{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3ZF6TVF5TQOKJB3QZRLZPTPPZO","short_pith_number":"pith:3ZF6TVF5","canonical_record":{"source":{"id":"2606.19060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T13:30:33Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"76eddd227bf9e493100f8cdec5f0e8d42f4ebb431ec8229824feec1bc49b87c7","abstract_canon_sha256":"8693da0880be33632a4601a88de78119c94ed17fdac3b95713a8b375349045a0"},"schema_version":"1.0"},"canonical_sha256":"de4be9d4bd9c1ca48770cc5797cdefcb8a8020fbb536bacd84f7ca0463d9465e","source":{"kind":"arxiv","id":"2606.19060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19060","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19060v1","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19060","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"3ZF6TVF5TQOK","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"3ZF6TVF5TQOKJB3Q","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"3ZF6TVF5","created_at":"2026-06-19T16:11:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3ZF6TVF5TQOKJB3QZRLZPTPPZO","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T13:30:33Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"76eddd227bf9e493100f8cdec5f0e8d42f4ebb431ec8229824feec1bc49b87c7","abstract_canon_sha256":"8693da0880be33632a4601a88de78119c94ed17fdac3b95713a8b375349045a0"},"schema_version":"1.0"},"canonical_sha256":"de4be9d4bd9c1ca48770cc5797cdefcb8a8020fbb536bacd84f7ca0463d9465e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:55.629414Z","signature_b64":"tshDqD6a366Xop+Ul2jTGTBlq0TyG1K69qqzLfZ5hNh0lptK53H00V+hixzPsy8kvCC1tdNIwcg0+sR+pvU6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de4be9d4bd9c1ca48770cc5797cdefcb8a8020fbb536bacd84f7ca0463d9465e","last_reissued_at":"2026-06-19T16:11:55.629026Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:55.629026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19060","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":"2026-06-19T16:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1Hn9yTm1b1l9uRP6mOO4QLap93IAcECK2v+1lWKV/7QKohlbzivzlbTnq6I6XzxdOAycHyuLpRkfKOlvOF5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:48:24.562009Z"},"content_sha256":"72cc31f195ff388bf8b6cf145f7843a50001bcbaac5b25f872dc588751beb1a9","schema_version":"1.0","event_id":"sha256:72cc31f195ff388bf8b6cf145f7843a50001bcbaac5b25f872dc588751beb1a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3ZF6TVF5TQOKJB3QZRLZPTPPZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delayed blow-up by transport noise for the 3D Navier-Stokes equation with Navier-slip boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Meng Zhao","submitted_at":"2026-06-17T13:30:33Z","abstract_excerpt":"We study the vorticity formulation of the 3D Navier-Stokes equation driven by transport noise in a periodic channel with Navier-slip boundary conditions. We consider both non-degenerate transport noise and degenerate tangential transport noise. For any prescribed $T>0$ and $\\epsilon>0$, we prove that, by choosing the noise intensity sufficiently large and concentrating the noise on sufficiently high modes, the solution exists up to $T$ with probability at least $1-\\epsilon$.\n  A main contribution of this work is to identify and analyze the interaction between enhanced dissipation induced by tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19060","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/2606.19060/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":"2026-06-19T16:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ijL3HLe9cuPGuHGF1qzO+TjpDE9m0PDKDYkvE7IXjYvnr0PX7DVUsb+S56cKvQeYGoE7mQQdBNgTTPilcQ0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:48:24.562931Z"},"content_sha256":"3e81b9905c78eb7b182e1d83134058ca4efd81079cf7330fe4cf4ea742982e58","schema_version":"1.0","event_id":"sha256:3e81b9905c78eb7b182e1d83134058ca4efd81079cf7330fe4cf4ea742982e58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/bundle.json","state_url":"https://pith.science/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/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":"2026-08-17T01:48:24Z","links":{"resolver":"https://pith.science/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO","bundle":"https://pith.science/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/bundle.json","state":"https://pith.science/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ZF6TVF5TQOKJB3QZRLZPTPPZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3ZF6TVF5TQOKJB3QZRLZPTPPZO","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":"8693da0880be33632a4601a88de78119c94ed17fdac3b95713a8b375349045a0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T13:30:33Z","title_canon_sha256":"76eddd227bf9e493100f8cdec5f0e8d42f4ebb431ec8229824feec1bc49b87c7"},"schema_version":"1.0","source":{"id":"2606.19060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19060","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19060v1","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19060","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"3ZF6TVF5TQOK","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_16","alias_value":"3ZF6TVF5TQOKJB3Q","created_at":"2026-06-19T16:11:55Z"},{"alias_kind":"pith_short_8","alias_value":"3ZF6TVF5","created_at":"2026-06-19T16:11:55Z"}],"graph_snapshots":[{"event_id":"sha256:3e81b9905c78eb7b182e1d83134058ca4efd81079cf7330fe4cf4ea742982e58","target":"graph","created_at":"2026-06-19T16:11:55Z","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/2606.19060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the vorticity formulation of the 3D Navier-Stokes equation driven by transport noise in a periodic channel with Navier-slip boundary conditions. We consider both non-degenerate transport noise and degenerate tangential transport noise. For any prescribed $T>0$ and $\\epsilon>0$, we prove that, by choosing the noise intensity sufficiently large and concentrating the noise on sufficiently high modes, the solution exists up to $T$ with probability at least $1-\\epsilon$.\n  A main contribution of this work is to identify and analyze the interaction between enhanced dissipation induced by tr","authors_text":"Meng Zhao","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T13:30:33Z","title":"Delayed blow-up by transport noise for the 3D Navier-Stokes equation with Navier-slip boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19060","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":"sha256:72cc31f195ff388bf8b6cf145f7843a50001bcbaac5b25f872dc588751beb1a9","target":"record","created_at":"2026-06-19T16:11:55Z","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":"8693da0880be33632a4601a88de78119c94ed17fdac3b95713a8b375349045a0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T13:30:33Z","title_canon_sha256":"76eddd227bf9e493100f8cdec5f0e8d42f4ebb431ec8229824feec1bc49b87c7"},"schema_version":"1.0","source":{"id":"2606.19060","kind":"arxiv","version":1}},"canonical_sha256":"de4be9d4bd9c1ca48770cc5797cdefcb8a8020fbb536bacd84f7ca0463d9465e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de4be9d4bd9c1ca48770cc5797cdefcb8a8020fbb536bacd84f7ca0463d9465e","first_computed_at":"2026-06-19T16:11:55.629026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:55.629026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tshDqD6a366Xop+Ul2jTGTBlq0TyG1K69qqzLfZ5hNh0lptK53H00V+hixzPsy8kvCC1tdNIwcg0+sR+pvU6Cw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:55.629414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72cc31f195ff388bf8b6cf145f7843a50001bcbaac5b25f872dc588751beb1a9","sha256:3e81b9905c78eb7b182e1d83134058ca4efd81079cf7330fe4cf4ea742982e58"],"state_sha256":"5dec5fbbf1384da2062abf34a28dcce7a9246395e09aa9800569cc8b2170b561"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSWE3DPuk/AX/r0MEiPCk+fCtHr+Tfg9MWWvaJ+qJ3k0UdGGH05iLu1Cy0bAwOFIOUQ5e/XrDmNrvQvR7gN8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:48:24.629950Z","bundle_sha256":"8c2671407e9836cfb1059a9b5180cd78fa4e4f57dec4f57643ef0637057484a1"}}