{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:46XSRU32DMJ6XF66FSH3GTP2XR","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":"d483983d8f270cea4d39f97085c0bc098291a44dca720f52e30b488539495daa","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-17T20:16:41Z","title_canon_sha256":"9d2951bad851fbfe002a5b54e133ae4068a6e39558f30ab4a8f96c198e700002"},"schema_version":"1.0","source":{"id":"1802.06284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06284","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06284v1","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06284","created_at":"2026-05-18T00:08:00Z"},{"alias_kind":"pith_short_12","alias_value":"46XSRU32DMJ6","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"46XSRU32DMJ6XF66","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"46XSRU32","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:0779e8320a0e3f4c52ace42a88ad9b1d7f22bd4feeeb2e892a9299f34839af7e","target":"graph","created_at":"2026-05-18T00:08:00Z","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":"We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of specific similarity measures in data analysis.","authors_text":"Dmytro Rubanov, Konstantin Avrachenkov, Pavel Chebotarev","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-17T20:16:41Z","title":"Similarities on Graphs: Kernels versus Proximity Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06284","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:e03a7ec5d66e66bfdb3dc1ec11896cde729b908aa42c45172f1fa2171341b7ff","target":"record","created_at":"2026-05-18T00:08:00Z","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":"d483983d8f270cea4d39f97085c0bc098291a44dca720f52e30b488539495daa","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-17T20:16:41Z","title_canon_sha256":"9d2951bad851fbfe002a5b54e133ae4068a6e39558f30ab4a8f96c198e700002"},"schema_version":"1.0","source":{"id":"1802.06284","kind":"arxiv","version":1}},"canonical_sha256":"e7af28d37a1b13eb97de2c8fb34dfabc771d95cc370164e42fc6fa9aa16900af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7af28d37a1b13eb97de2c8fb34dfabc771d95cc370164e42fc6fa9aa16900af","first_computed_at":"2026-05-18T00:08:00.558058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:00.558058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G1ybzq0xdR1Y9nX7cJn3EUcygfcHUCCsZrYlqBi+sJhmF27T1MNbvWnlCTueyH5QAFWLPrQotye5n1ZHTKb7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:00.558530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e03a7ec5d66e66bfdb3dc1ec11896cde729b908aa42c45172f1fa2171341b7ff","sha256:0779e8320a0e3f4c52ace42a88ad9b1d7f22bd4feeeb2e892a9299f34839af7e"],"state_sha256":"5726b26845440f21f3ac9747698ad1cdfbfd1b1132ab0e1a8434ad2028e66e01"}