{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J6LUQOLOIVRDJMTTSBGQH7GLN4","short_pith_number":"pith:J6LUQOLO","canonical_record":{"source":{"id":"2606.28575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T20:00:43Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"de3d6fa0bd08356b4dfcc811afcf61e1862d43f318ee5d8247a1aff3cf3a9e27","abstract_canon_sha256":"cf778f76ac2e9ee1b717fe8577072ba03deab5726d614b63fce25c2591841c93"},"schema_version":"1.0"},"canonical_sha256":"4f9748396e456234b273904d03fccb6f07058dadb4aa6b9b69ec21e5ee196235","source":{"kind":"arxiv","id":"2606.28575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28575","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28575v1","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28575","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_12","alias_value":"J6LUQOLOIVRD","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_16","alias_value":"J6LUQOLOIVRDJMTT","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_8","alias_value":"J6LUQOLO","created_at":"2026-06-30T00:15:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J6LUQOLOIVRDJMTTSBGQH7GLN4","target":"record","payload":{"canonical_record":{"source":{"id":"2606.28575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T20:00:43Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"de3d6fa0bd08356b4dfcc811afcf61e1862d43f318ee5d8247a1aff3cf3a9e27","abstract_canon_sha256":"cf778f76ac2e9ee1b717fe8577072ba03deab5726d614b63fce25c2591841c93"},"schema_version":"1.0"},"canonical_sha256":"4f9748396e456234b273904d03fccb6f07058dadb4aa6b9b69ec21e5ee196235","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T00:15:19.608169Z","signature_b64":"JoRIImE+sKA06EWi5TlycEE00MEnV5CHncr03Erc83RDSuKNQtupQX9q7QwQTInhhg1fhJqO+R1ycUn47djoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f9748396e456234b273904d03fccb6f07058dadb4aa6b9b69ec21e5ee196235","last_reissued_at":"2026-06-30T00:15:19.607773Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T00:15:19.607773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.28575","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":"2026-06-30T00:15:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vym+WG7QsNhfSnQceutd/YwudhoWlZxwbvwJf0JGdIVjjv5cvltDZvZzaeij7uMxdjEtfQnRUTfMfxWjcrljDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:22:48.363144Z"},"content_sha256":"1a62a9965a90307c6542e2028c5d488a78078482e039b58e55eae0b8b63bdef1","schema_version":"1.0","event_id":"sha256:1a62a9965a90307c6542e2028c5d488a78078482e039b58e55eae0b8b63bdef1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J6LUQOLOIVRDJMTTSBGQH7GLN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Antonio Agresti, Eliseo Luongo, Federico Butori","submitted_at":"2026-06-26T20:00:43Z","abstract_excerpt":"We study a logarithmically hyperviscous Navier-Stokes model on the three-dimensional torus with Lie-transport noise, which includes both transport and stretching. We prove that, for noise of sufficiently large intensity and high frequency, the system admits a unique global smooth solution with probability arbitrarily close to one. Unlike previous works, this physically motivated noise does not preserve energy or enstrophy, but rather circulation. Global well-posedness is established through a probabilistic mechanism that produces effective dissipation via a scaling limit. Crucially, this appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28575","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/2606.28575/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":"2026-06-30T00:15:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JduMPjKliihYyaOzIRG5Cttsrf4rSeI5YAqCW+L7PzuDDPmIHQmpBRjae23N0C0mCBTs2+uSZESOoSeu9Lv+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:22:48.363544Z"},"content_sha256":"a830d9edf507535d990fe984882631549720fecf93ebd8867f5dd7d8b9d537ea","schema_version":"1.0","event_id":"sha256:a830d9edf507535d990fe984882631549720fecf93ebd8867f5dd7d8b9d537ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/bundle.json","state_url":"https://pith.science/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/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":"2026-07-04T13:22:48Z","links":{"resolver":"https://pith.science/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4","bundle":"https://pith.science/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/bundle.json","state":"https://pith.science/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6LUQOLOIVRDJMTTSBGQH7GLN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J6LUQOLOIVRDJMTTSBGQH7GLN4","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":"cf778f76ac2e9ee1b717fe8577072ba03deab5726d614b63fce25c2591841c93","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T20:00:43Z","title_canon_sha256":"de3d6fa0bd08356b4dfcc811afcf61e1862d43f318ee5d8247a1aff3cf3a9e27"},"schema_version":"1.0","source":{"id":"2606.28575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28575","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28575v1","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28575","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_12","alias_value":"J6LUQOLOIVRD","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_16","alias_value":"J6LUQOLOIVRDJMTT","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_8","alias_value":"J6LUQOLO","created_at":"2026-06-30T00:15:19Z"}],"graph_snapshots":[{"event_id":"sha256:a830d9edf507535d990fe984882631549720fecf93ebd8867f5dd7d8b9d537ea","target":"graph","created_at":"2026-06-30T00:15:19Z","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/2606.28575/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a logarithmically hyperviscous Navier-Stokes model on the three-dimensional torus with Lie-transport noise, which includes both transport and stretching. We prove that, for noise of sufficiently large intensity and high frequency, the system admits a unique global smooth solution with probability arbitrarily close to one. Unlike previous works, this physically motivated noise does not preserve energy or enstrophy, but rather circulation. Global well-posedness is established through a probabilistic mechanism that produces effective dissipation via a scaling limit. Crucially, this appro","authors_text":"Antonio Agresti, Eliseo Luongo, Federico Butori","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T20:00:43Z","title":"Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28575","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":"sha256:1a62a9965a90307c6542e2028c5d488a78078482e039b58e55eae0b8b63bdef1","target":"record","created_at":"2026-06-30T00:15:19Z","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":"cf778f76ac2e9ee1b717fe8577072ba03deab5726d614b63fce25c2591841c93","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T20:00:43Z","title_canon_sha256":"de3d6fa0bd08356b4dfcc811afcf61e1862d43f318ee5d8247a1aff3cf3a9e27"},"schema_version":"1.0","source":{"id":"2606.28575","kind":"arxiv","version":1}},"canonical_sha256":"4f9748396e456234b273904d03fccb6f07058dadb4aa6b9b69ec21e5ee196235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f9748396e456234b273904d03fccb6f07058dadb4aa6b9b69ec21e5ee196235","first_computed_at":"2026-06-30T00:15:19.607773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T00:15:19.607773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JoRIImE+sKA06EWi5TlycEE00MEnV5CHncr03Erc83RDSuKNQtupQX9q7QwQTInhhg1fhJqO+R1ycUn47djoAw==","signature_status":"signed_v1","signed_at":"2026-06-30T00:15:19.608169Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a62a9965a90307c6542e2028c5d488a78078482e039b58e55eae0b8b63bdef1","sha256:a830d9edf507535d990fe984882631549720fecf93ebd8867f5dd7d8b9d537ea"],"state_sha256":"e6b1355f87501f5d5a96f9b82de36ee3fe0078ac1746024ea6a756ccc53d9a11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f48rLD2bshkmejrx9pOVrqjjEHjo2f5Hvb5q4ZwkhxsChLhhJfZ/0oZ4KaLLlxKe60r9BnbNSvmFUPP/UcN/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:22:48.365849Z","bundle_sha256":"d5c9c5968526148dec374634fce1276e15608c5b2b37e986ad42d557bf22f92a"}}