{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:O5YTJ677MXF5XT7KUOQZK7ZHYK","short_pith_number":"pith:O5YTJ677","canonical_record":{"source":{"id":"2406.08647","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GR","submitted_at":"2024-06-12T21:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"397a1bf0846e5816b916b4d8b7f6bf976a56c0ec0335bc76b5ae3e3ebe62c05e","abstract_canon_sha256":"3edd9625e1a5f7efcd2ec6335fe3d1b21e0b52f985f57774f68efb930d086da1"},"schema_version":"1.0"},"canonical_sha256":"777134fbff65cbdbcfeaa3a1957f27c2b64d25e1cbcd39d5702067435b78732c","source":{"kind":"arxiv","id":"2406.08647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.08647","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.08647v1","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.08647","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"O5YTJ677MXF5","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_16","alias_value":"O5YTJ677MXF5XT7K","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_8","alias_value":"O5YTJ677","created_at":"2026-07-05T08:31:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:O5YTJ677MXF5XT7KUOQZK7ZHYK","target":"record","payload":{"canonical_record":{"source":{"id":"2406.08647","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GR","submitted_at":"2024-06-12T21:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"397a1bf0846e5816b916b4d8b7f6bf976a56c0ec0335bc76b5ae3e3ebe62c05e","abstract_canon_sha256":"3edd9625e1a5f7efcd2ec6335fe3d1b21e0b52f985f57774f68efb930d086da1"},"schema_version":"1.0"},"canonical_sha256":"777134fbff65cbdbcfeaa3a1957f27c2b64d25e1cbcd39d5702067435b78732c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:31:20.765822Z","signature_b64":"KZt3ZJoxyMwasfm7OobfkH/oVIgCdCr0QmnBcD1cCms4Tw3JWKj8CXBZx5+KMAyED6iFtST2KA2QNrrO0+eOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"777134fbff65cbdbcfeaa3a1957f27c2b64d25e1cbcd39d5702067435b78732c","last_reissued_at":"2026-07-05T08:31:20.765293Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:31:20.765293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.08647","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":"2026-07-05T08:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dvS6cL2yL4TA0SWXQ3a665SgvxOLmAnYYadHE85I8jjCASlMvWDrzSbKYgxITJ38FkOjHZDyKSpQbwr/IA9YCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:13:33.946044Z"},"content_sha256":"450ca989eae8c5955f955c1ddf6796145a8fdfa59d21f22e4702790faae61e35","schema_version":"1.0","event_id":"sha256:450ca989eae8c5955f955c1ddf6796145a8fdfa59d21f22e4702790faae61e35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:O5YTJ677MXF5XT7KUOQZK7ZHYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimized Dual-Volumes for Tetrahedral Meshes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Alec Jacobson","submitted_at":"2024-06-12T21:13:52Z","abstract_excerpt":"Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \\emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite-volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi-definiteness of the implied Dirichlet energy, positivity of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.08647","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.08647/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USWSvVxIne4qpIUjmQXLLpVrKKLwBj0cWl0JqB122XNgUMg0P1+EBshlzCAjjRsTLZ7E08eb5X72+AkL4Ft1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:13:33.946596Z"},"content_sha256":"9b2796732a2d905232fa60a0883e1f98007a0ee069a778b684ae589c762df364","schema_version":"1.0","event_id":"sha256:9b2796732a2d905232fa60a0883e1f98007a0ee069a778b684ae589c762df364"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/bundle.json","state_url":"https://pith.science/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/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":"2026-08-15T08:13:33Z","links":{"resolver":"https://pith.science/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK","bundle":"https://pith.science/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/bundle.json","state":"https://pith.science/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5YTJ677MXF5XT7KUOQZK7ZHYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:O5YTJ677MXF5XT7KUOQZK7ZHYK","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":"3edd9625e1a5f7efcd2ec6335fe3d1b21e0b52f985f57774f68efb930d086da1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GR","submitted_at":"2024-06-12T21:13:52Z","title_canon_sha256":"397a1bf0846e5816b916b4d8b7f6bf976a56c0ec0335bc76b5ae3e3ebe62c05e"},"schema_version":"1.0","source":{"id":"2406.08647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.08647","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"2406.08647v1","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.08647","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"O5YTJ677MXF5","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_16","alias_value":"O5YTJ677MXF5XT7K","created_at":"2026-07-05T08:31:20Z"},{"alias_kind":"pith_short_8","alias_value":"O5YTJ677","created_at":"2026-07-05T08:31:20Z"}],"graph_snapshots":[{"event_id":"sha256:9b2796732a2d905232fa60a0883e1f98007a0ee069a778b684ae589c762df364","target":"graph","created_at":"2026-07-05T08:31:20Z","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/2406.08647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \\emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite-volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi-definiteness of the implied Dirichlet energy, positivity of t","authors_text":"Alec Jacobson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GR","submitted_at":"2024-06-12T21:13:52Z","title":"Optimized Dual-Volumes for Tetrahedral Meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.08647","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":"sha256:450ca989eae8c5955f955c1ddf6796145a8fdfa59d21f22e4702790faae61e35","target":"record","created_at":"2026-07-05T08:31:20Z","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":"3edd9625e1a5f7efcd2ec6335fe3d1b21e0b52f985f57774f68efb930d086da1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GR","submitted_at":"2024-06-12T21:13:52Z","title_canon_sha256":"397a1bf0846e5816b916b4d8b7f6bf976a56c0ec0335bc76b5ae3e3ebe62c05e"},"schema_version":"1.0","source":{"id":"2406.08647","kind":"arxiv","version":1}},"canonical_sha256":"777134fbff65cbdbcfeaa3a1957f27c2b64d25e1cbcd39d5702067435b78732c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"777134fbff65cbdbcfeaa3a1957f27c2b64d25e1cbcd39d5702067435b78732c","first_computed_at":"2026-07-05T08:31:20.765293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:31:20.765293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZt3ZJoxyMwasfm7OobfkH/oVIgCdCr0QmnBcD1cCms4Tw3JWKj8CXBZx5+KMAyED6iFtST2KA2QNrrO0+eOAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:31:20.765822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.08647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:450ca989eae8c5955f955c1ddf6796145a8fdfa59d21f22e4702790faae61e35","sha256:9b2796732a2d905232fa60a0883e1f98007a0ee069a778b684ae589c762df364"],"state_sha256":"560fe6bdc4536ed87bf5f970a62b5438d92c57f30ccc163ed8d841bb97737b5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsP2pC17Hl2MiR1BOOz5O278YHxB5ELXHaVVB/+7RnrZc1Zach0npijDaCgSwoTCogQBaAiTi0Ox9kul7N9yCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:13:33.951524Z","bundle_sha256":"3292163c640642178267cfa73dcd89bfb3effe55985c712d47af1a46c75be028"}}