{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3TXHLIPGCK6JTUH37OUCWYBE57","short_pith_number":"pith:3TXHLIPG","canonical_record":{"source":{"id":"1308.4205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-20T01:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"45196a03e687e63b81fd8d9b5fc5a811083f68be149da5c195e10de9cca3de85","abstract_canon_sha256":"2b27b24402c373e66343239700a13b006caafc423913a2e50183fd0ac90422e3"},"schema_version":"1.0"},"canonical_sha256":"dcee75a1e612bc99d0fbfba82b6024eff48551445092f3e546cdea9d6369fd7d","source":{"kind":"arxiv","id":"1308.4205","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4205","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4205v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4205","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"3TXHLIPGCK6J","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TXHLIPGCK6JTUH3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TXHLIPG","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3TXHLIPGCK6JTUH37OUCWYBE57","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-20T01:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"45196a03e687e63b81fd8d9b5fc5a811083f68be149da5c195e10de9cca3de85","abstract_canon_sha256":"2b27b24402c373e66343239700a13b006caafc423913a2e50183fd0ac90422e3"},"schema_version":"1.0"},"canonical_sha256":"dcee75a1e612bc99d0fbfba82b6024eff48551445092f3e546cdea9d6369fd7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:33.443018Z","signature_b64":"Wg5rgHusA8DM9s17uQalc8S6hdbkUoyyRRkis5iaIwfkGVmAiLVnU+CsKQXcXB9K4TloBDWXmknQi0LSwrL3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcee75a1e612bc99d0fbfba82b6024eff48551445092f3e546cdea9d6369fd7d","last_reissued_at":"2026-05-18T03:15:33.442058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:33.442058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4205","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":"2026-05-18T03:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0SeBHulVNIUKuZF/mHBlN+AdZhLN5Ey1DgaQuD7osCzjHfE5xdZJsCmB+0cPZ55Iw/OOLausaFpLiLevtrnHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:38:53.578766Z"},"content_sha256":"f9f65d5754c3ca350828204a1b41b519c7922f1dd77810a1d6a04536a642e3b7","schema_version":"1.0","event_id":"sha256:f9f65d5754c3ca350828204a1b41b519c7922f1dd77810a1d6a04536a642e3b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3TXHLIPGCK6JTUH37OUCWYBE57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reynolds Number of Transition as a Dynamic Constraint on Statistical Theory of Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Victor Yakhot","submitted_at":"2013-08-20T01:49:51Z","abstract_excerpt":"Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling constant) almost identical to the Reynolds number of the recently discovered transition to anomalous scaling of the moments of {\\bf \"velocity derivatives\"}. Using this result as a dynamic constraint, it is argued that in the vicinity of the fixed point (integral scale) the high-order non-linearities, generated by the procedure, are irrelevant. The infra-red divergen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4205","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":"2026-05-18T03:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oi29+LlLlxUYr06k/OtyBTuRBAsKZzz41SQqG0MjZw2YMGCoRP/N0hOME47jaE2WFSlKgO1BvYo7QTdonPoyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:38:53.579104Z"},"content_sha256":"633778b7b76188ea329b1f7fe3f2e72d2d06745df8da35f2af52afb2063f898c","schema_version":"1.0","event_id":"sha256:633778b7b76188ea329b1f7fe3f2e72d2d06745df8da35f2af52afb2063f898c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TXHLIPGCK6JTUH37OUCWYBE57/bundle.json","state_url":"https://pith.science/pith/3TXHLIPGCK6JTUH37OUCWYBE57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TXHLIPGCK6JTUH37OUCWYBE57/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":"2026-06-03T03:38:53Z","links":{"resolver":"https://pith.science/pith/3TXHLIPGCK6JTUH37OUCWYBE57","bundle":"https://pith.science/pith/3TXHLIPGCK6JTUH37OUCWYBE57/bundle.json","state":"https://pith.science/pith/3TXHLIPGCK6JTUH37OUCWYBE57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TXHLIPGCK6JTUH37OUCWYBE57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3TXHLIPGCK6JTUH37OUCWYBE57","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":"2b27b24402c373e66343239700a13b006caafc423913a2e50183fd0ac90422e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-20T01:49:51Z","title_canon_sha256":"45196a03e687e63b81fd8d9b5fc5a811083f68be149da5c195e10de9cca3de85"},"schema_version":"1.0","source":{"id":"1308.4205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4205","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4205v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4205","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"3TXHLIPGCK6J","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TXHLIPGCK6JTUH3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TXHLIPG","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:633778b7b76188ea329b1f7fe3f2e72d2d06745df8da35f2af52afb2063f898c","target":"graph","created_at":"2026-05-18T03:15:33Z","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":"Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling constant) almost identical to the Reynolds number of the recently discovered transition to anomalous scaling of the moments of {\\bf \"velocity derivatives\"}. Using this result as a dynamic constraint, it is argued that in the vicinity of the fixed point (integral scale) the high-order non-linearities, generated by the procedure, are irrelevant. The infra-red divergen","authors_text":"Victor Yakhot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-20T01:49:51Z","title":"Reynolds Number of Transition as a Dynamic Constraint on Statistical Theory of Turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4205","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:f9f65d5754c3ca350828204a1b41b519c7922f1dd77810a1d6a04536a642e3b7","target":"record","created_at":"2026-05-18T03:15:33Z","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":"2b27b24402c373e66343239700a13b006caafc423913a2e50183fd0ac90422e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-08-20T01:49:51Z","title_canon_sha256":"45196a03e687e63b81fd8d9b5fc5a811083f68be149da5c195e10de9cca3de85"},"schema_version":"1.0","source":{"id":"1308.4205","kind":"arxiv","version":1}},"canonical_sha256":"dcee75a1e612bc99d0fbfba82b6024eff48551445092f3e546cdea9d6369fd7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcee75a1e612bc99d0fbfba82b6024eff48551445092f3e546cdea9d6369fd7d","first_computed_at":"2026-05-18T03:15:33.442058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:33.442058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wg5rgHusA8DM9s17uQalc8S6hdbkUoyyRRkis5iaIwfkGVmAiLVnU+CsKQXcXB9K4TloBDWXmknQi0LSwrL3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:33.443018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9f65d5754c3ca350828204a1b41b519c7922f1dd77810a1d6a04536a642e3b7","sha256:633778b7b76188ea329b1f7fe3f2e72d2d06745df8da35f2af52afb2063f898c"],"state_sha256":"ddc5efeb9fb75b85d59c90e8a70b6ead21564fa3e39fc04a1cbcfe70072ecb25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9/FW211R+2DZysYhUGKf0mftQ159gCZ2xrfxiLK77w6f9qxgn5dekC8/XIyei6XyphkgPwbTpUkps6qr7K3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:38:53.581012Z","bundle_sha256":"d0d2ba54529642649edad0eb55aefa70cc8a24130d380ee5a3f111350ef887ed"}}