{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ERVKZPONWTN6JPXJRD5YRSFADI","short_pith_number":"pith:ERVKZPON","canonical_record":{"source":{"id":"1005.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-20T19:40:13Z","cross_cats_sorted":["math-ph","math.CV","math.MP","math.PR"],"title_canon_sha256":"0a79eec200c1be245e08c8d51df746c732f72a2eec7c5e057d8cb28d38720ef0","abstract_canon_sha256":"e22698a44dfeb09d18f028a032b0f81cd8f0193bf3ea0cc9ecea2991ecc251d6"},"schema_version":"1.0"},"canonical_sha256":"246aacbdcdb4dbe4bee988fb88c8a01a0446880358b725c1ac9d94caba91e2c2","source":{"kind":"arxiv","id":"1005.3804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3804","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3804v1","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3804","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"ERVKZPONWTN6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"ERVKZPONWTN6JPXJ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"ERVKZPON","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ERVKZPONWTN6JPXJRD5YRSFADI","target":"record","payload":{"canonical_record":{"source":{"id":"1005.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-20T19:40:13Z","cross_cats_sorted":["math-ph","math.CV","math.MP","math.PR"],"title_canon_sha256":"0a79eec200c1be245e08c8d51df746c732f72a2eec7c5e057d8cb28d38720ef0","abstract_canon_sha256":"e22698a44dfeb09d18f028a032b0f81cd8f0193bf3ea0cc9ecea2991ecc251d6"},"schema_version":"1.0"},"canonical_sha256":"246aacbdcdb4dbe4bee988fb88c8a01a0446880358b725c1ac9d94caba91e2c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:11.677734Z","signature_b64":"TetLRSBgl3SrYifO2AhLNGEIdaQ3WevWer/jieFep/hoZS6+lMJx9NCMAfSyLlGyQoV8C1mYEgdUhTznBB4hBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"246aacbdcdb4dbe4bee988fb88c8a01a0446880358b725c1ac9d94caba91e2c2","last_reissued_at":"2026-05-18T04:23:11.677274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:11.677274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.3804","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":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5VD8b2ZgqjrNx9unAx/RANistEBjRfMS2cxHrRRisk02euNiZUqxyZbT0q5p6rU8CxXk8Fa+PppR7KMG7/xDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:24:22.284833Z"},"content_sha256":"a0cd01c5e95f0d78a9d6c65d750eeaf8b54caeb4ab6ff1eba616dac27e84b8ea","schema_version":"1.0","event_id":"sha256:a0cd01c5e95f0d78a9d6c65d750eeaf8b54caeb4ab6ff1eba616dac27e84b8ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ERVKZPONWTN6JPXJRD5YRSFADI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Hassan Allouba","submitted_at":"2010-05-20T19:40:13Z","abstract_excerpt":"We introduce a new imaginary-Brownian-time-Brownian-angle process, which we also call the linear-Kuramoto-Sivashinsky process (LKSP). Building on our techniques in two recent articles involving the connection of Brownian-time processes to fourth order PDEs, we give an explicit solution to a linearized Kuramoto-Sivashinsky PDE in $\\scriptstyle d$-dimensional space: $\\scriptstyle{\\eight{u_t=-\\frac18\\Delta^2u-\\frac12\\Delta u-\\frac12u}}$.\n  The solution is given in terms of a functional of our LKSP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3804","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":""},"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":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/MXemo3VwUXASYxZIUBeAIsbTs8i8sO0JqjMDcNw6+0kM7r1C439uPt2idIGqnsZK/mLBTH+wGwaLHqHmm7ZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:24:22.285181Z"},"content_sha256":"42c9136779cf5872b9dbf4e6041b8445b2dcac08c7ed8733133d0cbe1c39fd71","schema_version":"1.0","event_id":"sha256:42c9136779cf5872b9dbf4e6041b8445b2dcac08c7ed8733133d0cbe1c39fd71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERVKZPONWTN6JPXJRD5YRSFADI/bundle.json","state_url":"https://pith.science/pith/ERVKZPONWTN6JPXJRD5YRSFADI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERVKZPONWTN6JPXJRD5YRSFADI/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":"2026-06-30T20:24:22Z","links":{"resolver":"https://pith.science/pith/ERVKZPONWTN6JPXJRD5YRSFADI","bundle":"https://pith.science/pith/ERVKZPONWTN6JPXJRD5YRSFADI/bundle.json","state":"https://pith.science/pith/ERVKZPONWTN6JPXJRD5YRSFADI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERVKZPONWTN6JPXJRD5YRSFADI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ERVKZPONWTN6JPXJRD5YRSFADI","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":"e22698a44dfeb09d18f028a032b0f81cd8f0193bf3ea0cc9ecea2991ecc251d6","cross_cats_sorted":["math-ph","math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-20T19:40:13Z","title_canon_sha256":"0a79eec200c1be245e08c8d51df746c732f72a2eec7c5e057d8cb28d38720ef0"},"schema_version":"1.0","source":{"id":"1005.3804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3804","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3804v1","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3804","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"ERVKZPONWTN6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"ERVKZPONWTN6JPXJ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"ERVKZPON","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:42c9136779cf5872b9dbf4e6041b8445b2dcac08c7ed8733133d0cbe1c39fd71","target":"graph","created_at":"2026-05-18T04:23:11Z","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"},"paper":{"abstract_excerpt":"We introduce a new imaginary-Brownian-time-Brownian-angle process, which we also call the linear-Kuramoto-Sivashinsky process (LKSP). Building on our techniques in two recent articles involving the connection of Brownian-time processes to fourth order PDEs, we give an explicit solution to a linearized Kuramoto-Sivashinsky PDE in $\\scriptstyle d$-dimensional space: $\\scriptstyle{\\eight{u_t=-\\frac18\\Delta^2u-\\frac12\\Delta u-\\frac12u}}$.\n  The solution is given in terms of a functional of our LKSP.","authors_text":"Hassan Allouba","cross_cats":["math-ph","math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-20T19:40:13Z","title":"A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3804","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:a0cd01c5e95f0d78a9d6c65d750eeaf8b54caeb4ab6ff1eba616dac27e84b8ea","target":"record","created_at":"2026-05-18T04:23:11Z","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":"e22698a44dfeb09d18f028a032b0f81cd8f0193bf3ea0cc9ecea2991ecc251d6","cross_cats_sorted":["math-ph","math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-20T19:40:13Z","title_canon_sha256":"0a79eec200c1be245e08c8d51df746c732f72a2eec7c5e057d8cb28d38720ef0"},"schema_version":"1.0","source":{"id":"1005.3804","kind":"arxiv","version":1}},"canonical_sha256":"246aacbdcdb4dbe4bee988fb88c8a01a0446880358b725c1ac9d94caba91e2c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"246aacbdcdb4dbe4bee988fb88c8a01a0446880358b725c1ac9d94caba91e2c2","first_computed_at":"2026-05-18T04:23:11.677274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:11.677274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TetLRSBgl3SrYifO2AhLNGEIdaQ3WevWer/jieFep/hoZS6+lMJx9NCMAfSyLlGyQoV8C1mYEgdUhTznBB4hBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:11.677734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0cd01c5e95f0d78a9d6c65d750eeaf8b54caeb4ab6ff1eba616dac27e84b8ea","sha256:42c9136779cf5872b9dbf4e6041b8445b2dcac08c7ed8733133d0cbe1c39fd71"],"state_sha256":"2666a70eff80324b9d7c084ec6f733708bf328f4d54c0267c85d947e8603e102"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7fMIpgJ6Bnmn5N/QhvH/jCJ6qW9FlVaTDPV22snQdmr19CkECeUlU+1mM3cKu6qv4NAxLtfmTb/a9r/VR2HDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:24:22.287197Z","bundle_sha256":"8efd24535ed6a78b0301cfdc96eedb67902f411e6a9382cd82a4162776eb095a"}}