{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XZB7ULFDAJM7VSBFI5IKAT3MFI","short_pith_number":"pith:XZB7ULFD","schema_version":"1.0","canonical_sha256":"be43fa2ca30259fac8254750a04f6c2a20a03c04f69e89b9bc0c8663086739b3","source":{"kind":"arxiv","id":"1812.05734","version":1},"attestation_state":"computed","paper":{"title":"Graphs that are cospectral for the distance Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boris Brimkov, Carolyn Reinhart, Kate Lorenzen, Ken Duna, Leslie Hogben, Mark Yarrow, Sung-Yell Song","submitted_at":"2018-12-13T23:49:31Z","abstract_excerpt":"The distance matrix $\\mathcal{D}(G)$ of a graph $G$ is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\\mathcal{D}^L(G)=T(G)-\\mathcal{D}(G)$, where $T(G)$ is the diagonal matrix of row sums of $\\mathcal{D}(G)$. We establish several general methods for producing $\\mathcal{D}^L$-cospectral graphs that can be used to construct infinite families. We provide examples showing that various properties are not preserved by $\\mathcal{D}^L$-cospectrality, including examples of $\\mathcal{D}^L$-cospectral strongly regular and circulant graphs. We establi"},"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":"1812.05734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-13T23:49:31Z","cross_cats_sorted":[],"title_canon_sha256":"665db3d9d0171f0be3b86bd07f8c38330cbd9cba40bd6af5d3ef9491c2ba7f7f","abstract_canon_sha256":"060a7e7c70a2f2b458ca07d529448fb613c936c8a8b27770e1770ba962b7f01d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:18.377445Z","signature_b64":"qcL7HNuZfO5HcnjQt46caZsMUXjmGMt7lwIB0Z6tIROCMuqOyW7ulAPGsmf1C6hN3Rz7goK/S9PM4Hh17B17BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be43fa2ca30259fac8254750a04f6c2a20a03c04f69e89b9bc0c8663086739b3","last_reissued_at":"2026-05-17T23:58:18.376821Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:18.376821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs that are cospectral for the distance Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boris Brimkov, Carolyn Reinhart, Kate Lorenzen, Ken Duna, Leslie Hogben, Mark Yarrow, Sung-Yell Song","submitted_at":"2018-12-13T23:49:31Z","abstract_excerpt":"The distance matrix $\\mathcal{D}(G)$ of a graph $G$ is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\\mathcal{D}^L(G)=T(G)-\\mathcal{D}(G)$, where $T(G)$ is the diagonal matrix of row sums of $\\mathcal{D}(G)$. We establish several general methods for producing $\\mathcal{D}^L$-cospectral graphs that can be used to construct infinite families. We provide examples showing that various properties are not preserved by $\\mathcal{D}^L$-cospectrality, including examples of $\\mathcal{D}^L$-cospectral strongly regular and circulant graphs. We establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05734","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":"1812.05734","created_at":"2026-05-17T23:58:18.376900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.05734v1","created_at":"2026-05-17T23:58:18.376900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05734","created_at":"2026-05-17T23:58:18.376900+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZB7ULFDAJM7","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZB7ULFDAJM7VSBF","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZB7ULFD","created_at":"2026-05-18T12:33:04.347982+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/XZB7ULFDAJM7VSBFI5IKAT3MFI","json":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI.json","graph_json":"https://pith.science/api/pith-number/XZB7ULFDAJM7VSBFI5IKAT3MFI/graph.json","events_json":"https://pith.science/api/pith-number/XZB7ULFDAJM7VSBFI5IKAT3MFI/events.json","paper":"https://pith.science/paper/XZB7ULFD"},"agent_actions":{"view_html":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI","download_json":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI.json","view_paper":"https://pith.science/paper/XZB7ULFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.05734&json=true","fetch_graph":"https://pith.science/api/pith-number/XZB7ULFDAJM7VSBFI5IKAT3MFI/graph.json","fetch_events":"https://pith.science/api/pith-number/XZB7ULFDAJM7VSBFI5IKAT3MFI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI/action/storage_attestation","attest_author":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI/action/author_attestation","sign_citation":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI/action/citation_signature","submit_replication":"https://pith.science/pith/XZB7ULFDAJM7VSBFI5IKAT3MFI/action/replication_record"}},"created_at":"2026-05-17T23:58:18.376900+00:00","updated_at":"2026-05-17T23:58:18.376900+00:00"}