{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BKXUH754PSS7JWDY3LG3YS3LF3","short_pith_number":"pith:BKXUH754","schema_version":"1.0","canonical_sha256":"0aaf43ffbc7ca5f4d878dacdbc4b6b2ee2fc431182d799b8546badf53006e40e","source":{"kind":"arxiv","id":"2606.10480","version":1},"attestation_state":"computed","paper":{"title":"Spectral and computational aspects of a regularized fractional Laplacian for non-local diffusion on graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alessandro Filippo, Mariarosa Mazza","submitted_at":"2026-06-09T06:50:25Z","abstract_excerpt":"The fractional Laplacian has been widely used to model non-local diffusion on graphs, allowing interactions that extend beyond immediate neighbors. However, it suffers from a structural inconsistency as it breaks compatibility with the topology of the original network. To address this issue, a combination of the standard and fractional Laplacians aimed at restoring compatibility while retaining the spectral richness of the fractional operator was recently proposed.\n  In this work, we provide a thorough analysis of the diffusion properties of the resulting regularized operator. We prove that it"},"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":"2606.10480","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-09T06:50:25Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a2cb17fffac643d8c595118177cd0bccb3018f0e19a312125a24f2734b499afb","abstract_canon_sha256":"5ec6cfd3b36751a3605be21b04f6831750f0f365cb77c5997f08e2d0a2a9ff45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:21.444262Z","signature_b64":"26gWqu1+fwAWODzxHc36weEsxKO01XyAwsPWcwrQDShYGb6pjV9SdQdwzYeP6Hj1N9to01sGHYEvXE/zsKJgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aaf43ffbc7ca5f4d878dacdbc4b6b2ee2fc431182d799b8546badf53006e40e","last_reissued_at":"2026-06-10T01:10:21.443289Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:21.443289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral and computational aspects of a regularized fractional Laplacian for non-local diffusion on graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alessandro Filippo, Mariarosa Mazza","submitted_at":"2026-06-09T06:50:25Z","abstract_excerpt":"The fractional Laplacian has been widely used to model non-local diffusion on graphs, allowing interactions that extend beyond immediate neighbors. However, it suffers from a structural inconsistency as it breaks compatibility with the topology of the original network. To address this issue, a combination of the standard and fractional Laplacians aimed at restoring compatibility while retaining the spectral richness of the fractional operator was recently proposed.\n  In this work, we provide a thorough analysis of the diffusion properties of the resulting regularized operator. We prove that it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10480","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10480/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.10480","created_at":"2026-06-10T01:10:21.443491+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10480v1","created_at":"2026-06-10T01:10:21.443491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10480","created_at":"2026-06-10T01:10:21.443491+00:00"},{"alias_kind":"pith_short_12","alias_value":"BKXUH754PSS7","created_at":"2026-06-10T01:10:21.443491+00:00"},{"alias_kind":"pith_short_16","alias_value":"BKXUH754PSS7JWDY","created_at":"2026-06-10T01:10:21.443491+00:00"},{"alias_kind":"pith_short_8","alias_value":"BKXUH754","created_at":"2026-06-10T01:10:21.443491+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/BKXUH754PSS7JWDY3LG3YS3LF3","json":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3.json","graph_json":"https://pith.science/api/pith-number/BKXUH754PSS7JWDY3LG3YS3LF3/graph.json","events_json":"https://pith.science/api/pith-number/BKXUH754PSS7JWDY3LG3YS3LF3/events.json","paper":"https://pith.science/paper/BKXUH754"},"agent_actions":{"view_html":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3","download_json":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3.json","view_paper":"https://pith.science/paper/BKXUH754","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10480&json=true","fetch_graph":"https://pith.science/api/pith-number/BKXUH754PSS7JWDY3LG3YS3LF3/graph.json","fetch_events":"https://pith.science/api/pith-number/BKXUH754PSS7JWDY3LG3YS3LF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3/action/storage_attestation","attest_author":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3/action/author_attestation","sign_citation":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3/action/citation_signature","submit_replication":"https://pith.science/pith/BKXUH754PSS7JWDY3LG3YS3LF3/action/replication_record"}},"created_at":"2026-06-10T01:10:21.443491+00:00","updated_at":"2026-06-10T01:10:21.443491+00:00"}