{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6ITB3POWFD26EBXVNV3VVF7GPP","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":"91a132f00d00a3c1069823b81ab9c4bcc9e44d0b9d54b18d106443bd424ada7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-15T03:36:17Z","title_canon_sha256":"61b90f4c3cc492a59979d4b43df5fa678355b75b966399775e583fcba6b2e3ae"},"schema_version":"1.0","source":{"id":"1611.04690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04690","created_at":"2026-05-18T00:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04690v1","created_at":"2026-05-18T00:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04690","created_at":"2026-05-18T00:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"6ITB3POWFD26","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6ITB3POWFD26EBXV","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6ITB3POW","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:324445bbcec6ba93f39c4dec236d112861a61a512c0d1f7d112560eb7baf0f35","target":"graph","created_at":"2026-05-18T00:58:50Z","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"},"paper":{"abstract_excerpt":"The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization, Numerical Analysis, and Monte Carlo Methods. Entering point cloud into Google returns nearly 3.5 million results! A point cloud for a finite volume manifold M is a finite subset or a sequence in M, with the essential feature that it is a representative sample of M. The definition of a point cloud varies with its use, particularly what constitutes being repr","authors_text":"Bob Palais, Hermann Karcher, Richard Palais","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-15T03:36:17Z","title":"PointClouds: Distributing Points Uniformly on a Surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04690","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":"sha256:7b0643a8159809507f27323c0e187e84d454b9e0ed60a9f93d96c070aea6c1ee","target":"record","created_at":"2026-05-18T00:58:50Z","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":"91a132f00d00a3c1069823b81ab9c4bcc9e44d0b9d54b18d106443bd424ada7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-15T03:36:17Z","title_canon_sha256":"61b90f4c3cc492a59979d4b43df5fa678355b75b966399775e583fcba6b2e3ae"},"schema_version":"1.0","source":{"id":"1611.04690","kind":"arxiv","version":1}},"canonical_sha256":"f2261dbdd628f5e206f56d775a97e67be8a8e0ae203acdefee17f6edb2f1b9e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2261dbdd628f5e206f56d775a97e67be8a8e0ae203acdefee17f6edb2f1b9e7","first_computed_at":"2026-05-18T00:58:50.165672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:50.165672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uog2uI3zhFccVcEB2Tyu0KGhkdYfF79KfniWpL/iq6w85PNDMoFPGRS3A84hSGBuLU6v+MnjvqvcDd+mk5hoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:50.166361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b0643a8159809507f27323c0e187e84d454b9e0ed60a9f93d96c070aea6c1ee","sha256:324445bbcec6ba93f39c4dec236d112861a61a512c0d1f7d112560eb7baf0f35"],"state_sha256":"361d9f284739413580c4bdfb8ef61ed858a93160ef3e599a467a92f20754d0f8"}