{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TEULVO6I4SZ4C2YMKJ3WDUS7B6","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":"33db6831bc0bb97546a02a072248dae4f7e6111ccddb22c60c69c1df6a81db57","cross_cats_sorted":["cs.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-09-10T13:40:34Z","title_canon_sha256":"8424b018a41dab7994324b4487d21f8a49320cac425766a0859eed8f15504de5"},"schema_version":"1.0","source":{"id":"2409.06506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.06506","created_at":"2026-07-05T09:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2409.06506v1","created_at":"2026-07-05T09:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.06506","created_at":"2026-07-05T09:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"TEULVO6I4SZ4","created_at":"2026-07-05T09:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"TEULVO6I4SZ4C2YM","created_at":"2026-07-05T09:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"TEULVO6I","created_at":"2026-07-05T09:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:ab8ded1b3dd3b50fd2140d1d08d19f3518f6ee0563c2f5af54f8531df6f3f344","target":"graph","created_at":"2026-07-05T09:05:25Z","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/2409.06506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The discrete Laplacian operator holds a crucial role in 3D geometry processing, yet it is still challenging to define it on point clouds. Previous works mainly focused on constructing a local triangulation around each point to approximate the underlying manifold for defining the Laplacian operator, which may not be robust or accurate. In contrast, we simply use the K-nearest neighbors (KNN) graph constructed from the input point cloud and learn the Laplacian operator on the KNN graph with graph neural networks (GNNs). However, the ground-truth Laplacian operator is defined on a manifold mesh w","authors_text":"Bo Pang, Guoping Wang, Peng-Shuai Wang, Yilong Li, Zhongtian Zheng","cross_cats":["cs.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-09-10T13:40:34Z","title":"Neural Laplacian Operator for 3D Point Clouds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.06506","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":"sha256:3b987dc6c7292ddf0902d5e1937ffc834e8fe919802077b6ccb67bb382c45be1","target":"record","created_at":"2026-07-05T09:05:25Z","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":"33db6831bc0bb97546a02a072248dae4f7e6111ccddb22c60c69c1df6a81db57","cross_cats_sorted":["cs.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-09-10T13:40:34Z","title_canon_sha256":"8424b018a41dab7994324b4487d21f8a49320cac425766a0859eed8f15504de5"},"schema_version":"1.0","source":{"id":"2409.06506","kind":"arxiv","version":1}},"canonical_sha256":"9928babbc8e4b3c16b0c527761d25f0f933b0be4ebd281a7428662ad38031148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9928babbc8e4b3c16b0c527761d25f0f933b0be4ebd281a7428662ad38031148","first_computed_at":"2026-07-05T09:05:25.574544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:25.574544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lgvZoKM2OnVGrsCQ33B0TsrZxRRj6JUtjTKy2c/al98j3+xBjvpnXPzFVjrU5Tlkro6FR4RQZ2IvzWtLiVrbCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:25.575005Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.06506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b987dc6c7292ddf0902d5e1937ffc834e8fe919802077b6ccb67bb382c45be1","sha256:ab8ded1b3dd3b50fd2140d1d08d19f3518f6ee0563c2f5af54f8531df6f3f344"],"state_sha256":"5c1d62691bc60d8120a10dd3b441db438eabad2c2222e5ebe56f9142175d27b5"}