{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:72V4BBNC44WEUP7YOEF5NIV2D7","short_pith_number":"pith:72V4BBNC","schema_version":"1.0","canonical_sha256":"feabc085a2e72c4a3ff8710bd6a2ba1fe8269ebd0b3611305a1f1e7d9b833e04","source":{"kind":"arxiv","id":"2507.06161","version":2},"attestation_state":"computed","paper":{"title":"Sinkhorn Normalization of Diffusion Kernels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Jean Feydy, Nathan Kessler, Robin Magnet","submitted_at":"2025-07-08T16:42:09Z","abstract_excerpt":"Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available. Most practitioners thus rely on simple convolution kernels and message-passing layers, which are biased against the boundaries of the domain. We bridge t"},"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":"2507.06161","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2025-07-08T16:42:09Z","cross_cats_sorted":[],"title_canon_sha256":"d0519e65acefd94b8d5585c5b1982f214cf978c2de7c337a93d8a052b40a60b2","abstract_canon_sha256":"2970b4c4aacc9ea15ed5473135dcb6291060d58ce42853b99f7031fb5bfd21ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:17.409705Z","signature_b64":"R0O5zTtH3Gwf6dAc6fICWq+xpXuFTPNIeRu0F1Y8uYRa8p6b1tg8dSAHQkAFgOF6fV3txaX2VeLK4/aHXcKvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feabc085a2e72c4a3ff8710bd6a2ba1fe8269ebd0b3611305a1f1e7d9b833e04","last_reissued_at":"2026-06-01T01:02:17.408612Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:17.408612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sinkhorn Normalization of Diffusion Kernels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Jean Feydy, Nathan Kessler, Robin Magnet","submitted_at":"2025-07-08T16:42:09Z","abstract_excerpt":"Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available. Most practitioners thus rely on simple convolution kernels and message-passing layers, which are biased against the boundaries of the domain. We bridge t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06161","kind":"arxiv","version":2},"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/2507.06161/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":"2507.06161","created_at":"2026-06-01T01:02:17.408745+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.06161v2","created_at":"2026-06-01T01:02:17.408745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06161","created_at":"2026-06-01T01:02:17.408745+00:00"},{"alias_kind":"pith_short_12","alias_value":"72V4BBNC44WE","created_at":"2026-06-01T01:02:17.408745+00:00"},{"alias_kind":"pith_short_16","alias_value":"72V4BBNC44WEUP7Y","created_at":"2026-06-01T01:02:17.408745+00:00"},{"alias_kind":"pith_short_8","alias_value":"72V4BBNC","created_at":"2026-06-01T01:02:17.408745+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/72V4BBNC44WEUP7YOEF5NIV2D7","json":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7.json","graph_json":"https://pith.science/api/pith-number/72V4BBNC44WEUP7YOEF5NIV2D7/graph.json","events_json":"https://pith.science/api/pith-number/72V4BBNC44WEUP7YOEF5NIV2D7/events.json","paper":"https://pith.science/paper/72V4BBNC"},"agent_actions":{"view_html":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7","download_json":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7.json","view_paper":"https://pith.science/paper/72V4BBNC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.06161&json=true","fetch_graph":"https://pith.science/api/pith-number/72V4BBNC44WEUP7YOEF5NIV2D7/graph.json","fetch_events":"https://pith.science/api/pith-number/72V4BBNC44WEUP7YOEF5NIV2D7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7/action/storage_attestation","attest_author":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7/action/author_attestation","sign_citation":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7/action/citation_signature","submit_replication":"https://pith.science/pith/72V4BBNC44WEUP7YOEF5NIV2D7/action/replication_record"}},"created_at":"2026-06-01T01:02:17.408745+00:00","updated_at":"2026-06-01T01:02:17.408745+00:00"}