{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ENUX7QYWCAU3UOM2TV6MGF73GI","short_pith_number":"pith:ENUX7QYW","canonical_record":{"source":{"id":"1703.06423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-19T11:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"6d636d6a8dfb3c677f49532c24cfab18555ab93d6099ef3df75e1660eb286d60","abstract_canon_sha256":"89458d5c158c5e13c5f1b90d5e49fc66d89132335dc5ba1b9be5e47106e62683"},"schema_version":"1.0"},"canonical_sha256":"23697fc3161029ba399a9d7cc317fb32302d271fe50cc2dfbd20e591a0f61049","source":{"kind":"arxiv","id":"1703.06423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06423","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06423v1","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06423","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"ENUX7QYWCAU3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ENUX7QYWCAU3UOM2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ENUX7QYW","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ENUX7QYWCAU3UOM2TV6MGF73GI","target":"record","payload":{"canonical_record":{"source":{"id":"1703.06423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-19T11:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"6d636d6a8dfb3c677f49532c24cfab18555ab93d6099ef3df75e1660eb286d60","abstract_canon_sha256":"89458d5c158c5e13c5f1b90d5e49fc66d89132335dc5ba1b9be5e47106e62683"},"schema_version":"1.0"},"canonical_sha256":"23697fc3161029ba399a9d7cc317fb32302d271fe50cc2dfbd20e591a0f61049","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:22.931072Z","signature_b64":"prxAz2XE9WJxmcGuSP8kgl/zv+hMp55R8LCPu0mo2d5lY/E+pjNgarFZT16kyiYB/9R5e8j//TeN98EHj4k9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23697fc3161029ba399a9d7cc317fb32302d271fe50cc2dfbd20e591a0f61049","last_reissued_at":"2026-05-18T00:48:22.930561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:22.930561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.06423","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":"2026-05-18T00:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gPiUUY+I+S8yKdm3jc1lhWOa/3Ae6NbfLuBZnT0efcku/pM0VU8Dqm9LYNBJGbYQrdrQz11vG1b/a6OUeZ/CBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:53:50.703099Z"},"content_sha256":"8b11ce467693cdb7b759d9776783f605814416b155e1d881bb657e541b42f180","schema_version":"1.0","event_id":"sha256:8b11ce467693cdb7b759d9776783f605814416b155e1d881bb657e541b42f180"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ENUX7QYWCAU3UOM2TV6MGF73GI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hardness of Embedding Grids and Walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bingkai Lin, Martin Grohe, Yijia Chen","submitted_at":"2017-03-19T11:24:26Z","abstract_excerpt":"The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of \"pattern graphs\" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise.\n  Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06423","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":"2026-05-18T00:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWq0flIJOhcgOT7UtAVNjsD6VSGwJ/R/vo+f9iTEGs2U7iVAU81p4IcK18eg8mx4rFhYhf/FIySG5O2UPinADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:53:50.703452Z"},"content_sha256":"ea460fcab513df7e4448d7353d30bd5d278b00db95ca94615c49b6cf555d3532","schema_version":"1.0","event_id":"sha256:ea460fcab513df7e4448d7353d30bd5d278b00db95ca94615c49b6cf555d3532"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/bundle.json","state_url":"https://pith.science/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/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":"2026-06-02T19:53:50Z","links":{"resolver":"https://pith.science/pith/ENUX7QYWCAU3UOM2TV6MGF73GI","bundle":"https://pith.science/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/bundle.json","state":"https://pith.science/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENUX7QYWCAU3UOM2TV6MGF73GI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ENUX7QYWCAU3UOM2TV6MGF73GI","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":"89458d5c158c5e13c5f1b90d5e49fc66d89132335dc5ba1b9be5e47106e62683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-19T11:24:26Z","title_canon_sha256":"6d636d6a8dfb3c677f49532c24cfab18555ab93d6099ef3df75e1660eb286d60"},"schema_version":"1.0","source":{"id":"1703.06423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06423","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06423v1","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06423","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"ENUX7QYWCAU3","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ENUX7QYWCAU3UOM2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ENUX7QYW","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:ea460fcab513df7e4448d7353d30bd5d278b00db95ca94615c49b6cf555d3532","target":"graph","created_at":"2026-05-18T00:48:22Z","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 dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of \"pattern graphs\" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise.\n  Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls.","authors_text":"Bingkai Lin, Martin Grohe, Yijia Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-19T11:24:26Z","title":"The Hardness of Embedding Grids and Walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06423","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":"sha256:8b11ce467693cdb7b759d9776783f605814416b155e1d881bb657e541b42f180","target":"record","created_at":"2026-05-18T00:48:22Z","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":"89458d5c158c5e13c5f1b90d5e49fc66d89132335dc5ba1b9be5e47106e62683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-19T11:24:26Z","title_canon_sha256":"6d636d6a8dfb3c677f49532c24cfab18555ab93d6099ef3df75e1660eb286d60"},"schema_version":"1.0","source":{"id":"1703.06423","kind":"arxiv","version":1}},"canonical_sha256":"23697fc3161029ba399a9d7cc317fb32302d271fe50cc2dfbd20e591a0f61049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23697fc3161029ba399a9d7cc317fb32302d271fe50cc2dfbd20e591a0f61049","first_computed_at":"2026-05-18T00:48:22.930561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:22.930561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prxAz2XE9WJxmcGuSP8kgl/zv+hMp55R8LCPu0mo2d5lY/E+pjNgarFZT16kyiYB/9R5e8j//TeN98EHj4k9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:22.931072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b11ce467693cdb7b759d9776783f605814416b155e1d881bb657e541b42f180","sha256:ea460fcab513df7e4448d7353d30bd5d278b00db95ca94615c49b6cf555d3532"],"state_sha256":"2e0da32d8b22586bd2d51484795efa8096798281649efeceff08d9b95107af5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lj9rMEhokHabIADQl46e5VksGJiLbV/+GFtazQ00V5JR8MO+4LC1gRkgaCsqiYIgxoDO7IIb1UuD4vgV8dhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:53:50.705341Z","bundle_sha256":"8b547efd9dfe1c1168624d24aff21d61764bb7a8848d9bd5673f44f90d3191f8"}}