{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CBKGOOJBZL4DV3U3TCVDYDJ34V","short_pith_number":"pith:CBKGOOJB","canonical_record":{"source":{"id":"1502.05910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-20T15:44:17Z","cross_cats_sorted":["cs.CC","cs.DM","cs.LO"],"title_canon_sha256":"1ae03a9b1e956630b842bc828c7d896da6f3faf65e2dff9167f9eb6d717ed040","abstract_canon_sha256":"1cdc52ab4715d6634b82cce47cf47008fa05f043b80af2aeef28498f026f20b7"},"schema_version":"1.0"},"canonical_sha256":"1054673921caf83aee9b98aa3c0d3be56d5c1a2bd5f0e17c68ce747e3c7cd3e7","source":{"kind":"arxiv","id":"1502.05910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05910","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05910v1","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05910","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"CBKGOOJBZL4D","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CBKGOOJBZL4DV3U3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CBKGOOJB","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CBKGOOJBZL4DV3U3TCVDYDJ34V","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-20T15:44:17Z","cross_cats_sorted":["cs.CC","cs.DM","cs.LO"],"title_canon_sha256":"1ae03a9b1e956630b842bc828c7d896da6f3faf65e2dff9167f9eb6d717ed040","abstract_canon_sha256":"1cdc52ab4715d6634b82cce47cf47008fa05f043b80af2aeef28498f026f20b7"},"schema_version":"1.0"},"canonical_sha256":"1054673921caf83aee9b98aa3c0d3be56d5c1a2bd5f0e17c68ce747e3c7cd3e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:44.524028Z","signature_b64":"uI7AgCEpMB01n+OcD4KdhIX1H9bLBf7tnRkb85mJybZj91otRvWDlzZ56IMuNRFgCDqPnaohjdLbZ0I1uBVlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1054673921caf83aee9b98aa3c0d3be56d5c1a2bd5f0e17c68ce747e3c7cd3e7","last_reissued_at":"2026-05-18T02:26:44.523627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:44.523627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05910","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":"2026-05-18T02:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"STRqjIbrCDfMM1OKdpEURJ0lKZHBlH6k/+RQJKV3n0wso7PSlBpGIzGylDYLjHv07h0rWpMECAL3ImKBtVbSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:42:45.991067Z"},"content_sha256":"dc28a67a75e32b7e8c679b4475f39a4d296f4d9b7709a5af666729506eaee2ce","schema_version":"1.0","event_id":"sha256:dc28a67a75e32b7e8c679b4475f39a4d296f4d9b7709a5af666729506eaee2ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CBKGOOJBZL4DV3U3TCVDYDJ34V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed-parameter Tractable Distances to Sparse Graph Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.LO"],"primary_cat":"cs.DS","authors_text":"Anuj Dawar, Jannis Bulian","submitted_at":"2015-02-20T15:44:17Z","abstract_excerpt":"We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to C is fixed-parameter tractable. The results are based on two general techniques. The first of these, building on recent work of Grohe et al. establishes that any class of graphs that is slicewise nowhere dense and slicewise first-order definable is FPT. The second shows that determining the elimination distance of a graph G to a minor-closed class C is FPT."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05910","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":"2026-05-18T02:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7SC1CYc+2J7e5q/cGltKqyMvlV4Gk+dcVzdhUIuGwm+COSbBQciUB9oz0rYIMZP4lGZf1HL45EbqzSt+CJvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:42:45.991436Z"},"content_sha256":"6443c34f6957cbc229972fef63bb8b790c2f61e5576a08ab2b6fa1cc1842f9dd","schema_version":"1.0","event_id":"sha256:6443c34f6957cbc229972fef63bb8b790c2f61e5576a08ab2b6fa1cc1842f9dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/bundle.json","state_url":"https://pith.science/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/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":"2026-06-11T09:42:45Z","links":{"resolver":"https://pith.science/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V","bundle":"https://pith.science/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/bundle.json","state":"https://pith.science/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBKGOOJBZL4DV3U3TCVDYDJ34V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CBKGOOJBZL4DV3U3TCVDYDJ34V","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":"1cdc52ab4715d6634b82cce47cf47008fa05f043b80af2aeef28498f026f20b7","cross_cats_sorted":["cs.CC","cs.DM","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-20T15:44:17Z","title_canon_sha256":"1ae03a9b1e956630b842bc828c7d896da6f3faf65e2dff9167f9eb6d717ed040"},"schema_version":"1.0","source":{"id":"1502.05910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05910","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05910v1","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05910","created_at":"2026-05-18T02:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"CBKGOOJBZL4D","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CBKGOOJBZL4DV3U3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CBKGOOJB","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:6443c34f6957cbc229972fef63bb8b790c2f61e5576a08ab2b6fa1cc1842f9dd","target":"graph","created_at":"2026-05-18T02:26:44Z","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":"We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to C is fixed-parameter tractable. The results are based on two general techniques. The first of these, building on recent work of Grohe et al. establishes that any class of graphs that is slicewise nowhere dense and slicewise first-order definable is FPT. The second shows that determining the elimination distance of a graph G to a minor-closed class C is FPT.","authors_text":"Anuj Dawar, Jannis Bulian","cross_cats":["cs.CC","cs.DM","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-20T15:44:17Z","title":"Fixed-parameter Tractable Distances to Sparse Graph Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05910","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:dc28a67a75e32b7e8c679b4475f39a4d296f4d9b7709a5af666729506eaee2ce","target":"record","created_at":"2026-05-18T02:26:44Z","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":"1cdc52ab4715d6634b82cce47cf47008fa05f043b80af2aeef28498f026f20b7","cross_cats_sorted":["cs.CC","cs.DM","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-20T15:44:17Z","title_canon_sha256":"1ae03a9b1e956630b842bc828c7d896da6f3faf65e2dff9167f9eb6d717ed040"},"schema_version":"1.0","source":{"id":"1502.05910","kind":"arxiv","version":1}},"canonical_sha256":"1054673921caf83aee9b98aa3c0d3be56d5c1a2bd5f0e17c68ce747e3c7cd3e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1054673921caf83aee9b98aa3c0d3be56d5c1a2bd5f0e17c68ce747e3c7cd3e7","first_computed_at":"2026-05-18T02:26:44.523627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:44.523627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uI7AgCEpMB01n+OcD4KdhIX1H9bLBf7tnRkb85mJybZj91otRvWDlzZ56IMuNRFgCDqPnaohjdLbZ0I1uBVlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:44.524028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc28a67a75e32b7e8c679b4475f39a4d296f4d9b7709a5af666729506eaee2ce","sha256:6443c34f6957cbc229972fef63bb8b790c2f61e5576a08ab2b6fa1cc1842f9dd"],"state_sha256":"78ec589672c908946fa9865166e9985181aa7cd68b3568804f650165b4e9cc9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYq/6ybWJRsoL2Rf5fMnezagbp3HKDQSn+LGGWvt08YeIhTdI1xBH4q0ixGrI+iEgSl+earv1KuDFe/BSlVrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:42:45.993270Z","bundle_sha256":"7d613cac3bc1691222b661f7521772702bfb44b0b53fdd3a80e9cd0315e53770"}}