{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN","short_pith_number":"pith:I4P3TFQY","canonical_record":{"source":{"id":"2608.11553","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T01:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"fa0f14fbbece6f8ce3f9c2b57d6b07563b929c67bbda89f126c2fa650665ef53","abstract_canon_sha256":"5ee98c8e0874a5b575b0c09087d9505c2b7bc50d8951e5524753297e316dcc68"},"schema_version":"1.0"},"canonical_sha256":"471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8","source":{"kind":"arxiv","id":"2608.11553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11553","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11553v1","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11553","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"I4P3TFQY7OID","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_16","alias_value":"I4P3TFQY7OIDVKWP","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_8","alias_value":"I4P3TFQY","created_at":"2026-08-13T00:22:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11553","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T01:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"fa0f14fbbece6f8ce3f9c2b57d6b07563b929c67bbda89f126c2fa650665ef53","abstract_canon_sha256":"5ee98c8e0874a5b575b0c09087d9505c2b7bc50d8951e5524753297e316dcc68"},"schema_version":"1.0"},"canonical_sha256":"471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T00:22:10.254129Z","signature_b64":"yAl83HJ0DacODrwHNGpP4JKe0Qv4IIY/lKxqHc/onts2mEzMb/yWHYJhQ+MIgrfaLoLzf/YoAUS+DpTK+yDVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8","last_reissued_at":"2026-08-13T00:22:10.252254Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T00:22:10.252254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11553","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":"2026-08-13T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcaSJTZoCltPHHpn/vR5C9ZKiVT4BdtetEadEJJl9ujYSxvKFrJSQQ50BhFjk5lirkiXrhkrdlb/+lyElJt6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T17:21:50.083359Z"},"content_sha256":"bf6fd336eccdb308e56d117e6c2d6e014bc6989d23c126489e49126075ceb688","schema_version":"1.0","event_id":"sha256:bf6fd336eccdb308e56d117e6c2d6e014bc6989d23c126489e49126075ceb688"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Beir\\~ao da Veiga, Jiaqi Yang","submitted_at":"2026-08-12T01:40:31Z","abstract_excerpt":"We construct an explicit pure-swirl solution of the forced three-dimensional Navier--Stokes equations in a circular cylinder. For every $T>0$ and $1\\le p,q<\\infty$ with $1/p+1/q>1$, the force belongs to $L^q(0,T;L^p(D))$ and is smooth for $t<T$. Moreover, the same construction always yields the additional energy-class property $f\\in L^1(0,T;L^2(D))$. The solution is classical on $[0,T)$, extends strongly in $L^2(D)$ to the unique Leray--Hopf solution at time $T$, and satisfies the energy equality, while $\\|v(t)\\|_{L^\\infty(D)}\\to\\infty$ as $t\\uparrow T$. We determine the exact mixed-norm range"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11553","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/2608.11553/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":"2026-08-13T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsJuLcBoZERP2anAxCQTC15m/L2+wCnd8lLP7vkYD+NRipILbfZMJzQzU77aSkfyqqtgW8DwdGhPbcVouiozCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T17:21:50.083695Z"},"content_sha256":"620451bc8d204a288067476b562389555a455655a21b55c2cb3ec69d15e6132d","schema_version":"1.0","event_id":"sha256:620451bc8d204a288067476b562389555a455655a21b55c2cb3ec69d15e6132d"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11511-009-0039-6) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"G. Koch, N. Nadirashvili, G. Seregin and V. ˇSver´ ak,Liouville theorems for the Navier–Stokes equations and applications, Acta Math.203(2009), no. 1, 83–105, doi:10.1007/s11511-009- 0039-6","arxiv_id":"2608.11553","detector":"doi_compliance","evidence":{"ref_index":13,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11511-009-","reconstructed_doi":"10.1007/s11511-009-0039-6"},"severity":"advisory","ref_index":13,"audited_at":"2026-08-16T01:08:14.486230Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11511-009-0039-6","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"0e5880b1d8b4a082fd325933fe6e15803ac001acd6ad418d3dde3df1560c039b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":20337,"payload_sha256":"48829c4fbb92a68e43ae2d2eabdadd5f4be93f2979956b89c67af00860f4018a","signature_b64":"/jnbywhvMvPA77aiMGuuFwTnkMXxuKA8LkYM5YMZwvSEzoLQ8DyEMamGbgNTXfuLtGHqV38JcMBohpbfYiCSDw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-16T01:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y/SE/ZeJxPVE63Jd8YO5vr5EZ7M+blUtau/t1zcJA0S+Q81ZI17ehSOzhcqqFHvi5ETKQSw+P1T+vP0E7KdjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T17:21:50.086786Z"},"content_sha256":"4a85b70a1e6e9ea7451967a09c758dcc75407a6ec0eade4a77657cc0db716ce9","schema_version":"1.0","event_id":"sha256:4a85b70a1e6e9ea7451967a09c758dcc75407a6ec0eade4a77657cc0db716ce9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/bundle.json","state_url":"https://pith.science/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/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":"2026-08-22T17:21:50Z","links":{"resolver":"https://pith.science/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN","bundle":"https://pith.science/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/bundle.json","state":"https://pith.science/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4P3TFQY7OIDVKWPZOKAOH4WHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I4P3TFQY7OIDVKWPZOKAOH4WHN","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5ee98c8e0874a5b575b0c09087d9505c2b7bc50d8951e5524753297e316dcc68","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T01:40:31Z","title_canon_sha256":"fa0f14fbbece6f8ce3f9c2b57d6b07563b929c67bbda89f126c2fa650665ef53"},"schema_version":"1.0","source":{"id":"2608.11553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11553","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11553v1","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11553","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"I4P3TFQY7OID","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_16","alias_value":"I4P3TFQY7OIDVKWP","created_at":"2026-08-13T00:22:10Z"},{"alias_kind":"pith_short_8","alias_value":"I4P3TFQY","created_at":"2026-08-13T00:22:10Z"}],"graph_snapshots":[{"event_id":"sha256:620451bc8d204a288067476b562389555a455655a21b55c2cb3ec69d15e6132d","target":"graph","created_at":"2026-08-13T00:22:10Z","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/2608.11553/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct an explicit pure-swirl solution of the forced three-dimensional Navier--Stokes equations in a circular cylinder. For every $T>0$ and $1\\le p,q<\\infty$ with $1/p+1/q>1$, the force belongs to $L^q(0,T;L^p(D))$ and is smooth for $t<T$. Moreover, the same construction always yields the additional energy-class property $f\\in L^1(0,T;L^2(D))$. The solution is classical on $[0,T)$, extends strongly in $L^2(D)$ to the unique Leray--Hopf solution at time $T$, and satisfies the energy equality, while $\\|v(t)\\|_{L^\\infty(D)}\\to\\infty$ as $t\\uparrow T$. We determine the exact mixed-norm range","authors_text":"Hugo Beir\\~ao da Veiga, Jiaqi Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T01:40:31Z","title":"Pure-swirl loss of boundedness under $L^1_tL^2_x$ forcing: exact mixed-norm ranges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11553","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:bf6fd336eccdb308e56d117e6c2d6e014bc6989d23c126489e49126075ceb688","target":"record","created_at":"2026-08-13T00:22:10Z","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":"5ee98c8e0874a5b575b0c09087d9505c2b7bc50d8951e5524753297e316dcc68","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T01:40:31Z","title_canon_sha256":"fa0f14fbbece6f8ce3f9c2b57d6b07563b929c67bbda89f126c2fa650665ef53"},"schema_version":"1.0","source":{"id":"2608.11553","kind":"arxiv","version":1}},"canonical_sha256":"471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"471fb99618fb903aaacfcb94071f963b677010160d86466b4b71342d917fb8f8","first_computed_at":"2026-08-13T00:22:10.252254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T00:22:10.252254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yAl83HJ0DacODrwHNGpP4JKe0Qv4IIY/lKxqHc/onts2mEzMb/yWHYJhQ+MIgrfaLoLzf/YoAUS+DpTK+yDVDg==","signature_status":"signed_v1","signed_at":"2026-08-13T00:22:10.254129Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf6fd336eccdb308e56d117e6c2d6e014bc6989d23c126489e49126075ceb688","sha256:620451bc8d204a288067476b562389555a455655a21b55c2cb3ec69d15e6132d","sha256:4a85b70a1e6e9ea7451967a09c758dcc75407a6ec0eade4a77657cc0db716ce9"],"state_sha256":"84bbd9e4293ab943d66102974418631db9194d29205d55e83f3c9bf2120a6fe0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N25fuIS82gvnP81u5EhOj0J2cOA9WxquWoO4gBxg1B6GmnxVxK7BfwfBLOiZLvCnwgbOALkFIDibbsoITeG3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T17:21:50.088230Z","bundle_sha256":"804be297ae6004a6babef1a498cd8bd46a4b5886104d0a8981e4b90d95747cec"}}