{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:2HQVTFFBSS2TJBPLVLG5VPRQGC","short_pith_number":"pith:2HQVTFFB","canonical_record":{"source":{"id":"hep-th/9306152","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-06-29T02:21:31Z","cross_cats_sorted":["cond-mat","hep-lat"],"title_canon_sha256":"1047bff22bf06b4075dce6d854b3a2ec77940b280e5ecb973624072027b4d559","abstract_canon_sha256":"f3a83162e4213f96caa053ef5a8a3f01a8a20ba3413b8757640503a8d4e64739"},"schema_version":"1.0"},"canonical_sha256":"d1e15994a194b53485ebaacddabe3030882a8dd5f6248d460c662f78c7a43609","source":{"kind":"arxiv","id":"hep-th/9306152","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9306152","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9306152v2","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9306152","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"2HQVTFFBSS2T","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_16","alias_value":"2HQVTFFBSS2TJBPL","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_8","alias_value":"2HQVTFFB","created_at":"2026-07-04T15:07:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:2HQVTFFBSS2TJBPLVLG5VPRQGC","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9306152","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-06-29T02:21:31Z","cross_cats_sorted":["cond-mat","hep-lat"],"title_canon_sha256":"1047bff22bf06b4075dce6d854b3a2ec77940b280e5ecb973624072027b4d559","abstract_canon_sha256":"f3a83162e4213f96caa053ef5a8a3f01a8a20ba3413b8757640503a8d4e64739"},"schema_version":"1.0"},"canonical_sha256":"d1e15994a194b53485ebaacddabe3030882a8dd5f6248d460c662f78c7a43609","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:07:34.472281Z","signature_b64":"xnvlNPyqcMe7w0L7mcg1DsTjvaXjhtx2ALClQaXvrMWieQhtphIeonIqmX7tvUzkF3Cyync7daDid6v7QQ9NBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e15994a194b53485ebaacddabe3030882a8dd5f6248d460c662f78c7a43609","last_reissued_at":"2026-07-04T15:07:34.471937Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:07:34.471937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9306152","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":"2026-07-04T15:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FayKVm54wS+C2ogYLqQfiZ6JpnRpOmTiH/LzLM9MSSsr/1doxTJK3UZ3rwOs800YyA8oOXh6+n5DyBaYhUTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:12:15.094573Z"},"content_sha256":"c4f22440c54b3aa131ffba3b61fe0cb68652bfa3e8695a49d397304e274a6ea6","schema_version":"1.0","event_id":"sha256:c4f22440c54b3aa131ffba3b61fe0cb68652bfa3e8695a49d397304e274a6ea6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:2HQVTFFBSS2TJBPLVLG5VPRQGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turbulence as Statistics of Vortex Cells","license":"","headline":"","cross_cats":["cond-mat","hep-lat"],"primary_cat":"hep-th","authors_text":"A.A.Migdal","submitted_at":"1993-06-29T02:21:31Z","abstract_excerpt":"We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange coordinates of this surface plus the conformal metric. Using the Hamiltonian dynamics we find an invariant probability distribution which satisfies the Liouville equation. The violations of the time reversal invariance come from certain topological terms in effective energy of our Gibbs-like distribution. We study the topological aspects of the statistics and use"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306152","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/hep-th/9306152/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":"2026-07-04T15:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARURHUTX6idirGYz6uDGr7jX7t/vt0zL6sCa/pUlTdNzOVw+Sj5rb/F40gw7SWFr/KaOBS6HxoRFndSJeJ1cBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:12:15.095087Z"},"content_sha256":"1ebfb680d1bafd6d15515ca6f7f941822ae1340d5421bf68b767f8dce6f2b5d8","schema_version":"1.0","event_id":"sha256:1ebfb680d1bafd6d15515ca6f7f941822ae1340d5421bf68b767f8dce6f2b5d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/bundle.json","state_url":"https://pith.science/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/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":"2026-08-16T13:12:15Z","links":{"resolver":"https://pith.science/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC","bundle":"https://pith.science/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/bundle.json","state":"https://pith.science/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HQVTFFBSS2TJBPLVLG5VPRQGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:2HQVTFFBSS2TJBPLVLG5VPRQGC","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":"f3a83162e4213f96caa053ef5a8a3f01a8a20ba3413b8757640503a8d4e64739","cross_cats_sorted":["cond-mat","hep-lat"],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-29T02:21:31Z","title_canon_sha256":"1047bff22bf06b4075dce6d854b3a2ec77940b280e5ecb973624072027b4d559"},"schema_version":"1.0","source":{"id":"hep-th/9306152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9306152","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9306152v2","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9306152","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"2HQVTFFBSS2T","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_16","alias_value":"2HQVTFFBSS2TJBPL","created_at":"2026-07-04T15:07:34Z"},{"alias_kind":"pith_short_8","alias_value":"2HQVTFFB","created_at":"2026-07-04T15:07:34Z"}],"graph_snapshots":[{"event_id":"sha256:1ebfb680d1bafd6d15515ca6f7f941822ae1340d5421bf68b767f8dce6f2b5d8","target":"graph","created_at":"2026-07-04T15:07:34Z","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/hep-th/9306152/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange coordinates of this surface plus the conformal metric. Using the Hamiltonian dynamics we find an invariant probability distribution which satisfies the Liouville equation. The violations of the time reversal invariance come from certain topological terms in effective energy of our Gibbs-like distribution. We study the topological aspects of the statistics and use","authors_text":"A.A.Migdal","cross_cats":["cond-mat","hep-lat"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-06-29T02:21:31Z","title":"Turbulence as Statistics of Vortex Cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306152","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:c4f22440c54b3aa131ffba3b61fe0cb68652bfa3e8695a49d397304e274a6ea6","target":"record","created_at":"2026-07-04T15:07:34Z","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":"f3a83162e4213f96caa053ef5a8a3f01a8a20ba3413b8757640503a8d4e64739","cross_cats_sorted":["cond-mat","hep-lat"],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-29T02:21:31Z","title_canon_sha256":"1047bff22bf06b4075dce6d854b3a2ec77940b280e5ecb973624072027b4d559"},"schema_version":"1.0","source":{"id":"hep-th/9306152","kind":"arxiv","version":2}},"canonical_sha256":"d1e15994a194b53485ebaacddabe3030882a8dd5f6248d460c662f78c7a43609","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e15994a194b53485ebaacddabe3030882a8dd5f6248d460c662f78c7a43609","first_computed_at":"2026-07-04T15:07:34.471937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:07:34.471937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xnvlNPyqcMe7w0L7mcg1DsTjvaXjhtx2ALClQaXvrMWieQhtphIeonIqmX7tvUzkF3Cyync7daDid6v7QQ9NBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:07:34.472281Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9306152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4f22440c54b3aa131ffba3b61fe0cb68652bfa3e8695a49d397304e274a6ea6","sha256:1ebfb680d1bafd6d15515ca6f7f941822ae1340d5421bf68b767f8dce6f2b5d8"],"state_sha256":"e8be14c91f791889e46412774de4501c7a4d8819cde84177f2870f9de837341b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOCapC7jp0eDCkp6+vR7+pG+16tBzs/K1kpy+JEiIOz06ud8eB+pJ6ZFnA1q3dd82mypnnHzv4kjeSW9EZheBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:12:15.100175Z","bundle_sha256":"940d2ba8eafba7d09fab6dfb2b8bc01b594145c23077bee546e6b741e289e24b"}}