{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WCHECAH3UKHPAV3XSJURWFRS6W","short_pith_number":"pith:WCHECAH3","schema_version":"1.0","canonical_sha256":"b08e4100fba28ef0577792691b1632f5a40e29b32e45722dda91be6aed418803","source":{"kind":"arxiv","id":"1412.2865","version":2},"attestation_state":"computed","paper":{"title":"Location-domination and matching in cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Foucaud, Michael A. Henning","submitted_at":"2014-12-09T06:25:49Z","abstract_excerpt":"A dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex outside $D$ is adjacent to a vertex in $D$. A locating-dominating set of $G$ is a dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \\cap D \\neq N(v) \\cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-domination number of $G$, denoted $\\gamma_L(G)$, is"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.2865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T06:25:49Z","cross_cats_sorted":[],"title_canon_sha256":"305bb11be4a54329ee9ba8517da696b7eb6d0cb9c54e982741e0412fcb396dcb","abstract_canon_sha256":"130a5cbe39ebd81d191bb4951315d455d1a227178c5b15ff79268ed365e69a8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:41.581048Z","signature_b64":"CHgbAsVyJPz6kBmkgIq4RLQ5KNMpke0iBTio6BxDPX+HLuQMt24/7yAlxD2JMePczg7Dx7SD/rU8XsRbi8ZkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b08e4100fba28ef0577792691b1632f5a40e29b32e45722dda91be6aed418803","last_reissued_at":"2026-05-18T01:22:41.580599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:41.580599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Location-domination and matching in cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Foucaud, Michael A. Henning","submitted_at":"2014-12-09T06:25:49Z","abstract_excerpt":"A dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex outside $D$ is adjacent to a vertex in $D$. A locating-dominating set of $G$ is a dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \\cap D \\neq N(v) \\cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-domination number of $G$, denoted $\\gamma_L(G)$, is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2865","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.2865","created_at":"2026-05-18T01:22:41.580670+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2865v2","created_at":"2026-05-18T01:22:41.580670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2865","created_at":"2026-05-18T01:22:41.580670+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCHECAH3UKHP","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCHECAH3UKHPAV3X","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCHECAH3","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W","json":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W.json","graph_json":"https://pith.science/api/pith-number/WCHECAH3UKHPAV3XSJURWFRS6W/graph.json","events_json":"https://pith.science/api/pith-number/WCHECAH3UKHPAV3XSJURWFRS6W/events.json","paper":"https://pith.science/paper/WCHECAH3"},"agent_actions":{"view_html":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W","download_json":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W.json","view_paper":"https://pith.science/paper/WCHECAH3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2865&json=true","fetch_graph":"https://pith.science/api/pith-number/WCHECAH3UKHPAV3XSJURWFRS6W/graph.json","fetch_events":"https://pith.science/api/pith-number/WCHECAH3UKHPAV3XSJURWFRS6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W/action/storage_attestation","attest_author":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W/action/author_attestation","sign_citation":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W/action/citation_signature","submit_replication":"https://pith.science/pith/WCHECAH3UKHPAV3XSJURWFRS6W/action/replication_record"}},"created_at":"2026-05-18T01:22:41.580670+00:00","updated_at":"2026-05-18T01:22:41.580670+00:00"}