{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P6YU47T6LY5Y3JOUOGSVGILXMM","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":"4177f99a8c8c57be52cab63e0dfb1ff64497358b93bc22215d9fc9b648f3f0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T04:13:31Z","title_canon_sha256":"b088502aaa30d1a7a4d49e03b823b87212dcd9080fcd558fa8656f3260c43071"},"schema_version":"1.0","source":{"id":"1610.09783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09783","created_at":"2026-05-18T01:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09783v1","created_at":"2026-05-18T01:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09783","created_at":"2026-05-18T01:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"P6YU47T6LY5Y","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"P6YU47T6LY5Y3JOU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"P6YU47T6","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4105388cddd24ec7d507fe22814de6840169d35706996c4920b996821710499d","target":"graph","created_at":"2026-05-18T01:00:47Z","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 $M$ be a mixed graph and $H(M)$ be its Hermitian-adjacency matrix. If we add every edge and arc in $M$ a Randi\\'c weight, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randi\\'c matrix $R_{H}(M)=(r_{h})_{kl}$ of a mixed graph $M$, where $(r_{h})_{kl}=-(r_{h})_{lk}=\\frac{\\textbf{i}}{\\sqrt{d_{k}d_{l}}}$ ($\\textbf{i}=\\sqrt{-1}$) if $(v_{k},v_{l})$ is an arc of $M$, $(r_{h})_{kl}=(r_{h})_{lk}=\\frac{1}{\\sqrt{d_{k}d_{l}}}$ if $v_{k}v_{l}$ is an undirected edge of $M$, and $(r_{h})_{kl}=0$ otherwise","authors_text":"Ligong Wang, Qiannan Zhou, Yong Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T04:13:31Z","title":"Hermitian-Randi\\'c matrix and Hermitian-Randi\\'c energy of mixed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09783","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":"sha256:51c18586a2a0358f06ea4b759936f67f8e3b1adaa76d3c43fab8ac7612ae6406","target":"record","created_at":"2026-05-18T01:00:47Z","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":"4177f99a8c8c57be52cab63e0dfb1ff64497358b93bc22215d9fc9b648f3f0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-31T04:13:31Z","title_canon_sha256":"b088502aaa30d1a7a4d49e03b823b87212dcd9080fcd558fa8656f3260c43071"},"schema_version":"1.0","source":{"id":"1610.09783","kind":"arxiv","version":1}},"canonical_sha256":"7fb14e7e7e5e3b8da5d471a55321776320df576e29b9245f39dc492789a01aaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb14e7e7e5e3b8da5d471a55321776320df576e29b9245f39dc492789a01aaa","first_computed_at":"2026-05-18T01:00:47.194108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:47.194108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aM/4+vryYNQhyPlYA+z/YYRHkClF5RH4P5wnp/m4T2CIssDLqseUi1qLkrvgaHBA+7+SmBvfWGto6H5kny5YDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:47.194543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51c18586a2a0358f06ea4b759936f67f8e3b1adaa76d3c43fab8ac7612ae6406","sha256:4105388cddd24ec7d507fe22814de6840169d35706996c4920b996821710499d"],"state_sha256":"144f44b8beeb25c208064606582bb73e88e5fc1a5e7f0e7f4d3bc25926f1bd20"}