{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WKXVGELWI7QQEDAKBYG5HKJAQL","short_pith_number":"pith:WKXVGELW","canonical_record":{"source":{"id":"2409.17697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-26T10:06:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"74b6f21f4f230ca8c9cdea324805eaae01d168e28435f4f456a2f40c03477b9c","abstract_canon_sha256":"94724c301d066899c96d73880a7cd59e6d08cb0a66a558ff3d4918f602ee9e82"},"schema_version":"1.0"},"canonical_sha256":"b2af53117647e1020c0a0e0dd3a92082fa40f7e36e0ca0611d2702400a1ce742","source":{"kind":"arxiv","id":"2409.17697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.17697","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2409.17697v2","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.17697","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"WKXVGELWI7QQ","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"WKXVGELWI7QQEDAK","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"WKXVGELW","created_at":"2026-06-26T01:15:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WKXVGELWI7QQEDAKBYG5HKJAQL","target":"record","payload":{"canonical_record":{"source":{"id":"2409.17697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-26T10:06:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"74b6f21f4f230ca8c9cdea324805eaae01d168e28435f4f456a2f40c03477b9c","abstract_canon_sha256":"94724c301d066899c96d73880a7cd59e6d08cb0a66a558ff3d4918f602ee9e82"},"schema_version":"1.0"},"canonical_sha256":"b2af53117647e1020c0a0e0dd3a92082fa40f7e36e0ca0611d2702400a1ce742","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:42.746061Z","signature_b64":"PCDPvAvRmL3jOnJHuZ0W9I+wjSQD77/00a4bogFLssZqoshzPCre+FLkX9jPUgKmv2kPGi5USjN0IfXK5v4XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2af53117647e1020c0a0e0dd3a92082fa40f7e36e0ca0611d2702400a1ce742","last_reissued_at":"2026-06-26T01:15:42.745507Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:42.745507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.17697","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lqLay7JraBZdccCZLn+UErqe9M4HjZThPBYRkCnUB7kGk22ifxSDaePGHYgErtea4DOTE+D8jyJI1hCWVd8SCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:16:21.357450Z"},"content_sha256":"dce5774eba189692af2ff7571ae42f8fc1c89b334fe9c5bd8fb0a4fbb37e0b5b","schema_version":"1.0","event_id":"sha256:dce5774eba189692af2ff7571ae42f8fc1c89b334fe9c5bd8fb0a4fbb37e0b5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WKXVGELWI7QQEDAKBYG5HKJAQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inviscid Limit of the Stochastic Hyperviscous Navier-Stokes Equations and Invariant Measures for the Euler Equations in $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Matteo Ferrari, Zdzis{\\l}aw Brze\\'zniak","submitted_at":"2024-09-26T10:06:20Z","abstract_excerpt":"We prove the existence and some moment estimates for an invariant measure $\\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\\mathbb R^2$ and with highly regular initial data. The result is achieved by first showing the existence of Markov stationary processes which solve the hyperviscous $2$D Navier-Stokes equations with kinematic viscosity $\\nu>0$ and an additive stochastic noise scaling as $\\sqrt \\nu$. We then study the inviscid limit and prove that, as $\\nu$ tends to $0$, these processes converge, in an appropriate trajectory space, to a pathwise st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17697","kind":"arxiv","version":2},"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/2409.17697/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":"2026-06-26T01:15:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vvb9RqgcwkQoG3crvo6aRJ8bMEKh9TNm8kJSQwXVb6Xa8ojLXGGPt5rhdr73Gb/f8set/RrR7XrIeDA3BNg4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:16:21.357830Z"},"content_sha256":"5ba6457c2966d9a8032b5cd877b4bb1c9d48756b26e46bf95563a6db694f518e","schema_version":"1.0","event_id":"sha256:5ba6457c2966d9a8032b5cd877b4bb1c9d48756b26e46bf95563a6db694f518e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/bundle.json","state_url":"https://pith.science/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/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":"2026-07-01T12:16:21Z","links":{"resolver":"https://pith.science/pith/WKXVGELWI7QQEDAKBYG5HKJAQL","bundle":"https://pith.science/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/bundle.json","state":"https://pith.science/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKXVGELWI7QQEDAKBYG5HKJAQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WKXVGELWI7QQEDAKBYG5HKJAQL","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":"94724c301d066899c96d73880a7cd59e6d08cb0a66a558ff3d4918f602ee9e82","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-26T10:06:20Z","title_canon_sha256":"74b6f21f4f230ca8c9cdea324805eaae01d168e28435f4f456a2f40c03477b9c"},"schema_version":"1.0","source":{"id":"2409.17697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.17697","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"2409.17697v2","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.17697","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"WKXVGELWI7QQ","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_16","alias_value":"WKXVGELWI7QQEDAK","created_at":"2026-06-26T01:15:42Z"},{"alias_kind":"pith_short_8","alias_value":"WKXVGELW","created_at":"2026-06-26T01:15:42Z"}],"graph_snapshots":[{"event_id":"sha256:5ba6457c2966d9a8032b5cd877b4bb1c9d48756b26e46bf95563a6db694f518e","target":"graph","created_at":"2026-06-26T01:15:42Z","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/2409.17697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence and some moment estimates for an invariant measure $\\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\\mathbb R^2$ and with highly regular initial data. The result is achieved by first showing the existence of Markov stationary processes which solve the hyperviscous $2$D Navier-Stokes equations with kinematic viscosity $\\nu>0$ and an additive stochastic noise scaling as $\\sqrt \\nu$. We then study the inviscid limit and prove that, as $\\nu$ tends to $0$, these processes converge, in an appropriate trajectory space, to a pathwise st","authors_text":"Matteo Ferrari, Zdzis{\\l}aw Brze\\'zniak","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-26T10:06:20Z","title":"Inviscid Limit of the Stochastic Hyperviscous Navier-Stokes Equations and Invariant Measures for the Euler Equations in $\\mathbb R^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17697","kind":"arxiv","version":2},"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:dce5774eba189692af2ff7571ae42f8fc1c89b334fe9c5bd8fb0a4fbb37e0b5b","target":"record","created_at":"2026-06-26T01:15:42Z","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":"94724c301d066899c96d73880a7cd59e6d08cb0a66a558ff3d4918f602ee9e82","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-26T10:06:20Z","title_canon_sha256":"74b6f21f4f230ca8c9cdea324805eaae01d168e28435f4f456a2f40c03477b9c"},"schema_version":"1.0","source":{"id":"2409.17697","kind":"arxiv","version":2}},"canonical_sha256":"b2af53117647e1020c0a0e0dd3a92082fa40f7e36e0ca0611d2702400a1ce742","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2af53117647e1020c0a0e0dd3a92082fa40f7e36e0ca0611d2702400a1ce742","first_computed_at":"2026-06-26T01:15:42.745507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:42.745507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PCDPvAvRmL3jOnJHuZ0W9I+wjSQD77/00a4bogFLssZqoshzPCre+FLkX9jPUgKmv2kPGi5USjN0IfXK5v4XBg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:42.746061Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.17697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dce5774eba189692af2ff7571ae42f8fc1c89b334fe9c5bd8fb0a4fbb37e0b5b","sha256:5ba6457c2966d9a8032b5cd877b4bb1c9d48756b26e46bf95563a6db694f518e"],"state_sha256":"99d74e0edd02b1577d59bba485d2d656076ce2f9eab723d2eb0bcaea73abc1d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9T11cuVD11PsjYcAtPJwndHnEgOJ9lq24S3pAl5jj7TWa9lrM1bOH1qI84KnwYkUp5atpzHmpuaIsaGA7yIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:16:21.359880Z","bundle_sha256":"92eb5b5e140e3556359d65b23698e146d45188dcc997c28765521c34152c8a8f"}}