{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:URQQAQ624FQZ2ONKTA6O4FMN7G","short_pith_number":"pith:URQQAQ62","canonical_record":{"source":{"id":"1810.04131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T16:56:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e2e6187405d019fb15f8270d4569aab98f4f8cc0a4a41636d46714caa5567481","abstract_canon_sha256":"19feaacc211e7f2ee780b7f6e885ab148bc357c9c7f56246ffa15b4d1ab4d842"},"schema_version":"1.0"},"canonical_sha256":"a4610043dae1619d39aa983cee158df9afba5d5fe91ab72e425c9d45690097e0","source":{"kind":"arxiv","id":"1810.04131","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04131","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04131v2","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04131","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"URQQAQ624FQZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"URQQAQ624FQZ2ONK","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"URQQAQ62","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:URQQAQ624FQZ2ONKTA6O4FMN7G","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T16:56:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e2e6187405d019fb15f8270d4569aab98f4f8cc0a4a41636d46714caa5567481","abstract_canon_sha256":"19feaacc211e7f2ee780b7f6e885ab148bc357c9c7f56246ffa15b4d1ab4d842"},"schema_version":"1.0"},"canonical_sha256":"a4610043dae1619d39aa983cee158df9afba5d5fe91ab72e425c9d45690097e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:17.886599Z","signature_b64":"OeiilK1HgvUNdxA/xo/ggm4nVVNkU6P7OsYA249dl5xTdDXB9PIhYcnyJJOzTMKTI3f6mwbPEShJgNmx6bTtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4610043dae1619d39aa983cee158df9afba5d5fe91ab72e425c9d45690097e0","last_reissued_at":"2026-05-17T23:40:17.885868Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:17.885868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04131","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":"2026-05-17T23:40:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MrXe2TCimegSEr5TW/fPffyKqkzFy3g0qaOfHY77Ww5m1FqufurqLP2QnGYHj/CdFAsLfFf6T0g9ilh4ZUiiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:15:20.157604Z"},"content_sha256":"963d64f1ed0ae95addac873656386b1c32def17c9adf3d1a0364fade34479f13","schema_version":"1.0","event_id":"sha256:963d64f1ed0ae95addac873656386b1c32def17c9adf3d1a0364fade34479f13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:URQQAQ624FQZ2ONKTA6O4FMN7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiscale Hydrophobic Lipid Dynamics Simulated by Efficient Integral Equation Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andreas Kl\\\"ockner, Matt Wala, Rolf J. Ryham, Shidong Jiang, Szu-Pei P. Fu, Yuan-Nan Young","submitted_at":"2018-10-09T16:56:37Z","abstract_excerpt":"In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first variation of a hydrophobic attraction domain functional. The variation yields a hydrophobic stress that is used to numerically calculate trajectories for a collection of two-dimensional particles. The functional minimizer that accounts for hydrophobicity at molecular-aqueous interfaces is a solution to a boundary value problem of the screened Laplace equation. We reformulate the boundary value problem as a second-kind int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04131","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":""},"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":"2026-05-17T23:40:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTK4V8JeK3qvjiZMS+yWNNUhcaBrVh4VWeXG9ndDLq5OQS0pjuvPr95VurCiA1zYgNzqtyfwPgJS2vlpudstDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:15:20.157962Z"},"content_sha256":"9a2e13bc340a93c195433daacbbe1aa12e7fc898316c6b461d37f7659ca12386","schema_version":"1.0","event_id":"sha256:9a2e13bc340a93c195433daacbbe1aa12e7fc898316c6b461d37f7659ca12386"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/bundle.json","state_url":"https://pith.science/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/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":"2026-06-02T08:15:20Z","links":{"resolver":"https://pith.science/pith/URQQAQ624FQZ2ONKTA6O4FMN7G","bundle":"https://pith.science/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/bundle.json","state":"https://pith.science/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URQQAQ624FQZ2ONKTA6O4FMN7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:URQQAQ624FQZ2ONKTA6O4FMN7G","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":"19feaacc211e7f2ee780b7f6e885ab148bc357c9c7f56246ffa15b4d1ab4d842","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T16:56:37Z","title_canon_sha256":"e2e6187405d019fb15f8270d4569aab98f4f8cc0a4a41636d46714caa5567481"},"schema_version":"1.0","source":{"id":"1810.04131","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04131","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04131v2","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04131","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"URQQAQ624FQZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"URQQAQ624FQZ2ONK","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"URQQAQ62","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:9a2e13bc340a93c195433daacbbe1aa12e7fc898316c6b461d37f7659ca12386","target":"graph","created_at":"2026-05-17T23:40:17Z","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":"In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first variation of a hydrophobic attraction domain functional. The variation yields a hydrophobic stress that is used to numerically calculate trajectories for a collection of two-dimensional particles. The functional minimizer that accounts for hydrophobicity at molecular-aqueous interfaces is a solution to a boundary value problem of the screened Laplace equation. We reformulate the boundary value problem as a second-kind int","authors_text":"Andreas Kl\\\"ockner, Matt Wala, Rolf J. Ryham, Shidong Jiang, Szu-Pei P. Fu, Yuan-Nan Young","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T16:56:37Z","title":"Multiscale Hydrophobic Lipid Dynamics Simulated by Efficient Integral Equation Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04131","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":"sha256:963d64f1ed0ae95addac873656386b1c32def17c9adf3d1a0364fade34479f13","target":"record","created_at":"2026-05-17T23:40:17Z","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":"19feaacc211e7f2ee780b7f6e885ab148bc357c9c7f56246ffa15b4d1ab4d842","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-09T16:56:37Z","title_canon_sha256":"e2e6187405d019fb15f8270d4569aab98f4f8cc0a4a41636d46714caa5567481"},"schema_version":"1.0","source":{"id":"1810.04131","kind":"arxiv","version":2}},"canonical_sha256":"a4610043dae1619d39aa983cee158df9afba5d5fe91ab72e425c9d45690097e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4610043dae1619d39aa983cee158df9afba5d5fe91ab72e425c9d45690097e0","first_computed_at":"2026-05-17T23:40:17.885868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:17.885868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OeiilK1HgvUNdxA/xo/ggm4nVVNkU6P7OsYA249dl5xTdDXB9PIhYcnyJJOzTMKTI3f6mwbPEShJgNmx6bTtCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:17.886599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04131","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:963d64f1ed0ae95addac873656386b1c32def17c9adf3d1a0364fade34479f13","sha256:9a2e13bc340a93c195433daacbbe1aa12e7fc898316c6b461d37f7659ca12386"],"state_sha256":"8b2f15051c4b87d970c9945963063b702e863eb122cba681baa88baff0cad59b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wlW2UwKRYdrYbwiea6yRjE68C339swWrEf7IyjIQ8MdcBNfs+faRp3AyoskMriRGO9HhPyX+iF+L9zmQUe8ABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:15:20.159943Z","bundle_sha256":"1955e4711d871cc8521025f46f9ab0cfe1fe1411c814fe4acdee7dff04c7681f"}}