{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PVTRADLIBXQE5U4227J5K3BOTB","short_pith_number":"pith:PVTRADLI","canonical_record":{"source":{"id":"1908.04838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-13T19:42:20Z","cross_cats_sorted":["math.AP","nlin.CD","physics.ao-ph"],"title_canon_sha256":"5786db8ec6688423e3e65a5b5d709a5a6d6be70e348f858e764277c6434edce5","abstract_canon_sha256":"47f23e988ddb171dea76784539a16222c95ee100e41afe40c51ed3a4674dd264"},"schema_version":"1.0"},"canonical_sha256":"7d67100d680de04ed39ad7d3d56c2e9852de4ed0d4f33faa2e7333b4de9def1d","source":{"kind":"arxiv","id":"1908.04838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04838","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04838v1","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04838","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"PVTRADLIBXQE","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"PVTRADLIBXQE5U42","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"PVTRADLI","created_at":"2026-07-05T01:55:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PVTRADLIBXQE5U4227J5K3BOTB","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-13T19:42:20Z","cross_cats_sorted":["math.AP","nlin.CD","physics.ao-ph"],"title_canon_sha256":"5786db8ec6688423e3e65a5b5d709a5a6d6be70e348f858e764277c6434edce5","abstract_canon_sha256":"47f23e988ddb171dea76784539a16222c95ee100e41afe40c51ed3a4674dd264"},"schema_version":"1.0"},"canonical_sha256":"7d67100d680de04ed39ad7d3d56c2e9852de4ed0d4f33faa2e7333b4de9def1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:55:42.580957Z","signature_b64":"b10HfQDhosKKx4x8OLdLlY4xG4MsiWBuRwtsjOr4ZwTmj9i9q7lEn2U0+XGWixBu2Kgq5CUeNN4ZOnmbdo0rDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d67100d680de04ed39ad7d3d56c2e9852de4ed0d4f33faa2e7333b4de9def1d","last_reissued_at":"2026-07-05T01:55:42.580414Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:55:42.580414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04838","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":"2026-07-05T01:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UMQba+ILVTTAm0nX6wurlG/gf0bLggw6HP47NKR3yp0vk4OeWC26Jcnla4yl07RG7tBxJhZ63jTDS9+vGfIEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:38:25.057000Z"},"content_sha256":"73a575cdb5c55b83fca586aeec28de71cb7c9c618e148e9b525100c8004bafbf","schema_version":"1.0","event_id":"sha256:73a575cdb5c55b83fca586aeec28de71cb7c9c618e148e9b525100c8004bafbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PVTRADLIBXQE5U4227J5K3BOTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","nlin.CD","physics.ao-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Arjun Berera, Richard D. J. G. Ho, Y. Charles Li, Z. C. Feng","submitted_at":"2019-08-13T19:42:20Z","abstract_excerpt":"Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{\\sigma \\sqrt{Re} t}$ (where $\\sigma \\sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{\\sigma \\sqrt{Re} \\sqrt{t} +\\sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04838","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/1908.04838/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":"2026-07-05T01:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k10rR2YEqOoSeYnMtx9LtayMdZfWrw7/fqzd8zHJRfBoHBlqEeeDL4mivmmHhkUsX3kkhOwSHXgE8LC1Kc7pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:38:25.057515Z"},"content_sha256":"184ee87c50c59bf66e4650bc18151363868310b2363769cc07b8c877e72d4d33","schema_version":"1.0","event_id":"sha256:184ee87c50c59bf66e4650bc18151363868310b2363769cc07b8c877e72d4d33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVTRADLIBXQE5U4227J5K3BOTB/bundle.json","state_url":"https://pith.science/pith/PVTRADLIBXQE5U4227J5K3BOTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVTRADLIBXQE5U4227J5K3BOTB/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":"2026-08-14T22:38:25Z","links":{"resolver":"https://pith.science/pith/PVTRADLIBXQE5U4227J5K3BOTB","bundle":"https://pith.science/pith/PVTRADLIBXQE5U4227J5K3BOTB/bundle.json","state":"https://pith.science/pith/PVTRADLIBXQE5U4227J5K3BOTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVTRADLIBXQE5U4227J5K3BOTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PVTRADLIBXQE5U4227J5K3BOTB","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":"47f23e988ddb171dea76784539a16222c95ee100e41afe40c51ed3a4674dd264","cross_cats_sorted":["math.AP","nlin.CD","physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-13T19:42:20Z","title_canon_sha256":"5786db8ec6688423e3e65a5b5d709a5a6d6be70e348f858e764277c6434edce5"},"schema_version":"1.0","source":{"id":"1908.04838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04838","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04838v1","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04838","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"PVTRADLIBXQE","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"PVTRADLIBXQE5U42","created_at":"2026-07-05T01:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"PVTRADLI","created_at":"2026-07-05T01:55:42Z"}],"graph_snapshots":[{"event_id":"sha256:184ee87c50c59bf66e4650bc18151363868310b2363769cc07b8c877e72d4d33","target":"graph","created_at":"2026-07-05T01:55:42Z","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/1908.04838/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{\\sigma \\sqrt{Re} t}$ (where $\\sigma \\sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{\\sigma \\sqrt{Re} \\sqrt{t} +\\sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3","authors_text":"Arjun Berera, Richard D. J. G. Ho, Y. Charles Li, Z. C. Feng","cross_cats":["math.AP","nlin.CD","physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-13T19:42:20Z","title":"Superfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04838","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":"sha256:73a575cdb5c55b83fca586aeec28de71cb7c9c618e148e9b525100c8004bafbf","target":"record","created_at":"2026-07-05T01:55:42Z","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":"47f23e988ddb171dea76784539a16222c95ee100e41afe40c51ed3a4674dd264","cross_cats_sorted":["math.AP","nlin.CD","physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-13T19:42:20Z","title_canon_sha256":"5786db8ec6688423e3e65a5b5d709a5a6d6be70e348f858e764277c6434edce5"},"schema_version":"1.0","source":{"id":"1908.04838","kind":"arxiv","version":1}},"canonical_sha256":"7d67100d680de04ed39ad7d3d56c2e9852de4ed0d4f33faa2e7333b4de9def1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d67100d680de04ed39ad7d3d56c2e9852de4ed0d4f33faa2e7333b4de9def1d","first_computed_at":"2026-07-05T01:55:42.580414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:55:42.580414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b10HfQDhosKKx4x8OLdLlY4xG4MsiWBuRwtsjOr4ZwTmj9i9q7lEn2U0+XGWixBu2Kgq5CUeNN4ZOnmbdo0rDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:55:42.580957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a575cdb5c55b83fca586aeec28de71cb7c9c618e148e9b525100c8004bafbf","sha256:184ee87c50c59bf66e4650bc18151363868310b2363769cc07b8c877e72d4d33"],"state_sha256":"543d8414a3eda25b78fd58c70286dbcdc73eba170e4a82188679ed53b8adc81d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syv50WiQ33YTcXFRCEEivVI3XKhTQaZMGIUS4miaWcVd0ITU+OnmOJwsYw3TQ+oYT+JKnNzB9BoluDD44IKmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T22:38:25.060817Z","bundle_sha256":"cdea3fbd7ef2b494e472cc61d656b93a4bdc554905741511d2239c93d15bbbd8"}}