{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GJFAHHODBVSM3YVGHSF3ZZ74RH","short_pith_number":"pith:GJFAHHOD","canonical_record":{"source":{"id":"1908.01422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"db0479a59cf3dd39b9a9edf61d19159238e20615701360c7899278294ce97976","abstract_canon_sha256":"ec091a05ecb5ecaac2b6e52b2d04f7c4dfbb1904229e48282edf32b1bb04154f"},"schema_version":"1.0"},"canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","source":{"kind":"arxiv","id":"1908.01422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01422","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01422v1","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01422","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"GJFAHHODBVSM","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJFAHHODBVSM3YVG","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJFAHHOD","created_at":"2026-07-04T23:51:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GJFAHHODBVSM3YVGHSF3ZZ74RH","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"db0479a59cf3dd39b9a9edf61d19159238e20615701360c7899278294ce97976","abstract_canon_sha256":"ec091a05ecb5ecaac2b6e52b2d04f7c4dfbb1904229e48282edf32b1bb04154f"},"schema_version":"1.0"},"canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:30.290630Z","signature_b64":"mF/vCMH4eav0HSwAce+scBuTH0n/qvAZRuHRg14+q4o33r7lpZT6UZ9swzKE0ToxLlwXUCJdTE44FvF7GhLNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","last_reissued_at":"2026-07-04T23:51:30.290154Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:30.290154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01422","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":"2026-07-04T23:51:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7RTalDQzCf7fggNBa78OmN8e7lL+jzNFI2eACHBLHCFnEPsl2fBJJEatjpTDR9YeBfwWm8AkHIxpAk6gMEJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:46:22.545662Z"},"content_sha256":"b3bef3898cec5381dd6efc0534999010ed9aeec43dfe95837f7e66b3f39e0cde","schema_version":"1.0","event_id":"sha256:b3bef3898cec5381dd6efc0534999010ed9aeec43dfe95837f7e66b3f39e0cde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GJFAHHODBVSM3YVGHSF3ZZ74RH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"hep-th","authors_text":"Alexander Migdal","submitted_at":"2019-08-04T23:17:55Z","abstract_excerpt":"We developed analytic approach to the non-planar loop equation, which we derived in previous papers \\cite{M19a},\\cite{M19b},\\cite{M19c}. We found quadratic integral equation for the vorticity distribution $\\Omega(r)$ we introduced on a minimal surface. There are no corrections to the minimal surface though: it is still defined by mean external curvature equal to zero, for arbitrary non-planar loop. We also analyzed the loop equations with viscosity term in Navier-Stokes equations. This term creates boundary condition for $\\Omega(r\\in C)$. The leading viscosity correction term mixes the moments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01422","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/1908.01422/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":"2026-07-04T23:51:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTEGhJiFPuZxkxFPVgtCMxUlx6EqAgzbUlGxL/xbMYqBPR49cdXeJeCSTdoSc28dAPrimFUIB1zATrPySdVeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:46:22.546178Z"},"content_sha256":"64d323ed8b8b291155df2e4679ff54107f469eef667725fb7c43f3dae9cd5333","schema_version":"1.0","event_id":"sha256:64d323ed8b8b291155df2e4679ff54107f469eef667725fb7c43f3dae9cd5333"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/bundle.json","state_url":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/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":"2026-08-09T08:46:22Z","links":{"resolver":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH","bundle":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/bundle.json","state":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GJFAHHODBVSM3YVGHSF3ZZ74RH","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":"ec091a05ecb5ecaac2b6e52b2d04f7c4dfbb1904229e48282edf32b1bb04154f","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","title_canon_sha256":"db0479a59cf3dd39b9a9edf61d19159238e20615701360c7899278294ce97976"},"schema_version":"1.0","source":{"id":"1908.01422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01422","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01422v1","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01422","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"GJFAHHODBVSM","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJFAHHODBVSM3YVG","created_at":"2026-07-04T23:51:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJFAHHOD","created_at":"2026-07-04T23:51:30Z"}],"graph_snapshots":[{"event_id":"sha256:64d323ed8b8b291155df2e4679ff54107f469eef667725fb7c43f3dae9cd5333","target":"graph","created_at":"2026-07-04T23:51:30Z","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/1908.01422/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We developed analytic approach to the non-planar loop equation, which we derived in previous papers \\cite{M19a},\\cite{M19b},\\cite{M19c}. We found quadratic integral equation for the vorticity distribution $\\Omega(r)$ we introduced on a minimal surface. There are no corrections to the minimal surface though: it is still defined by mean external curvature equal to zero, for arbitrary non-planar loop. We also analyzed the loop equations with viscosity term in Navier-Stokes equations. This term creates boundary condition for $\\Omega(r\\in C)$. The leading viscosity correction term mixes the moments","authors_text":"Alexander Migdal","cross_cats":["nlin.CD","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","title":"Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01422","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:b3bef3898cec5381dd6efc0534999010ed9aeec43dfe95837f7e66b3f39e0cde","target":"record","created_at":"2026-07-04T23:51:30Z","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":"ec091a05ecb5ecaac2b6e52b2d04f7c4dfbb1904229e48282edf32b1bb04154f","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","title_canon_sha256":"db0479a59cf3dd39b9a9edf61d19159238e20615701360c7899278294ce97976"},"schema_version":"1.0","source":{"id":"1908.01422","kind":"arxiv","version":1}},"canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","first_computed_at":"2026-07-04T23:51:30.290154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:30.290154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mF/vCMH4eav0HSwAce+scBuTH0n/qvAZRuHRg14+q4o33r7lpZT6UZ9swzKE0ToxLlwXUCJdTE44FvF7GhLNCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:30.290630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3bef3898cec5381dd6efc0534999010ed9aeec43dfe95837f7e66b3f39e0cde","sha256:64d323ed8b8b291155df2e4679ff54107f469eef667725fb7c43f3dae9cd5333"],"state_sha256":"35ed6442ba392a8d771c0a0c7bf71b47b6980a2a4b88e1af613751715d3f095f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vD1kLPoCzqKeRiQ302TH7oCo1JQJR+NcOXbx7VzZMXU1taJG+dBNM0iYY1OoBX9HlECjIe199hUtW6CbmmAbBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T08:46:22.551303Z","bundle_sha256":"5d7364250c246f7879085f0958e2510d6ff20a64e1373265e36f12365975e2a8"}}