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Furthermore, the \\textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \\cup nK_1$ is super edge-magic or $+\\infty$ if there exists no such integer.\n  \\emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph t"},"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":"1401.4522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-18T08:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"e5858d6582f3f97d618347a8ac75b4e5b8eba4a246dd0f6ff9fba89659f70a36","abstract_canon_sha256":"7850b56b224661710b9b0dae2b15dae619a9518e9b308d322d216d9a1c4b7293"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:07.422044Z","signature_b64":"GHOYJDGE2cX6kzeUz/rNaJiZTCXyJrlT2TXHfe7vwmMpwK4EGmHjH2oCl3saE+T1Z99RZWi0MKaNwB5ptKJRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9b839efa46126b38958a80aa369b5f04c32cd3b552ef8c8e7e891d90a16ada7","last_reissued_at":"2026-05-18T02:53:07.421551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:07.421551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Super edge-magic deficiency of join-product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.A.G. Ngurah, Rinovia Simanjuntak","submitted_at":"2014-01-18T08:15:14Z","abstract_excerpt":"A graph $G$ is called \\textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \\cup E(G)$ to $\\{1, 2, \\ldots, |V(G) \\cup E(G)|\\}$ such that $f(V(G)) = \\{1, 2, \\ldots, |V(G)|\\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \\textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \\cup nK_1$ is super edge-magic or $+\\infty$ if there exists no such integer.\n  \\emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4522","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":"1401.4522","created_at":"2026-05-18T02:53:07.421621+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.4522v2","created_at":"2026-05-18T02:53:07.421621+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4522","created_at":"2026-05-18T02:53:07.421621+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZG4DT35EMETL","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZG4DT35EMETLHCKY","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZG4DT35E","created_at":"2026-05-18T12:28:59.999130+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/ZG4DT35EMETLHCKYVAFKG2NV6B","json":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B.json","graph_json":"https://pith.science/api/pith-number/ZG4DT35EMETLHCKYVAFKG2NV6B/graph.json","events_json":"https://pith.science/api/pith-number/ZG4DT35EMETLHCKYVAFKG2NV6B/events.json","paper":"https://pith.science/paper/ZG4DT35E"},"agent_actions":{"view_html":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B","download_json":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B.json","view_paper":"https://pith.science/paper/ZG4DT35E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.4522&json=true","fetch_graph":"https://pith.science/api/pith-number/ZG4DT35EMETLHCKYVAFKG2NV6B/graph.json","fetch_events":"https://pith.science/api/pith-number/ZG4DT35EMETLHCKYVAFKG2NV6B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B/action/storage_attestation","attest_author":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B/action/author_attestation","sign_citation":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B/action/citation_signature","submit_replication":"https://pith.science/pith/ZG4DT35EMETLHCKYVAFKG2NV6B/action/replication_record"}},"created_at":"2026-05-18T02:53:07.421621+00:00","updated_at":"2026-05-18T02:53:07.421621+00:00"}