{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GCTONERRY67EQ6NSON5N2WWTK3","short_pith_number":"pith:GCTONERR","schema_version":"1.0","canonical_sha256":"30a6e69231c7be4879b2737add5ad356d8d8de0288c3864119cdb917787bded7","source":{"kind":"arxiv","id":"1710.01295","version":2},"attestation_state":"computed","paper":{"title":"Isotropic covariance functions on graphs and their edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ethan Anderes, Jakob G. Rasmussen, Jesper M{\\o}ller","submitted_at":"2017-10-03T17:53:36Z","abstract_excerpt":"We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory"},"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":"1710.01295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-03T17:53:36Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5b8b649c0d5d5526faee25f832676bd9be19483871dcbcb8265e85a94b17df93","abstract_canon_sha256":"e14f7092b933f589cbbaa756d5b712520ee6bef6c58545cfc33f25984f971cbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:12.812628Z","signature_b64":"I9vDoyvStXNTpz3xoL0U+MibjLW/f8nTpiC5s2YDLv8nT8x6h3iYaJxXTwvlCiQCMKXcTYuZdgv8ysJbG3LSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30a6e69231c7be4879b2737add5ad356d8d8de0288c3864119cdb917787bded7","last_reissued_at":"2026-05-17T23:47:12.812011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:12.812011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isotropic covariance functions on graphs and their edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ethan Anderes, Jakob G. Rasmussen, Jesper M{\\o}ller","submitted_at":"2017-10-03T17:53:36Z","abstract_excerpt":"We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01295","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":"1710.01295","created_at":"2026-05-17T23:47:12.812093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.01295v2","created_at":"2026-05-17T23:47:12.812093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01295","created_at":"2026-05-17T23:47:12.812093+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCTONERRY67E","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCTONERRY67EQ6NS","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCTONERR","created_at":"2026-05-18T12:31:15.632608+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/GCTONERRY67EQ6NSON5N2WWTK3","json":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3.json","graph_json":"https://pith.science/api/pith-number/GCTONERRY67EQ6NSON5N2WWTK3/graph.json","events_json":"https://pith.science/api/pith-number/GCTONERRY67EQ6NSON5N2WWTK3/events.json","paper":"https://pith.science/paper/GCTONERR"},"agent_actions":{"view_html":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3","download_json":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3.json","view_paper":"https://pith.science/paper/GCTONERR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.01295&json=true","fetch_graph":"https://pith.science/api/pith-number/GCTONERRY67EQ6NSON5N2WWTK3/graph.json","fetch_events":"https://pith.science/api/pith-number/GCTONERRY67EQ6NSON5N2WWTK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3/action/storage_attestation","attest_author":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3/action/author_attestation","sign_citation":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3/action/citation_signature","submit_replication":"https://pith.science/pith/GCTONERRY67EQ6NSON5N2WWTK3/action/replication_record"}},"created_at":"2026-05-17T23:47:12.812093+00:00","updated_at":"2026-05-17T23:47:12.812093+00:00"}