{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5SSRBFTYSHAIMPD7TCBQCL3XUQ","short_pith_number":"pith:5SSRBFTY","schema_version":"1.0","canonical_sha256":"eca510967891c0863c7f9883012f77a414c87acec02787d199b3d5d9e0be554a","source":{"kind":"arxiv","id":"2608.00234","version":1},"attestation_state":"computed","paper":{"title":"Delayed Dissipation for Two-Dimensional Vortex Sheets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Victor Armegioiu","submitted_at":"2026-07-31T19:29:04Z","abstract_excerpt":"We quantify viscous energy loss for two-dimensional Delort vortex sheets. Let $u^\\nu$ be Leray-Hopf solutions on $\\mathbb{T}^2$ with uniformly bounded kinetic energy and total vorticity variation, and write $\\omega_0^\\nu=\\mu_0^\\nu+f_0^\\nu$, where $\\mu_0^\\nu\\geq0$ and $f_0^\\nu$ is bounded in $L^p$, $p>1$. For every fixed $0<\\delta<T$, $\\nu\\int_\\delta^T\\|\\omega^\\nu(t)\\|_2^2\\,\\mathrm{d}t\\lesssim_{\\delta,T}\\frac{1}{|\\log\\nu|}$. This improves the $O(|\\log\\nu|^{-1/2})$ bound of De Rosa and Marcotullio under the same assumptions and thereby disproves their Conjecture 1.6 (arXiv:2602.15670, v1). The p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.00234","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T19:29:04Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"365b4295f304026d2fd50712326ea46e59088415239bd8c30b6d07a9986fd472","abstract_canon_sha256":"6a147196ef7742868ebb36528b50b4c0578e15411d6f484adf4222ef59ddddfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:34:27.097439Z","signature_b64":"sEQv6bcgPysZ536BPsUR56PE6wnryqRfupHWWDqB+o2zXjy4/sFku1n8Qzj+GruzV5RoYCBIHJsH8MV49UiXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eca510967891c0863c7f9883012f77a414c87acec02787d199b3d5d9e0be554a","last_reissued_at":"2026-08-04T00:34:27.096059Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:34:27.096059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Delayed Dissipation for Two-Dimensional Vortex Sheets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Victor Armegioiu","submitted_at":"2026-07-31T19:29:04Z","abstract_excerpt":"We quantify viscous energy loss for two-dimensional Delort vortex sheets. Let $u^\\nu$ be Leray-Hopf solutions on $\\mathbb{T}^2$ with uniformly bounded kinetic energy and total vorticity variation, and write $\\omega_0^\\nu=\\mu_0^\\nu+f_0^\\nu$, where $\\mu_0^\\nu\\geq0$ and $f_0^\\nu$ is bounded in $L^p$, $p>1$. For every fixed $0<\\delta<T$, $\\nu\\int_\\delta^T\\|\\omega^\\nu(t)\\|_2^2\\,\\mathrm{d}t\\lesssim_{\\delta,T}\\frac{1}{|\\log\\nu|}$. This improves the $O(|\\log\\nu|^{-1/2})$ bound of De Rosa and Marcotullio under the same assumptions and thereby disproves their Conjecture 1.6 (arXiv:2602.15670, v1). 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