{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3D4P6FBD7SG4KS26GHX2KMVVOU","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":"b24b48e1821b3012423075da15fdc0cc4f8e488af771db04f4478b026fd4ac5b","cross_cats_sorted":["cs.LG","physics.data-an","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2025-01-26T05:02:54Z","title_canon_sha256":"76d222da45cefd69740952d5040ff5db7f1f1eb307abfd2460da02f11e48f98e"},"schema_version":"1.0","source":{"id":"2502.00038","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00038","created_at":"2026-07-05T11:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00038v3","created_at":"2026-07-05T11:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00038","created_at":"2026-07-05T11:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"3D4P6FBD7SG4","created_at":"2026-07-05T11:56:17Z"},{"alias_kind":"pith_short_16","alias_value":"3D4P6FBD7SG4KS26","created_at":"2026-07-05T11:56:17Z"},{"alias_kind":"pith_short_8","alias_value":"3D4P6FBD","created_at":"2026-07-05T11:56:17Z"}],"graph_snapshots":[{"event_id":"sha256:97c360876efd8e2af449ae0a2caf426701bc9445e01635afd51d5df633038f85","target":"graph","created_at":"2026-07-05T11:56:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.00038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The notion of barycentre graph is of crucial importance for machine learning algorithms that process graph-valued data. The barycentre graph is a \"summary graph\" that captures the mean topology and connectivity structure of a training dataset of graphs. The construction of a barycentre requires the definition of a metric to quantify distances between pairs of graphs. In this work, we use a multiscale spectral distance that is defined using the eigenvalues of the normalized graph Laplacian. The eigenvalues -- but not the eigenvectors -- of the normalized Laplacian of the barycentre graph can be","authors_text":"Fran\\c{c}ois G. Meyer","cross_cats":["cs.LG","physics.data-an","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2025-01-26T05:02:54Z","title":"The Spectral Barycentre of a Set of Graphs with Community Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00038","kind":"arxiv","version":3},"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":"sha256:2df77c9e766adca62379c244a01340db58f882efd45065b7da3cb45e8616ea2d","target":"record","created_at":"2026-07-05T11:56:17Z","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":"b24b48e1821b3012423075da15fdc0cc4f8e488af771db04f4478b026fd4ac5b","cross_cats_sorted":["cs.LG","physics.data-an","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2025-01-26T05:02:54Z","title_canon_sha256":"76d222da45cefd69740952d5040ff5db7f1f1eb307abfd2460da02f11e48f98e"},"schema_version":"1.0","source":{"id":"2502.00038","kind":"arxiv","version":3}},"canonical_sha256":"d8f8ff1423fc8dc54b5e31efa532b575331b542f04b168703451c503d741e5f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8f8ff1423fc8dc54b5e31efa532b575331b542f04b168703451c503d741e5f8","first_computed_at":"2026-07-05T11:56:17.340969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:17.340969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VxTAYl1yx81dO9DQWs08VcVWrtZXZrE/sVCEusqxM9bpx11ubRXjM5VlJ9vt9++qt4Q8xpQtrY1SBlAZBwWiBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:17.341440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.00038","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2df77c9e766adca62379c244a01340db58f882efd45065b7da3cb45e8616ea2d","sha256:97c360876efd8e2af449ae0a2caf426701bc9445e01635afd51d5df633038f85"],"state_sha256":"3c191e81fb2c9feb6bb8ef1f0852311994b8a194818ac4a8585e80d2bc7bb449"}