{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PL4GFH6KSD4CYV3PEHHLADN6PH","short_pith_number":"pith:PL4GFH6K","canonical_record":{"source":{"id":"1408.5943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T23:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"2c484fd17b1b6e4b2ab073997055acbb7db41dca7af92622ac34545e2eadb6a1","abstract_canon_sha256":"4c516475e37cc9c4c9b36dd5f2fce8eb8f0ca010ab402dece7ebd52fba0b96ca"},"schema_version":"1.0"},"canonical_sha256":"7af8629fca90f82c576f21ceb00dbe79fa4c0e7643fd81a5a5ff22409d74f090","source":{"kind":"arxiv","id":"1408.5943","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5943","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5943v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5943","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"PL4GFH6KSD4C","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PL4GFH6KSD4CYV3P","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PL4GFH6K","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PL4GFH6KSD4CYV3PEHHLADN6PH","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T23:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"2c484fd17b1b6e4b2ab073997055acbb7db41dca7af92622ac34545e2eadb6a1","abstract_canon_sha256":"4c516475e37cc9c4c9b36dd5f2fce8eb8f0ca010ab402dece7ebd52fba0b96ca"},"schema_version":"1.0"},"canonical_sha256":"7af8629fca90f82c576f21ceb00dbe79fa4c0e7643fd81a5a5ff22409d74f090","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.749381Z","signature_b64":"DNOIzig3jhA44nGgKiu0WSbSthedEmZdxJTQ67mE+0usKtXNu6t6Vbb4AkbuNzHtUPVyLTcTDzjVIt3voh0vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af8629fca90f82c576f21ceb00dbe79fa4c0e7643fd81a5a5ff22409d74f090","last_reissued_at":"2026-05-18T00:42:13.748470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.748470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5943","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5UCdqn//OsZBDs9uLlEyA0GXX6W2sVZhGXUEET7hIdh5stXSzK27N882znaceGmomCI8vu5FQW7jDxHHNpzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:27:05.749658Z"},"content_sha256":"e58f0f5ec8e0510dd90eb5bcf5349a64816f9148edc0040348f0861e5248a13e","schema_version":"1.0","event_id":"sha256:e58f0f5ec8e0510dd90eb5bcf5349a64816f9148edc0040348f0861e5248a13e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PL4GFH6KSD4CYV3PEHHLADN6PH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cong X. Kang, Eunjeong Yi, Linda Eroh","submitted_at":"2014-08-25T23:05:35Z","abstract_excerpt":"The \\emph{metric dimension} $\\dim(G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen vertices. The \\emph{zero forcing number} $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)\\!\\setminus\\!S$ are colored white) such that $V(G)$ is turned black after finitely many applications of \"the color-change rule\": a white vertex is converted black if it is the only white neighbor of a black vertex. We show that $\\dim(T) \\leq Z(T)$ for a tree $T$, and that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5943","kind":"arxiv","version":2},"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":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9Y4tdOgVxG/MfjMPkUZRxqgZELcTCi+eY5Q40hmMsfET7RQjVIYwl/oCmWhKdTscgL1B23dzw4yPxiCesm6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:27:05.750341Z"},"content_sha256":"3bc4d6d4d1d075f2ca09b4a56c2e5b5d8135cd4fea84e22fe5206798c8bcf7e3","schema_version":"1.0","event_id":"sha256:3bc4d6d4d1d075f2ca09b4a56c2e5b5d8135cd4fea84e22fe5206798c8bcf7e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/bundle.json","state_url":"https://pith.science/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/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":"2026-06-06T20:27:05Z","links":{"resolver":"https://pith.science/pith/PL4GFH6KSD4CYV3PEHHLADN6PH","bundle":"https://pith.science/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/bundle.json","state":"https://pith.science/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PL4GFH6KSD4CYV3PEHHLADN6PH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PL4GFH6KSD4CYV3PEHHLADN6PH","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":"4c516475e37cc9c4c9b36dd5f2fce8eb8f0ca010ab402dece7ebd52fba0b96ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T23:05:35Z","title_canon_sha256":"2c484fd17b1b6e4b2ab073997055acbb7db41dca7af92622ac34545e2eadb6a1"},"schema_version":"1.0","source":{"id":"1408.5943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5943","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5943v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5943","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"PL4GFH6KSD4C","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PL4GFH6KSD4CYV3P","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PL4GFH6K","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:3bc4d6d4d1d075f2ca09b4a56c2e5b5d8135cd4fea84e22fe5206798c8bcf7e3","target":"graph","created_at":"2026-05-18T00:42:13Z","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 \\emph{metric dimension} $\\dim(G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen vertices. The \\emph{zero forcing number} $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)\\!\\setminus\\!S$ are colored white) such that $V(G)$ is turned black after finitely many applications of \"the color-change rule\": a white vertex is converted black if it is the only white neighbor of a black vertex. We show that $\\dim(T) \\leq Z(T)$ for a tree $T$, and that","authors_text":"Cong X. Kang, Eunjeong Yi, Linda Eroh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T23:05:35Z","title":"A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5943","kind":"arxiv","version":2},"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:e58f0f5ec8e0510dd90eb5bcf5349a64816f9148edc0040348f0861e5248a13e","target":"record","created_at":"2026-05-18T00:42:13Z","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":"4c516475e37cc9c4c9b36dd5f2fce8eb8f0ca010ab402dece7ebd52fba0b96ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T23:05:35Z","title_canon_sha256":"2c484fd17b1b6e4b2ab073997055acbb7db41dca7af92622ac34545e2eadb6a1"},"schema_version":"1.0","source":{"id":"1408.5943","kind":"arxiv","version":2}},"canonical_sha256":"7af8629fca90f82c576f21ceb00dbe79fa4c0e7643fd81a5a5ff22409d74f090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7af8629fca90f82c576f21ceb00dbe79fa4c0e7643fd81a5a5ff22409d74f090","first_computed_at":"2026-05-18T00:42:13.748470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.748470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNOIzig3jhA44nGgKiu0WSbSthedEmZdxJTQ67mE+0usKtXNu6t6Vbb4AkbuNzHtUPVyLTcTDzjVIt3voh0vCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.749381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e58f0f5ec8e0510dd90eb5bcf5349a64816f9148edc0040348f0861e5248a13e","sha256:3bc4d6d4d1d075f2ca09b4a56c2e5b5d8135cd4fea84e22fe5206798c8bcf7e3"],"state_sha256":"f145b77c0279e82af342baf92b51fcb33b1a8191c30651c25fb94bff33c1765d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17mOj+p/FNyMeg7+3xpDP4zsPakwhwOhw/I3N3hn5U6HZ9V9ob+EsOHADRF1gCG7TxyaONq31dm/5cw32s1lDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:27:05.753564Z","bundle_sha256":"2124c42d73a3e6e43aa1c47dabb7113707477019bfe46c1bb54105e56b4d9587"}}