{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QCMWROLUSP2DPEZABPSNGW7IFE","short_pith_number":"pith:QCMWROLU","canonical_record":{"source":{"id":"1803.05286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-14T14:01:37Z","cross_cats_sorted":[],"title_canon_sha256":"ab3f94dfada417c4ce821153e8b993732d2a169e62f1d747d2f1eb279f2d1a5b","abstract_canon_sha256":"ee588a729fdc008dccf26bf0147d4847a3fbb731aac3069932e8e352b9606837"},"schema_version":"1.0"},"canonical_sha256":"809968b97493f43793200be4d35be82927a12ef3861c04aeffaa76de2a0a4af6","source":{"kind":"arxiv","id":"1803.05286","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05286","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05286v1","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05286","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"QCMWROLUSP2D","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QCMWROLUSP2DPEZA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QCMWROLU","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QCMWROLUSP2DPEZABPSNGW7IFE","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-14T14:01:37Z","cross_cats_sorted":[],"title_canon_sha256":"ab3f94dfada417c4ce821153e8b993732d2a169e62f1d747d2f1eb279f2d1a5b","abstract_canon_sha256":"ee588a729fdc008dccf26bf0147d4847a3fbb731aac3069932e8e352b9606837"},"schema_version":"1.0"},"canonical_sha256":"809968b97493f43793200be4d35be82927a12ef3861c04aeffaa76de2a0a4af6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.716522Z","signature_b64":"GHYW1sKwBxdHRTpUbD02gtJxT7E6muDQdMtaAwQSw2Slcr/GgT4u/wzAtoLDc4kOD4dInJg0Ys4jIKSFLaKDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"809968b97493f43793200be4d35be82927a12ef3861c04aeffaa76de2a0a4af6","last_reissued_at":"2026-05-18T00:21:01.716078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.716078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05286","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":"2026-05-18T00:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3BMvzNaemxPl6YUWRpOls6HAlzqqAoMkWYC1XXg+x4udZmrp+aGG1LuCtMDOVXYdwLjlOPbdS5korHmr7E3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:51:30.452335Z"},"content_sha256":"bf050d6b6671d7d231b1c4cb18444d157d0766c5a21ee2c27f6c9bbc50d9070b","schema_version":"1.0","event_id":"sha256:bf050d6b6671d7d231b1c4cb18444d157d0766c5a21ee2c27f6c9bbc50d9070b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QCMWROLUSP2DPEZABPSNGW7IFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turbulence Modeling via the Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Benoit Cushman-Roisin, Brenden P. Epps","submitted_at":"2018-03-14T14:01:37Z","abstract_excerpt":"Herein, we derive the fractional Laplacian operator as a means to represent the mean friction force arising in a turbulent flow: $ \\rho \\frac{D\\bar{\\bf u}}{Dt} = -\\nabla p + \\mu_\\alpha \\nabla^2\\bar{\\bf u} + \\rho C_\\alpha \\iiint_{\\!-\\infty}^\\infty\n  \\frac{ \\bar{\\bf u}{\\scriptstyle(t,{\\bf x}')} - \\bar{\\bf u}{\\scriptstyle(t,{\\bf x})} }{|{\\bf x}'-{\\bf x}|^{\\alpha+3}} \\,d{\\bf x}' $, where $\\bar{\\bf u}{\\scriptstyle(t,{\\bf x})}$ is the ensemble-averaged velocity field, $\\mu_\\alpha$ is an enhanced molecular viscosity, and $C_\\alpha$ is a turbulent mixing coefficient (with units (length)$^\\alpha$/(time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05286","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":"2026-05-18T00:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9M7sAxU93ui7ylTCm+zNfpbdkAczLpkDwfpjB70K96fXQ2joOw+Nl9pcHwQ5a0DBQ+oJgqU2DaGu5BH70mzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:51:30.452690Z"},"content_sha256":"0859d06f6561b5e0193597916edf07f1d583ebaf136feb4022ded1e462c3c5e7","schema_version":"1.0","event_id":"sha256:0859d06f6561b5e0193597916edf07f1d583ebaf136feb4022ded1e462c3c5e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QCMWROLUSP2DPEZABPSNGW7IFE/bundle.json","state_url":"https://pith.science/pith/QCMWROLUSP2DPEZABPSNGW7IFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QCMWROLUSP2DPEZABPSNGW7IFE/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":"2026-06-01T15:51:30Z","links":{"resolver":"https://pith.science/pith/QCMWROLUSP2DPEZABPSNGW7IFE","bundle":"https://pith.science/pith/QCMWROLUSP2DPEZABPSNGW7IFE/bundle.json","state":"https://pith.science/pith/QCMWROLUSP2DPEZABPSNGW7IFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QCMWROLUSP2DPEZABPSNGW7IFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QCMWROLUSP2DPEZABPSNGW7IFE","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":"ee588a729fdc008dccf26bf0147d4847a3fbb731aac3069932e8e352b9606837","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-14T14:01:37Z","title_canon_sha256":"ab3f94dfada417c4ce821153e8b993732d2a169e62f1d747d2f1eb279f2d1a5b"},"schema_version":"1.0","source":{"id":"1803.05286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05286","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05286v1","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05286","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"QCMWROLUSP2D","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QCMWROLUSP2DPEZA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QCMWROLU","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:0859d06f6561b5e0193597916edf07f1d583ebaf136feb4022ded1e462c3c5e7","target":"graph","created_at":"2026-05-18T00:21:01Z","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":"Herein, we derive the fractional Laplacian operator as a means to represent the mean friction force arising in a turbulent flow: $ \\rho \\frac{D\\bar{\\bf u}}{Dt} = -\\nabla p + \\mu_\\alpha \\nabla^2\\bar{\\bf u} + \\rho C_\\alpha \\iiint_{\\!-\\infty}^\\infty\n  \\frac{ \\bar{\\bf u}{\\scriptstyle(t,{\\bf x}')} - \\bar{\\bf u}{\\scriptstyle(t,{\\bf x})} }{|{\\bf x}'-{\\bf x}|^{\\alpha+3}} \\,d{\\bf x}' $, where $\\bar{\\bf u}{\\scriptstyle(t,{\\bf x})}$ is the ensemble-averaged velocity field, $\\mu_\\alpha$ is an enhanced molecular viscosity, and $C_\\alpha$ is a turbulent mixing coefficient (with units (length)$^\\alpha$/(time","authors_text":"Benoit Cushman-Roisin, Brenden P. Epps","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-14T14:01:37Z","title":"Turbulence Modeling via the Fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05286","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:bf050d6b6671d7d231b1c4cb18444d157d0766c5a21ee2c27f6c9bbc50d9070b","target":"record","created_at":"2026-05-18T00:21:01Z","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":"ee588a729fdc008dccf26bf0147d4847a3fbb731aac3069932e8e352b9606837","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-03-14T14:01:37Z","title_canon_sha256":"ab3f94dfada417c4ce821153e8b993732d2a169e62f1d747d2f1eb279f2d1a5b"},"schema_version":"1.0","source":{"id":"1803.05286","kind":"arxiv","version":1}},"canonical_sha256":"809968b97493f43793200be4d35be82927a12ef3861c04aeffaa76de2a0a4af6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"809968b97493f43793200be4d35be82927a12ef3861c04aeffaa76de2a0a4af6","first_computed_at":"2026-05-18T00:21:01.716078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:01.716078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GHYW1sKwBxdHRTpUbD02gtJxT7E6muDQdMtaAwQSw2Slcr/GgT4u/wzAtoLDc4kOD4dInJg0Ys4jIKSFLaKDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:01.716522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf050d6b6671d7d231b1c4cb18444d157d0766c5a21ee2c27f6c9bbc50d9070b","sha256:0859d06f6561b5e0193597916edf07f1d583ebaf136feb4022ded1e462c3c5e7"],"state_sha256":"745c6a7f5127165a98737265f800fb2d155896ae33ff4e651270c3865e953cfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wLLQgGBy0h2Cw5Y8SeUmxsRh9n6WkrDsztse2zMBLmRH51WDS+RKg1BSRc5S8gQoGjaRmM3wUWSYgNSWuPCWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:51:30.454742Z","bundle_sha256":"7e91989abbf36250507557194f96764281ffd9ca14527833f3fa0fce0d9a2bf6"}}