{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:77A5XGYTNEE222X5JHMEFXJLTP","short_pith_number":"pith:77A5XGYT","schema_version":"1.0","canonical_sha256":"ffc1db9b136909ad6afd49d842dd2b9bec031152c6eb800e5e407cec699df657","source":{"kind":"arxiv","id":"1101.1428","version":1},"attestation_state":"computed","paper":{"title":"Convergence Rate of the Symmetrically Normalized Graph Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Laurent Jacques","submitted_at":"2011-01-07T13:13:51Z","abstract_excerpt":"This short note aims at (re)proving that the symmetrically normalized graph Laplacian $L=\\Id - D^{-1/2}WD^{-1/2}$ (from a graph defined from a Gaussian weighting kernel on a sampled smooth manifold) converges towards the continuous Manifold Laplacian when the sampling become infinitely dense. The convergence rate with respect to the number of samples $N$ is $O(1/N)$."},"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":"1101.1428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-07T13:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"c998d279f78ead95825f7bfd882b0ed726f7efce90da6e075f679c32ca5a16ac","abstract_canon_sha256":"269c260e6858d1b955afe29c61d50af661a37461424561d92c00fab38091bb41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:52.842110Z","signature_b64":"LxbIi29sDM4h4/cbpK1WbLmgG5RvhMYz/0ZYRfcfEDk5uEJ6vrhKIuyNwp1B+g41Vq8lMfarwrQDO7zmKPrKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc1db9b136909ad6afd49d842dd2b9bec031152c6eb800e5e407cec699df657","last_reissued_at":"2026-05-18T04:31:52.841725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:52.841725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Rate of the Symmetrically Normalized Graph Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Laurent Jacques","submitted_at":"2011-01-07T13:13:51Z","abstract_excerpt":"This short note aims at (re)proving that the symmetrically normalized graph Laplacian $L=\\Id - D^{-1/2}WD^{-1/2}$ (from a graph defined from a Gaussian weighting kernel on a sampled smooth manifold) converges towards the continuous Manifold Laplacian when the sampling become infinitely dense. The convergence rate with respect to the number of samples $N$ is $O(1/N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1428","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.1428","created_at":"2026-05-18T04:31:52.841779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1428v1","created_at":"2026-05-18T04:31:52.841779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1428","created_at":"2026-05-18T04:31:52.841779+00:00"},{"alias_kind":"pith_short_12","alias_value":"77A5XGYTNEE2","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"77A5XGYTNEE222X5","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"77A5XGYT","created_at":"2026-05-18T12:26:22.705136+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/77A5XGYTNEE222X5JHMEFXJLTP","json":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP.json","graph_json":"https://pith.science/api/pith-number/77A5XGYTNEE222X5JHMEFXJLTP/graph.json","events_json":"https://pith.science/api/pith-number/77A5XGYTNEE222X5JHMEFXJLTP/events.json","paper":"https://pith.science/paper/77A5XGYT"},"agent_actions":{"view_html":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP","download_json":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP.json","view_paper":"https://pith.science/paper/77A5XGYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1428&json=true","fetch_graph":"https://pith.science/api/pith-number/77A5XGYTNEE222X5JHMEFXJLTP/graph.json","fetch_events":"https://pith.science/api/pith-number/77A5XGYTNEE222X5JHMEFXJLTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP/action/storage_attestation","attest_author":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP/action/author_attestation","sign_citation":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP/action/citation_signature","submit_replication":"https://pith.science/pith/77A5XGYTNEE222X5JHMEFXJLTP/action/replication_record"}},"created_at":"2026-05-18T04:31:52.841779+00:00","updated_at":"2026-05-18T04:31:52.841779+00:00"}