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A graph $G$ is said to be $D$-distance magic if all vertices has the same $D$-vertex-weight, it is said to be $D$-distance antimagic if all vertices have distinct $D$-vertex-weights, and it is called $(a,d)-D$-distance antimagic if the $D$-vertex-weights constitute an arithmetic progression with difference $d$ and starting value"},"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":"1312.7405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-28T08:22:19Z","cross_cats_sorted":[],"title_canon_sha256":"aa3f876c3462f8092ad678b5d121d92be966b4f7972ce725d671694fb11e34b8","abstract_canon_sha256":"d685cc01dbfb858ce7c1c75d9935b19bc7839fd59b88da087d18b1205f595b21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:43.579884Z","signature_b64":"Obb/Zp8Z13SBG383GmuECtUtn8KAEROgNKnu/LwqozJtRJyzAW3GmgFvvhp6OQBnv21OaueILg3M0PwhUG+bAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93b1f01537afd57ff2e79184f1ad72bbb120367dd59f4702cb012abdfedee37f","last_reissued_at":"2026-05-18T03:03:43.579140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:43.579140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Distance Antimagic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kristiana Wijaya, Rinovia Simanjuntak","submitted_at":"2013-12-28T08:22:19Z","abstract_excerpt":"For an arbitrary set of distances $D\\subseteq \\{0,1, \\ldots, diam(G)\\}$, a $D$-weight of a vertex $x$ in a graph $G$ under a vertex labeling $f:V\\rightarrow \\{1,2, \\ldots , v\\}$ is defined as $w_D(x)=\\sum_{y\\in N_D(x)} f(y)$, where $N_D(x) = \\{y \\in V| d(x,y) \\in D\\}$. A graph $G$ is said to be $D$-distance magic if all vertices has the same $D$-vertex-weight, it is said to be $D$-distance antimagic if all vertices have distinct $D$-vertex-weights, and it is called $(a,d)-D$-distance antimagic if the $D$-vertex-weights constitute an arithmetic progression with difference $d$ and starting value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7405","kind":"arxiv","version":1},"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":"1312.7405","created_at":"2026-05-18T03:03:43.579260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7405v1","created_at":"2026-05-18T03:03:43.579260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7405","created_at":"2026-05-18T03:03:43.579260+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOY7AFJXV7KX","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOY7AFJXV7KX74XH","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOY7AFJX","created_at":"2026-05-18T12:27:59.945178+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/SOY7AFJXV7KX74XHSGCPDLLSXO","json":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO.json","graph_json":"https://pith.science/api/pith-number/SOY7AFJXV7KX74XHSGCPDLLSXO/graph.json","events_json":"https://pith.science/api/pith-number/SOY7AFJXV7KX74XHSGCPDLLSXO/events.json","paper":"https://pith.science/paper/SOY7AFJX"},"agent_actions":{"view_html":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO","download_json":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO.json","view_paper":"https://pith.science/paper/SOY7AFJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7405&json=true","fetch_graph":"https://pith.science/api/pith-number/SOY7AFJXV7KX74XHSGCPDLLSXO/graph.json","fetch_events":"https://pith.science/api/pith-number/SOY7AFJXV7KX74XHSGCPDLLSXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO/action/storage_attestation","attest_author":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO/action/author_attestation","sign_citation":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO/action/citation_signature","submit_replication":"https://pith.science/pith/SOY7AFJXV7KX74XHSGCPDLLSXO/action/replication_record"}},"created_at":"2026-05-18T03:03:43.579260+00:00","updated_at":"2026-05-18T03:03:43.579260+00:00"}