{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7UB744OQZGTXJ5YKUVUD5KWXIB","short_pith_number":"pith:7UB744OQ","canonical_record":{"source":{"id":"2605.03182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-04T21:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"8e686058969549895cd4539341b814df716a637f55e9bfe53f79e8895b220d2b","abstract_canon_sha256":"ad3b3efa525d3f9cb3cd7c45872a157e44d9bf2b10e5b0ca6c099ec4c3618ae2"},"schema_version":"1.0"},"canonical_sha256":"fd03fe71d0c9a774f70aa5683eaad7405fa6a5f0ef6e8f4e922db16eb5fb3ac5","source":{"kind":"arxiv","id":"2605.03182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03182","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03182v2","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03182","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"7UB744OQZGTX","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_16","alias_value":"7UB744OQZGTXJ5YK","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_8","alias_value":"7UB744OQ","created_at":"2026-05-28T02:04:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7UB744OQZGTXJ5YKUVUD5KWXIB","target":"record","payload":{"canonical_record":{"source":{"id":"2605.03182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-04T21:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"8e686058969549895cd4539341b814df716a637f55e9bfe53f79e8895b220d2b","abstract_canon_sha256":"ad3b3efa525d3f9cb3cd7c45872a157e44d9bf2b10e5b0ca6c099ec4c3618ae2"},"schema_version":"1.0"},"canonical_sha256":"fd03fe71d0c9a774f70aa5683eaad7405fa6a5f0ef6e8f4e922db16eb5fb3ac5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:48.934546Z","signature_b64":"qRpbmUg5rBC94e0xdzOMScn3Vw6bLxMRVdA4t1ldxh2Ru7HO9fZQ0Y0MjY0KPA/R346IGlYtU9xceFS+XoFSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd03fe71d0c9a774f70aa5683eaad7405fa6a5f0ef6e8f4e922db16eb5fb3ac5","last_reissued_at":"2026-05-28T02:04:48.934106Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:48.934106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.03182","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":"2026-05-28T02:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGjcdOxYpbW2bP6HtP1RXQTVoeFuSYD0U3NeE9vSUNZUCGPM8CLRPGjORsd1GhEr1vxvcHR7b5DkG+VCxZnSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:37:17.806660Z"},"content_sha256":"3123694c91387875d18bbfb49765204021645c27d8d6d7324a229fbfcff0798e","schema_version":"1.0","event_id":"sha256:3123694c91387875d18bbfb49765204021645c27d8d6d7324a229fbfcff0798e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7UB744OQZGTXJ5YKUVUD5KWXIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential integrability of the solution to the stochastic Burgers equation driven by white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4).","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enrico Priola, Francesco C. De Vecchi, Josef Jan\\'ak","submitted_at":"2026-05-04T21:46:29Z","abstract_excerpt":"We study stochastic Burgers equation driven by a rough noise $(-\\Delta)^{\\gamma} dW_t$, where $\\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\\gamma \\in [0,1/4)$. We prove exponential estimates for the solution $X_t^x$, starting from $x \\in L^2(0,1)$, by showing that there exists some constant $\\lambda >0$ for which \\begin{equation} \\label{ds} \\mathbb{E}\n  \\left[\\exp\\left(\\lambda \\sup_{t\\in[0,T]}\\|X_t^x\\|_{L^2(0,1)}^2 \\right) \\right]< \\infty. \\end{equation} This estimate was known only in the case of trace class noise when $-1/2 <\\gamma < -1/4 $ since in tha"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that there exists some constant λ >0 for which E[ exp( λ sup_{t∈[0,T]} ||X_t^x ||_{L^2(0,1)}^2 ) ] < ∞ for γ ∈ [0,1/4).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Boué-Dupuis method together with the auxiliary argument from Da Prato-Debussche (Potential Anal. 2007) extends without modification to the regime γ ∈ [0,1/4) where the Itô formula is unavailable.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The solution X to the stochastic Burgers equation with noise roughness γ < 1/4 satisfies E[exp(λ sup_t ||X_t||_L2^2)] < ∞ for some λ > 0.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e3b64fc462612b3e55880bf4371803884deb4e6202ca36e1d56ccb71214061a1"},"source":{"id":"2605.03182","kind":"arxiv","version":2},"verdict":{"id":"a3885cf8-0019-4a77-b672-95ab18eb4a13","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:15:34.012903Z","strongest_claim":"We prove that there exists some constant λ >0 for which E[ exp( λ sup_{t∈[0,T]} ||X_t^x ||_{L^2(0,1)}^2 ) ] < ∞ for γ ∈ [0,1/4).","one_line_summary":"The solution X to the stochastic Burgers equation with noise roughness γ < 1/4 satisfies E[exp(λ sup_t ||X_t||_L2^2)] < ∞ for some λ > 0.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Boué-Dupuis method together with the auxiliary argument from Da Prato-Debussche (Potential Anal. 2007) extends without modification to the regime γ ∈ [0,1/4) where the Itô formula is unavailable.","pith_extraction_headline":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03182/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T14:35:53.363365Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T01:31:22.039907Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:36:11.770048Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8f51df3e9b594fa64ca4d35e0a0369fcc98b674ba69862da6688da6c261ede56"},"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":"a3885cf8-0019-4a77-b672-95ab18eb4a13"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T02:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgpTAShbxQoyzC7y2jTdismCLJ2T22MnMR3NNfscUJk4UEnf8VWwsb4Mkm+CshIxyI2A826a3I/BNe3aPJvxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:37:17.807195Z"},"content_sha256":"467a9c273e9b4fdc513df3384db5278dde95dbaef0e0e09eac71da5e26c0c1f1","schema_version":"1.0","event_id":"sha256:467a9c273e9b4fdc513df3384db5278dde95dbaef0e0e09eac71da5e26c0c1f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/bundle.json","state_url":"https://pith.science/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/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":"2026-06-08T21:37:17Z","links":{"resolver":"https://pith.science/pith/7UB744OQZGTXJ5YKUVUD5KWXIB","bundle":"https://pith.science/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/bundle.json","state":"https://pith.science/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UB744OQZGTXJ5YKUVUD5KWXIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7UB744OQZGTXJ5YKUVUD5KWXIB","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":"ad3b3efa525d3f9cb3cd7c45872a157e44d9bf2b10e5b0ca6c099ec4c3618ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-04T21:46:29Z","title_canon_sha256":"8e686058969549895cd4539341b814df716a637f55e9bfe53f79e8895b220d2b"},"schema_version":"1.0","source":{"id":"2605.03182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03182","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03182v2","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03182","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"7UB744OQZGTX","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_16","alias_value":"7UB744OQZGTXJ5YK","created_at":"2026-05-28T02:04:48Z"},{"alias_kind":"pith_short_8","alias_value":"7UB744OQ","created_at":"2026-05-28T02:04:48Z"}],"graph_snapshots":[{"event_id":"sha256:467a9c273e9b4fdc513df3384db5278dde95dbaef0e0e09eac71da5e26c0c1f1","target":"graph","created_at":"2026-05-28T02:04:48Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that there exists some constant λ >0 for which E[ exp( λ sup_{t∈[0,T]} ||X_t^x ||_{L^2(0,1)}^2 ) ] < ∞ for γ ∈ [0,1/4)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The Boué-Dupuis method together with the auxiliary argument from Da Prato-Debussche (Potential Anal. 2007) extends without modification to the regime γ ∈ [0,1/4) where the Itô formula is unavailable."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The solution X to the stochastic Burgers equation with noise roughness γ < 1/4 satisfies E[exp(λ sup_t ||X_t||_L2^2)] < ∞ for some λ > 0."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4)."}],"snapshot_sha256":"e3b64fc462612b3e55880bf4371803884deb4e6202ca36e1d56ccb71214061a1"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T14:35:53.363365Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T01:31:22.039907Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T15:36:11.770048Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.03182/integrity.json","findings":[],"snapshot_sha256":"8f51df3e9b594fa64ca4d35e0a0369fcc98b674ba69862da6688da6c261ede56","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study stochastic Burgers equation driven by a rough noise $(-\\Delta)^{\\gamma} dW_t$, where $\\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\\gamma \\in [0,1/4)$. We prove exponential estimates for the solution $X_t^x$, starting from $x \\in L^2(0,1)$, by showing that there exists some constant $\\lambda >0$ for which \\begin{equation} \\label{ds} \\mathbb{E}\n  \\left[\\exp\\left(\\lambda \\sup_{t\\in[0,T]}\\|X_t^x\\|_{L^2(0,1)}^2 \\right) \\right]< \\infty. \\end{equation} This estimate was known only in the case of trace class noise when $-1/2 <\\gamma < -1/4 $ since in tha","authors_text":"Enrico Priola, Francesco C. De Vecchi, Josef Jan\\'ak","cross_cats":[],"headline":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4).","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-04T21:46:29Z","title":"Exponential integrability of the solution to the stochastic Burgers equation driven by white noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.03182","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T17:15:34.012903Z","id":"a3885cf8-0019-4a77-b672-95ab18eb4a13","model_set":{"reader":"grok-4.3"},"one_line_summary":"The solution X to the stochastic Burgers equation with noise roughness γ < 1/4 satisfies E[exp(λ sup_t ||X_t||_L2^2)] < ∞ for some λ > 0.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The stochastic Burgers equation driven by rough white noise has finite exponential moments of the squared L2 norm for gamma in [0,1/4).","strongest_claim":"We prove that there exists some constant λ >0 for which E[ exp( λ sup_{t∈[0,T]} ||X_t^x ||_{L^2(0,1)}^2 ) ] < ∞ for γ ∈ [0,1/4).","weakest_assumption":"The Boué-Dupuis method together with the auxiliary argument from Da Prato-Debussche (Potential Anal. 2007) extends without modification to the regime γ ∈ [0,1/4) where the Itô formula is unavailable."}},"verdict_id":"a3885cf8-0019-4a77-b672-95ab18eb4a13"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3123694c91387875d18bbfb49765204021645c27d8d6d7324a229fbfcff0798e","target":"record","created_at":"2026-05-28T02:04:48Z","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":"ad3b3efa525d3f9cb3cd7c45872a157e44d9bf2b10e5b0ca6c099ec4c3618ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-04T21:46:29Z","title_canon_sha256":"8e686058969549895cd4539341b814df716a637f55e9bfe53f79e8895b220d2b"},"schema_version":"1.0","source":{"id":"2605.03182","kind":"arxiv","version":2}},"canonical_sha256":"fd03fe71d0c9a774f70aa5683eaad7405fa6a5f0ef6e8f4e922db16eb5fb3ac5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd03fe71d0c9a774f70aa5683eaad7405fa6a5f0ef6e8f4e922db16eb5fb3ac5","first_computed_at":"2026-05-28T02:04:48.934106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:48.934106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qRpbmUg5rBC94e0xdzOMScn3Vw6bLxMRVdA4t1ldxh2Ru7HO9fZQ0Y0MjY0KPA/R346IGlYtU9xceFS+XoFSDw==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:48.934546Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.03182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3123694c91387875d18bbfb49765204021645c27d8d6d7324a229fbfcff0798e","sha256:467a9c273e9b4fdc513df3384db5278dde95dbaef0e0e09eac71da5e26c0c1f1"],"state_sha256":"853b5c1d3d4f7de4ada26d09ac8c8df099f0ccb79c8818f908f9fb45847ef95e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gAcN+8XXUK1QSHjzwoLBRnKNyQ9Ql+C9z/KNoorLZfH+Z5GUJtg4u37b5Ll/S05CuE5KyWd0mDvUqHG1AwjgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:37:17.809764Z","bundle_sha256":"6273139bdcffdbe8b7cfe728e659b09613bd02bbb99453cc6bcfc5c0551c5b62"}}