{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7R7Q7L6H7ZI7BMEVMFKV2NGGI5","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":"493a3cd6a744f0d2ef1c914988fba896a6fc87fb289c1caaff700f622173eeb1","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2026-07-17T16:35:41Z","title_canon_sha256":"c8519d73afc1796e5c116ce127070b4815eeb21c9d3ecb2629af7bcc1d7ccc9a"},"schema_version":"1.0","source":{"id":"2607.16381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16381","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16381v1","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16381","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"7R7Q7L6H7ZI7","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"7R7Q7L6H7ZI7BMEV","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"7R7Q7L6H","created_at":"2026-07-21T00:20:14Z"}],"graph_snapshots":[{"event_id":"sha256:4eb8e33bfb8a90d8347ed7421483b19e02118d31dcbe1ba7a872a6993383b598","target":"graph","created_at":"2026-07-21T00:20:14Z","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/2607.16381/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a deterministic, scale-resolved formulation of energy transfer in the three-dimensional incompressible Navier-Stokes equations based on an explicit triadic decomposition of the nonlinear term in Fourier space. Using a systematic dyadic localization of the velocity field, we derive an exact representation of the nonlinear energy flux across scales and organize it in terms of interactions between well-defined scale components. Under suitable smoothness assumptions, we obtain an absolutely convergent triadic expansion and quantitative bounds that distinguish local and nonlocal contribu","authors_text":"Erik Bertram","cross_cats":["astro-ph.GA","astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2026-07-17T16:35:41Z","title":"From Triadic Interactions to Kolmogorov Scaling: A Deterministic, Scale-Resolved Formulation of Energy Flux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16381","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:d35003476bac4be6c4273471c8e2ac3bea57b52efb3a6fd291235e3512c8bab0","target":"record","created_at":"2026-07-21T00:20:14Z","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":"493a3cd6a744f0d2ef1c914988fba896a6fc87fb289c1caaff700f622173eeb1","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2026-07-17T16:35:41Z","title_canon_sha256":"c8519d73afc1796e5c116ce127070b4815eeb21c9d3ecb2629af7bcc1d7ccc9a"},"schema_version":"1.0","source":{"id":"2607.16381","kind":"arxiv","version":1}},"canonical_sha256":"fc7f0fafc7fe51f0b09561555d34c647598f52e76fa79eb9c27d217e84d44bce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc7f0fafc7fe51f0b09561555d34c647598f52e76fa79eb9c27d217e84d44bce","first_computed_at":"2026-07-21T00:20:14.947673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:14.947673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fcu7mgkAVRC4/cah80jIpSRVafi8t3ZXfMpL2UDc69cLqVwU6sem0IRbznsXDp4bJ/pjQoxErvKXQlgzSKYtAw==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:14.948611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d35003476bac4be6c4273471c8e2ac3bea57b52efb3a6fd291235e3512c8bab0","sha256:4eb8e33bfb8a90d8347ed7421483b19e02118d31dcbe1ba7a872a6993383b598"],"state_sha256":"82b648b50d76833b905cca329f0c1821c0359214624e02f050831970aed2fb00"}