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1kp9nBsLw/q4A+kzQ133AwEFI+WSHJchEpq2Ce715xMDZcc1A5LCbkP9OHPJrV3usCUb1D9wXUBP4A61Jwk5Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:34.898126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4927372076e2760315202b233d404825e291d343833478c1b8e3869c5fade4a","sha256:ab4edd5af11dee8c238681348076801fb331d768f48c692212935c16e5139c04"],"state_sha256":"e93a3e1ba39c81949cf9dde2667d2c6f96a48bf70cbe270c8d654262acc8ca70"}