{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KDDUARKJNEEAMPCRKKLC4QYTAE","short_pith_number":"pith:KDDUARKJ","canonical_record":{"source":{"id":"1908.06779","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-19T13:13:03Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"a2fdee7ac152f52a17d95e152cae3560a1abda7ba4057949e15e693f1518e99b","abstract_canon_sha256":"80cc766e9a59509450ec1cad09736c44873da9414c6914a1b0bc7b670f53900f"},"schema_version":"1.0"},"canonical_sha256":"50c74045496908063c5152962e4313012451c4e5adf2f3aeda94fc29f0c60a28","source":{"kind":"arxiv","id":"1908.06779","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06779","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06779v2","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06779","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"KDDUARKJNEEA","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_16","alias_value":"KDDUARKJNEEAMPCR","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_8","alias_value":"KDDUARKJ","created_at":"2026-07-05T01:11:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KDDUARKJNEEAMPCRKKLC4QYTAE","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06779","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-19T13:13:03Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"a2fdee7ac152f52a17d95e152cae3560a1abda7ba4057949e15e693f1518e99b","abstract_canon_sha256":"80cc766e9a59509450ec1cad09736c44873da9414c6914a1b0bc7b670f53900f"},"schema_version":"1.0"},"canonical_sha256":"50c74045496908063c5152962e4313012451c4e5adf2f3aeda94fc29f0c60a28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:11:41.325002Z","signature_b64":"R8n+9HRf+IRga9EMgs7PZU25qd6279/fEb4q9j2J1GJ44TiCfGLA3jsD/R5w2iVSDE84fIxnhwpJ1k2klDNEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50c74045496908063c5152962e4313012451c4e5adf2f3aeda94fc29f0c60a28","last_reissued_at":"2026-07-05T01:11:41.324438Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:11:41.324438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06779","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLLR6ODRGlwB6T2rYtTeqlzMGqR/PAH4Y2qTRsUq/0ss4jyEYKrOc2TxO4zFVq0kL//ZsxcRM9QIFV+0tM5ADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:32:51.705003Z"},"content_sha256":"4906835eebbe9c726f15b8c37a9119d94d983a662085a8720d36c35d6a2a2987","schema_version":"1.0","event_id":"sha256:4906835eebbe9c726f15b8c37a9119d94d983a662085a8720d36c35d6a2a2987"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KDDUARKJNEEAMPCRKKLC4QYTAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Weighted Mean Curvature Derivative of a Space-Filling Diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"cs.CG","authors_text":"Arseniy Akopyan, Herbert Edelsbrunner","submitted_at":"2019-08-19T13:13:03Z","abstract_excerpt":"Representing an atom by a solid sphere in $3$-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [HRC13,RHK06] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [EdKo03], the weighted area"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06779","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/1908.06779/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":"2026-07-05T01:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1p18FmPn8hGFWyNukevX+Ta4Cv/wSN/9Jk3EEGHXXSdXDeu0dfHaFNus3g1lwaCgE1HuTmsN0Gw+loiE8VeyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:32:51.705557Z"},"content_sha256":"91ac51e6d12a9de47b42a9be452a7b3ac1e8bc65d98cca50284b5c8b9301b759","schema_version":"1.0","event_id":"sha256:91ac51e6d12a9de47b42a9be452a7b3ac1e8bc65d98cca50284b5c8b9301b759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/bundle.json","state_url":"https://pith.science/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/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":"2026-08-16T06:32:51Z","links":{"resolver":"https://pith.science/pith/KDDUARKJNEEAMPCRKKLC4QYTAE","bundle":"https://pith.science/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/bundle.json","state":"https://pith.science/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDDUARKJNEEAMPCRKKLC4QYTAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KDDUARKJNEEAMPCRKKLC4QYTAE","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":"80cc766e9a59509450ec1cad09736c44873da9414c6914a1b0bc7b670f53900f","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-19T13:13:03Z","title_canon_sha256":"a2fdee7ac152f52a17d95e152cae3560a1abda7ba4057949e15e693f1518e99b"},"schema_version":"1.0","source":{"id":"1908.06779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06779","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06779v2","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06779","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"KDDUARKJNEEA","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_16","alias_value":"KDDUARKJNEEAMPCR","created_at":"2026-07-05T01:11:41Z"},{"alias_kind":"pith_short_8","alias_value":"KDDUARKJ","created_at":"2026-07-05T01:11:41Z"}],"graph_snapshots":[{"event_id":"sha256:91ac51e6d12a9de47b42a9be452a7b3ac1e8bc65d98cca50284b5c8b9301b759","target":"graph","created_at":"2026-07-05T01:11:41Z","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/1908.06779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Representing an atom by a solid sphere in $3$-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [HRC13,RHK06] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [EdKo03], the weighted area","authors_text":"Arseniy Akopyan, Herbert Edelsbrunner","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-19T13:13:03Z","title":"The Weighted Mean Curvature Derivative of a Space-Filling Diagram"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06779","kind":"arxiv","version":2},"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":"sha256:4906835eebbe9c726f15b8c37a9119d94d983a662085a8720d36c35d6a2a2987","target":"record","created_at":"2026-07-05T01:11:41Z","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":"80cc766e9a59509450ec1cad09736c44873da9414c6914a1b0bc7b670f53900f","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-19T13:13:03Z","title_canon_sha256":"a2fdee7ac152f52a17d95e152cae3560a1abda7ba4057949e15e693f1518e99b"},"schema_version":"1.0","source":{"id":"1908.06779","kind":"arxiv","version":2}},"canonical_sha256":"50c74045496908063c5152962e4313012451c4e5adf2f3aeda94fc29f0c60a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50c74045496908063c5152962e4313012451c4e5adf2f3aeda94fc29f0c60a28","first_computed_at":"2026-07-05T01:11:41.324438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:11:41.324438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R8n+9HRf+IRga9EMgs7PZU25qd6279/fEb4q9j2J1GJ44TiCfGLA3jsD/R5w2iVSDE84fIxnhwpJ1k2klDNEDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:11:41.325002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4906835eebbe9c726f15b8c37a9119d94d983a662085a8720d36c35d6a2a2987","sha256:91ac51e6d12a9de47b42a9be452a7b3ac1e8bc65d98cca50284b5c8b9301b759"],"state_sha256":"d85364cd8f2d3a9295b7cafaa1ed89d23a12cd8b09c6f007095bcbf3a7b3259d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"guEgkkS4ssMZYSI0tFE9aYsJJ9WFrMANjQejM1YTOiDqI9DVAhDEs2SYI2VctvhrJAcwby6DJksGBDLyUfu3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:32:51.711625Z","bundle_sha256":"1dc6917a848ef7163a89371c514bdac792028afc65455aee82ed9bff122f6c5d"}}