{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YM3SQPP7P3JCB7BQUHWTHHM2XA","short_pith_number":"pith:YM3SQPP7","canonical_record":{"source":{"id":"1812.05457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-13T14:39:35Z","cross_cats_sorted":["nlin.AO","physics.data-an"],"title_canon_sha256":"0608ef897de6609820f729914da469a474455be79486a8ad5f590b77b0879a59","abstract_canon_sha256":"e0338efb22ae4987ccbe42cd260ed1b888157fd5660f910904f054dcf3b09019"},"schema_version":"1.0"},"canonical_sha256":"c337283dff7ed220fc30a1ed339d9ab827a62af8ee31e2b23c0d06585d9ba3ea","source":{"kind":"arxiv","id":"1812.05457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05457","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05457v1","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05457","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"YM3SQPP7P3JC","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YM3SQPP7P3JCB7BQ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YM3SQPP7","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YM3SQPP7P3JCB7BQUHWTHHM2XA","target":"record","payload":{"canonical_record":{"source":{"id":"1812.05457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-13T14:39:35Z","cross_cats_sorted":["nlin.AO","physics.data-an"],"title_canon_sha256":"0608ef897de6609820f729914da469a474455be79486a8ad5f590b77b0879a59","abstract_canon_sha256":"e0338efb22ae4987ccbe42cd260ed1b888157fd5660f910904f054dcf3b09019"},"schema_version":"1.0"},"canonical_sha256":"c337283dff7ed220fc30a1ed339d9ab827a62af8ee31e2b23c0d06585d9ba3ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:58.150832Z","signature_b64":"ihZ4IYlQ/GYiuf/uXeuLbQL+lyHkdbJhFSczim7nnqnqMrGVJT6FrvcpNrr8WhOlGYuYO4zEPhPwxv4NVVbCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c337283dff7ed220fc30a1ed339d9ab827a62af8ee31e2b23c0d06585d9ba3ea","last_reissued_at":"2026-05-17T23:44:58.150190Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:58.150190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.05457","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/E1X3rDHhd7paH8SNXUTIQ9pGA+IQ1Lkem20l4080JuOCg3ApW1V/rOKf9AByiogilUEtk5bgZZSYGBL3VtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:45:17.641866Z"},"content_sha256":"9cdc68d23dabfd47406b68e8c1adabebd856ab09808343773f0b56dc5a88cf93","schema_version":"1.0","event_id":"sha256:9cdc68d23dabfd47406b68e8c1adabebd856ab09808343773f0b56dc5a88cf93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YM3SQPP7P3JCB7BQUHWTHHM2XA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Comparison via the Non-backtracking Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","physics.data-an"],"primary_cat":"cs.SI","authors_text":"Andrew Mellor, Angelica Grusovin","submitted_at":"2018-12-13T14:39:35Z","abstract_excerpt":"The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however often these are not metrics (rendering standard data-mining techniques infeasible), or are computationally infeasible for large graphs. In this work we define a new metric based on the spectrum of the non-backtracking graph operator and show that it can not only be used to compare graphs generated through different mechanisms, but can reliably compare graphs of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05457","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTTydRDgFhUwFb7qmyqAYlaOO2Qx+nVOasWDy/gKrnTxoqvwrKhUymKlVmTjxj7wYa8JKnQWHzBjx+c1aPH2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:45:17.642505Z"},"content_sha256":"113ddbe5559854f063ab40c425774a552b307f7b930cb0292bb8b69a04ab38f0","schema_version":"1.0","event_id":"sha256:113ddbe5559854f063ab40c425774a552b307f7b930cb0292bb8b69a04ab38f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/bundle.json","state_url":"https://pith.science/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T11:45:17Z","links":{"resolver":"https://pith.science/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA","bundle":"https://pith.science/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/bundle.json","state":"https://pith.science/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YM3SQPP7P3JCB7BQUHWTHHM2XA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YM3SQPP7P3JCB7BQUHWTHHM2XA","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":"e0338efb22ae4987ccbe42cd260ed1b888157fd5660f910904f054dcf3b09019","cross_cats_sorted":["nlin.AO","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-13T14:39:35Z","title_canon_sha256":"0608ef897de6609820f729914da469a474455be79486a8ad5f590b77b0879a59"},"schema_version":"1.0","source":{"id":"1812.05457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05457","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05457v1","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05457","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"YM3SQPP7P3JC","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YM3SQPP7P3JCB7BQ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YM3SQPP7","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:113ddbe5559854f063ab40c425774a552b307f7b930cb0292bb8b69a04ab38f0","target":"graph","created_at":"2026-05-17T23:44:58Z","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":"The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however often these are not metrics (rendering standard data-mining techniques infeasible), or are computationally infeasible for large graphs. In this work we define a new metric based on the spectrum of the non-backtracking graph operator and show that it can not only be used to compare graphs generated through different mechanisms, but can reliably compare graphs of","authors_text":"Andrew Mellor, Angelica Grusovin","cross_cats":["nlin.AO","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-13T14:39:35Z","title":"Graph Comparison via the Non-backtracking Spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05457","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":"sha256:9cdc68d23dabfd47406b68e8c1adabebd856ab09808343773f0b56dc5a88cf93","target":"record","created_at":"2026-05-17T23:44:58Z","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":"e0338efb22ae4987ccbe42cd260ed1b888157fd5660f910904f054dcf3b09019","cross_cats_sorted":["nlin.AO","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-13T14:39:35Z","title_canon_sha256":"0608ef897de6609820f729914da469a474455be79486a8ad5f590b77b0879a59"},"schema_version":"1.0","source":{"id":"1812.05457","kind":"arxiv","version":1}},"canonical_sha256":"c337283dff7ed220fc30a1ed339d9ab827a62af8ee31e2b23c0d06585d9ba3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c337283dff7ed220fc30a1ed339d9ab827a62af8ee31e2b23c0d06585d9ba3ea","first_computed_at":"2026-05-17T23:44:58.150190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:58.150190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihZ4IYlQ/GYiuf/uXeuLbQL+lyHkdbJhFSczim7nnqnqMrGVJT6FrvcpNrr8WhOlGYuYO4zEPhPwxv4NVVbCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:58.150832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cdc68d23dabfd47406b68e8c1adabebd856ab09808343773f0b56dc5a88cf93","sha256:113ddbe5559854f063ab40c425774a552b307f7b930cb0292bb8b69a04ab38f0"],"state_sha256":"50a34d4d252af6efbca10deca21578508ae937b20404829ba43e4710b8ad4dba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lBmsN1d7h62S/uEkHvIOGGQm2VgeHl0nf+GtgiUdTnsygiYyt5hlJv6kdE6bT3c/fDSGq8nAfPP1isz+DCLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:45:17.645297Z","bundle_sha256":"e1872f0fcf66ecdf62041432bef79da890c3321ef8e4baec944275079798186a"}}