{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LRMHLJFW6OK6X3HKUD77FMZ6JB","short_pith_number":"pith:LRMHLJFW","canonical_record":{"source":{"id":"1608.04082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2016-08-14T09:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"17dc06af99c57c495ea1b055faae75116ec5e39ba91396fb247570af93b6e915","abstract_canon_sha256":"c2d9014500dfd345e3ed00dd96c000b2c456b784cb5391ba6439887ba6681695"},"schema_version":"1.0"},"canonical_sha256":"5c5875a4b6f395ebeceaa0fff2b33e4858283d36d932ff66a0a350944da9ecae","source":{"kind":"arxiv","id":"1608.04082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04082","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04082v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04082","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"LRMHLJFW6OK6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRMHLJFW6OK6X3HK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRMHLJFW","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LRMHLJFW6OK6X3HKUD77FMZ6JB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2016-08-14T09:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"17dc06af99c57c495ea1b055faae75116ec5e39ba91396fb247570af93b6e915","abstract_canon_sha256":"c2d9014500dfd345e3ed00dd96c000b2c456b784cb5391ba6439887ba6681695"},"schema_version":"1.0"},"canonical_sha256":"5c5875a4b6f395ebeceaa0fff2b33e4858283d36d932ff66a0a350944da9ecae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:04.317718Z","signature_b64":"1CJ561tSls81xZEtNR4mZMNROTfYePmEBBLN/yNlZjEIHHRnKtQxHGhc5+H7eEAEhWR+jJFMp0PX/HcU6ddZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c5875a4b6f395ebeceaa0fff2b33e4858283d36d932ff66a0a350944da9ecae","last_reissued_at":"2026-05-18T01:09:04.317355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:04.317355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04082","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phXGpNhSaHluhKTtjhuyACos7NBF00CvquG6V+DroCgWurKxU4gx7P4j8pMqZIZEdPlZmJIar+Vj8AoJwIe4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:15:39.928274Z"},"content_sha256":"246caf720cdfbb9cbba509b950fc5628d6a75a5af65fbf84d1196eb4c6440a26","schema_version":"1.0","event_id":"sha256:246caf720cdfbb9cbba509b950fc5628d6a75a5af65fbf84d1196eb4c6440a26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LRMHLJFW6OK6X3HKUD77FMZ6JB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A weighted binary average of point-normal pairs with application to subdivision schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Evgeny Lipovetsky, Nira Dyn","submitted_at":"2016-08-14T09:55:34Z","abstract_excerpt":"Subdivision is a well-known and established method for generating smooth curves and surfaces from discrete data by repeated refinements. The typical input for such a process is a mesh of vertices. In this work we propose to refine 2D data consisting of vertices of a polygon and a normal at each vertex. Our core refinement procedure is based on a circle average, which is a new non-linear weighted average of two points and their corresponding normals. The ability to locally approximate curves by the circle average is demonstrated. With this ability, the circle average is a candidate for modifyin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04082","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWM+Qkg3dnbbC/EcRu7P5UFiOuTv9AF5GEaIVGYrZBDHVPZ4PoOkSw0kDTb38ZN/GgIznCxrnbhHmXYPp1ifDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:15:39.928646Z"},"content_sha256":"21fd57fdd8978eb1b7f37ee4798f63032f1dd896da94df2b10ed72f716d245e2","schema_version":"1.0","event_id":"sha256:21fd57fdd8978eb1b7f37ee4798f63032f1dd896da94df2b10ed72f716d245e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/bundle.json","state_url":"https://pith.science/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T03:15:39Z","links":{"resolver":"https://pith.science/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB","bundle":"https://pith.science/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/bundle.json","state":"https://pith.science/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRMHLJFW6OK6X3HKUD77FMZ6JB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LRMHLJFW6OK6X3HKUD77FMZ6JB","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":"c2d9014500dfd345e3ed00dd96c000b2c456b784cb5391ba6439887ba6681695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2016-08-14T09:55:34Z","title_canon_sha256":"17dc06af99c57c495ea1b055faae75116ec5e39ba91396fb247570af93b6e915"},"schema_version":"1.0","source":{"id":"1608.04082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04082","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04082v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04082","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"LRMHLJFW6OK6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRMHLJFW6OK6X3HK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRMHLJFW","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:21fd57fdd8978eb1b7f37ee4798f63032f1dd896da94df2b10ed72f716d245e2","target":"graph","created_at":"2026-05-18T01:09:04Z","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":"Subdivision is a well-known and established method for generating smooth curves and surfaces from discrete data by repeated refinements. The typical input for such a process is a mesh of vertices. In this work we propose to refine 2D data consisting of vertices of a polygon and a normal at each vertex. Our core refinement procedure is based on a circle average, which is a new non-linear weighted average of two points and their corresponding normals. The ability to locally approximate curves by the circle average is demonstrated. With this ability, the circle average is a candidate for modifyin","authors_text":"Evgeny Lipovetsky, Nira Dyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2016-08-14T09:55:34Z","title":"A weighted binary average of point-normal pairs with application to subdivision schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04082","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":"sha256:246caf720cdfbb9cbba509b950fc5628d6a75a5af65fbf84d1196eb4c6440a26","target":"record","created_at":"2026-05-18T01:09:04Z","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":"c2d9014500dfd345e3ed00dd96c000b2c456b784cb5391ba6439887ba6681695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2016-08-14T09:55:34Z","title_canon_sha256":"17dc06af99c57c495ea1b055faae75116ec5e39ba91396fb247570af93b6e915"},"schema_version":"1.0","source":{"id":"1608.04082","kind":"arxiv","version":1}},"canonical_sha256":"5c5875a4b6f395ebeceaa0fff2b33e4858283d36d932ff66a0a350944da9ecae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c5875a4b6f395ebeceaa0fff2b33e4858283d36d932ff66a0a350944da9ecae","first_computed_at":"2026-05-18T01:09:04.317355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:04.317355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1CJ561tSls81xZEtNR4mZMNROTfYePmEBBLN/yNlZjEIHHRnKtQxHGhc5+H7eEAEhWR+jJFMp0PX/HcU6ddZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:04.317718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:246caf720cdfbb9cbba509b950fc5628d6a75a5af65fbf84d1196eb4c6440a26","sha256:21fd57fdd8978eb1b7f37ee4798f63032f1dd896da94df2b10ed72f716d245e2"],"state_sha256":"ef3bcddff61b3e53b68cb38c91931b7319c8b50ace0f4e23a20ff7f3b81d8765"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHWTR7gSFFiTgbP3LeWZ2AKdjmV7JOoA/CCfWiamTSf27e7xG2iHAU5Pun+VCKIvDw5A5RCJOQsMXthlLndQCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T03:15:39.930606Z","bundle_sha256":"b71f78e5ed05a3d771661f58c1cd2ac40a798f81f473582153fda9e88082be2e"}}