{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:W2T5UHDJAUW5MTGLT2WOUIRWUK","short_pith_number":"pith:W2T5UHDJ","schema_version":"1.0","canonical_sha256":"b6a7da1c69052dd64ccb9eacea2236a2b5ab45d7d103f7d5df8d72432fc50290","source":{"kind":"arxiv","id":"1903.05005","version":2},"attestation_state":"computed","paper":{"title":"$D$-Magic and Antimagic Labelings of Hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Munemasa, Palton Anuwiksa, Rinovia Simanjuntak","submitted_at":"2019-03-12T15:50:03Z","abstract_excerpt":"For a set of distances $D$, a graph $G$ of order $n$ is said to be $D-$magic if there exists a bijection $f:V\\rightarrow \\{1,2, \\ldots, n\\}$ and a constant $k$ such that for any vertex $x$, $\\sum_{y\\in N_D(x)} f(y) =k$, where $N_D(x)=\\{y|d(y,x)=j, j\\in D\\}$.\n  In this paper we shall find sets of distances $D$s, such that the hypercube is $D-$magic. We shall utilise well-known properties of (bipartite) distance-regular graphs to construct the $D-$magic labelings."},"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":"1903.05005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-12T15:50:03Z","cross_cats_sorted":[],"title_canon_sha256":"835fe9d720248ce06bc70bca49882a2caf01c13279bd90e1e4104858593ef180","abstract_canon_sha256":"e77c2d5b5168ae3f49e03a65ea4f2d7af80f92d52d4d97ef4cdafc1d8edb84ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:13.681862Z","signature_b64":"3OtRDdUyIXZp0FKImQo8pUACSpfCVeBu/F1vhjgxjrGup775hrMEKgjYgMTslmiLW240OmLvQhQz4fOIaGJxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6a7da1c69052dd64ccb9eacea2236a2b5ab45d7d103f7d5df8d72432fc50290","last_reissued_at":"2026-05-17T23:51:13.681349Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:13.681349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$D$-Magic and Antimagic Labelings of Hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Munemasa, Palton Anuwiksa, Rinovia Simanjuntak","submitted_at":"2019-03-12T15:50:03Z","abstract_excerpt":"For a set of distances $D$, a graph $G$ of order $n$ is said to be $D-$magic if there exists a bijection $f:V\\rightarrow \\{1,2, \\ldots, n\\}$ and a constant $k$ such that for any vertex $x$, $\\sum_{y\\in N_D(x)} f(y) =k$, where $N_D(x)=\\{y|d(y,x)=j, j\\in D\\}$.\n  In this paper we shall find sets of distances $D$s, such that the hypercube is $D-$magic. We shall utilise well-known properties of (bipartite) distance-regular graphs to construct the $D-$magic labelings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05005","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":"1903.05005","created_at":"2026-05-17T23:51:13.681440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.05005v2","created_at":"2026-05-17T23:51:13.681440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05005","created_at":"2026-05-17T23:51:13.681440+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2T5UHDJAUW5","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2T5UHDJAUW5MTGL","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2T5UHDJ","created_at":"2026-05-18T12:33:30.264802+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/W2T5UHDJAUW5MTGLT2WOUIRWUK","json":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK.json","graph_json":"https://pith.science/api/pith-number/W2T5UHDJAUW5MTGLT2WOUIRWUK/graph.json","events_json":"https://pith.science/api/pith-number/W2T5UHDJAUW5MTGLT2WOUIRWUK/events.json","paper":"https://pith.science/paper/W2T5UHDJ"},"agent_actions":{"view_html":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK","download_json":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK.json","view_paper":"https://pith.science/paper/W2T5UHDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.05005&json=true","fetch_graph":"https://pith.science/api/pith-number/W2T5UHDJAUW5MTGLT2WOUIRWUK/graph.json","fetch_events":"https://pith.science/api/pith-number/W2T5UHDJAUW5MTGLT2WOUIRWUK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK/action/storage_attestation","attest_author":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK/action/author_attestation","sign_citation":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK/action/citation_signature","submit_replication":"https://pith.science/pith/W2T5UHDJAUW5MTGLT2WOUIRWUK/action/replication_record"}},"created_at":"2026-05-17T23:51:13.681440+00:00","updated_at":"2026-05-17T23:51:13.681440+00:00"}