{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QFNV4I755H3LON5NMN24TALRMN","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":"ff703468a141b06ed1580e46d326cdfec294235ec7ff7b25ba9187055ccbd9a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-10T19:57:28Z","title_canon_sha256":"0df5ac92c70cf06014c26faf43204c8fadc1d3acc6678c4442c2fe41b0eff464"},"schema_version":"1.0","source":{"id":"1506.03442","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03442","created_at":"2026-05-18T01:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03442v1","created_at":"2026-05-18T01:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03442","created_at":"2026-05-18T01:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"QFNV4I755H3L","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFNV4I755H3LON5N","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFNV4I75","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:aa1b17af1dd27d421a18d4cf99e867a6bb0a7bd47fa8ce23f754505babc572ec","target":"graph","created_at":"2026-05-18T01:55:24Z","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 dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the \\emph{location-domination number} $\\lambda(G)$. An LD-set $S$ of a graph $G$ is \\emph{global} if it is an LD-set of both $G$ and its complement $\\overline{G}$. The \\emph{global location-domination number} $\\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$.\n  For any LD-set $S$ of a g","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Merce Mora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-10T19:57:28Z","title":"On global location-domination in bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03442","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":"sha256:4a4316a576761490cbb12b43dffef7ea7612a4412ffddb8819e80824e5d29bbe","target":"record","created_at":"2026-05-18T01:55:24Z","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":"ff703468a141b06ed1580e46d326cdfec294235ec7ff7b25ba9187055ccbd9a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-10T19:57:28Z","title_canon_sha256":"0df5ac92c70cf06014c26faf43204c8fadc1d3acc6678c4442c2fe41b0eff464"},"schema_version":"1.0","source":{"id":"1506.03442","kind":"arxiv","version":1}},"canonical_sha256":"815b5e23fde9f6b737ad6375c9817163726e15f409d3661a9d5d00bd4bf2acb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"815b5e23fde9f6b737ad6375c9817163726e15f409d3661a9d5d00bd4bf2acb6","first_computed_at":"2026-05-18T01:55:24.725203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:24.725203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WoqGPbyc0Xn1D/WFKYQYQsCKkwrjv8QADmBnN4mdhSyaOYGCxnFpwj0/tqlCefBi+136vRB3CF8R18Ul68EQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:24.725844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03442","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a4316a576761490cbb12b43dffef7ea7612a4412ffddb8819e80824e5d29bbe","sha256:aa1b17af1dd27d421a18d4cf99e867a6bb0a7bd47fa8ce23f754505babc572ec"],"state_sha256":"86135b7ebf39e466990c3232d9491c8bd011a2e0f6a5e62da62609e28064dc43"}