{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EGX4R7WOS5RSGYC7GJQXNZM2HK","short_pith_number":"pith:EGX4R7WO","canonical_record":{"source":{"id":"1804.10670","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-27T20:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"4c31559cb5978adba07243aaffe6e2ac27ef5f003b06e4766be889fc55ebb571","abstract_canon_sha256":"fc62245788262f347860d94bed7faf51df9a5140dc13e23a5a3d1db88955e831"},"schema_version":"1.0"},"canonical_sha256":"21afc8fece976323605f326176e59a3abdf5ffcac132deec4ed90f9b62c37837","source":{"kind":"arxiv","id":"1804.10670","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10670","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10670v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10670","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"EGX4R7WOS5RS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EGX4R7WOS5RSGYC7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EGX4R7WO","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EGX4R7WOS5RSGYC7GJQXNZM2HK","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10670","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-27T20:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"4c31559cb5978adba07243aaffe6e2ac27ef5f003b06e4766be889fc55ebb571","abstract_canon_sha256":"fc62245788262f347860d94bed7faf51df9a5140dc13e23a5a3d1db88955e831"},"schema_version":"1.0"},"canonical_sha256":"21afc8fece976323605f326176e59a3abdf5ffcac132deec4ed90f9b62c37837","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:15.907778Z","signature_b64":"RTMxGy0wtYwy5xFp3ggbEmoqoRCpzheM6jARxfKVD4AmeNqbS86AHA6qYu4F7kFFICi0xuR5GSbw6EgloDFhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21afc8fece976323605f326176e59a3abdf5ffcac132deec4ed90f9b62c37837","last_reissued_at":"2026-05-18T00:17:15.907303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:15.907303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10670","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u26xfDYEhgfCq6JCdInI9eJwEkUJHh4pr0C5ENX3Y1rvBlhw4iaMkCQTdXKqizZ5xggl+XoskNyacqJk54B1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:48:18.497125Z"},"content_sha256":"9543ee80dea548f4b41258a22b3631f85459af2194a8d1ee90d29d3fb71be7be","schema_version":"1.0","event_id":"sha256:9543ee80dea548f4b41258a22b3631f85459af2194a8d1ee90d29d3fb71be7be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EGX4R7WOS5RSGYC7GJQXNZM2HK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alternative parameterizations of Metric Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Felix Reidl, Gregory Gutin, Magnus Wahlstr\\\"om, M. S. Ramanujan","submitted_at":"2018-04-27T20:14:11Z","abstract_excerpt":"A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\\in V(G)$, there is $v\\in W$ such that ${\\rm dist}_G(v,x)\\neq{\\rm dist}_G(v,y)$, where ${\\rm dist}_G(u,v)$ denotes the length of a shortest path between $u$ and $v$ in the graph $G$. The metric dimension ${\\rm md}(G)$ of $G$ is the minimum cardinality of a resolving set. The Metric Dimension problem, i.e. deciding whether ${\\rm md}(G)\\le k$, is NP-complete even for interval graphs (Foucaud et al., 2017). We study Metric Dimension (for arbitrary graphs) from the lens of parameterized complexity. The problem par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10670","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":"2026-05-18T00:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DPkGim3OOnETFXGKFsiaWPcyP4Jf5LLEaohJVBw4YhDsbZ605649puA4gKSF8Cn5lWJEml8AKSnlAqH2txV0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:48:18.497596Z"},"content_sha256":"d72998e7278086b490719501e8fdce3bb8dc3931957bf189dda6b5cf45caa640","schema_version":"1.0","event_id":"sha256:d72998e7278086b490719501e8fdce3bb8dc3931957bf189dda6b5cf45caa640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/bundle.json","state_url":"https://pith.science/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/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":"2026-05-30T19:48:18Z","links":{"resolver":"https://pith.science/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK","bundle":"https://pith.science/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/bundle.json","state":"https://pith.science/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGX4R7WOS5RSGYC7GJQXNZM2HK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EGX4R7WOS5RSGYC7GJQXNZM2HK","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":"fc62245788262f347860d94bed7faf51df9a5140dc13e23a5a3d1db88955e831","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-27T20:14:11Z","title_canon_sha256":"4c31559cb5978adba07243aaffe6e2ac27ef5f003b06e4766be889fc55ebb571"},"schema_version":"1.0","source":{"id":"1804.10670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10670","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10670v1","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10670","created_at":"2026-05-18T00:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"EGX4R7WOS5RS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EGX4R7WOS5RSGYC7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EGX4R7WO","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:d72998e7278086b490719501e8fdce3bb8dc3931957bf189dda6b5cf45caa640","target":"graph","created_at":"2026-05-18T00:17:15Z","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":"A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\\in V(G)$, there is $v\\in W$ such that ${\\rm dist}_G(v,x)\\neq{\\rm dist}_G(v,y)$, where ${\\rm dist}_G(u,v)$ denotes the length of a shortest path between $u$ and $v$ in the graph $G$. The metric dimension ${\\rm md}(G)$ of $G$ is the minimum cardinality of a resolving set. The Metric Dimension problem, i.e. deciding whether ${\\rm md}(G)\\le k$, is NP-complete even for interval graphs (Foucaud et al., 2017). We study Metric Dimension (for arbitrary graphs) from the lens of parameterized complexity. The problem par","authors_text":"Felix Reidl, Gregory Gutin, Magnus Wahlstr\\\"om, M. S. Ramanujan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-27T20:14:11Z","title":"Alternative parameterizations of Metric Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10670","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":"sha256:9543ee80dea548f4b41258a22b3631f85459af2194a8d1ee90d29d3fb71be7be","target":"record","created_at":"2026-05-18T00:17:15Z","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":"fc62245788262f347860d94bed7faf51df9a5140dc13e23a5a3d1db88955e831","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-27T20:14:11Z","title_canon_sha256":"4c31559cb5978adba07243aaffe6e2ac27ef5f003b06e4766be889fc55ebb571"},"schema_version":"1.0","source":{"id":"1804.10670","kind":"arxiv","version":1}},"canonical_sha256":"21afc8fece976323605f326176e59a3abdf5ffcac132deec4ed90f9b62c37837","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21afc8fece976323605f326176e59a3abdf5ffcac132deec4ed90f9b62c37837","first_computed_at":"2026-05-18T00:17:15.907303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:15.907303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RTMxGy0wtYwy5xFp3ggbEmoqoRCpzheM6jARxfKVD4AmeNqbS86AHA6qYu4F7kFFICi0xuR5GSbw6EgloDFhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:15.907778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9543ee80dea548f4b41258a22b3631f85459af2194a8d1ee90d29d3fb71be7be","sha256:d72998e7278086b490719501e8fdce3bb8dc3931957bf189dda6b5cf45caa640"],"state_sha256":"0aadd2820c1addfe44fd10b1f568410e14344fc27e08f8fcfb7465e49ffffe33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSCfUHnazq1J+vzy4pbivLSLYB3sR9sGUoiKPofh3mLWmgwprOOSL60FqDRD9SZfpv2LGVxLece66qyLEK5VCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:48:18.500962Z","bundle_sha256":"f7d172094b9ce6b397f6d1cd6ffb030841667dd8fd69ae50fbc497dc7021d133"}}