{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MB3R3P5DXFF54FIRUNSZ5O34CN","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":"9d9505202ea2777992f4f0c984066f9d85af99f17fca6c3dd96fd3a300dfed8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-19T02:12:27Z","title_canon_sha256":"1f2fe2d6ea9d3d3a4844329739198f7fb7fd56ddfb36605d403e9614228965d8"},"schema_version":"1.0","source":{"id":"1811.08322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08322","created_at":"2026-05-18T00:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08322v1","created_at":"2026-05-18T00:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08322","created_at":"2026-05-18T00:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"MB3R3P5DXFF5","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MB3R3P5DXFF54FIR","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MB3R3P5D","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:70053399d2270535f40da15721dff9eda0ebe90c71f90f1692677d97fda9aceb","target":"graph","created_at":"2026-05-18T00:00:14Z","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":"Let $D(G)$ and $D^Q(G)= Diag(Tr) + D(G)$ be the distance matrix and distance signless Laplacian matrix of a simple strongly connected digraph $G$, respectively, where $Diag(Tr)=\\textrm{diag}(D_1,D_2,$ $\\ldots,D_n)$ be the diagonal matrix with vertex transmissions of the digraph $G$. To track the gradual change of $D(G)$ into $D^Q(G)$, in this paper, we propose to study the convex combinations of $D(G)$ and $Diag(Tr)$ defined by $$D_\\alpha(G)=\\alpha Diag(Tr)+(1-\\alpha)D(G), \\ \\ 0\\leq \\alpha\\leq1.$$ This study reduces to merging the distance spectral and distance signless Laplacian spectral theo","authors_text":"Ligong Wang, Wasin So, Weige Xi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-19T02:12:27Z","title":"The generalized distance matrix of digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08322","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":"sha256:412730a02cd4e81dcae7ceb6419b636dd98059a70d33ba7cbaff6ff5e46023e4","target":"record","created_at":"2026-05-18T00:00:14Z","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":"9d9505202ea2777992f4f0c984066f9d85af99f17fca6c3dd96fd3a300dfed8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-19T02:12:27Z","title_canon_sha256":"1f2fe2d6ea9d3d3a4844329739198f7fb7fd56ddfb36605d403e9614228965d8"},"schema_version":"1.0","source":{"id":"1811.08322","kind":"arxiv","version":1}},"canonical_sha256":"60771dbfa3b94bde1511a3659ebb7c137d39a48e90bcfb4d2c9ffdc9d8c24f0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60771dbfa3b94bde1511a3659ebb7c137d39a48e90bcfb4d2c9ffdc9d8c24f0f","first_computed_at":"2026-05-18T00:00:14.340696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:14.340696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8n7yZZqBb02yRg2CmaEhHqJTcZ89ax53LzFl3wh4R3pGFG4QxFpZo1A0iFWSja+oQ8RM4Imd6DwcXPmt0Mf/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:14.341370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:412730a02cd4e81dcae7ceb6419b636dd98059a70d33ba7cbaff6ff5e46023e4","sha256:70053399d2270535f40da15721dff9eda0ebe90c71f90f1692677d97fda9aceb"],"state_sha256":"4762137c24e269a2ed506df2e2578da75a0c86a047165d19256f2fc81a1f4cf1"}