{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LEQGWK4YC3AZH4FU4IX5GNFU5A","short_pith_number":"pith:LEQGWK4Y","canonical_record":{"source":{"id":"1208.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-24T18:21:17Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"135443bedde71ac3b77a7101927e613e54c24cb54ad9437825bf9538fb0aae75","abstract_canon_sha256":"d8001a1e9cc33400f11f159ac9270645ca77a7c9a81143fa4ce982f97de0fc8d"},"schema_version":"1.0"},"canonical_sha256":"59206b2b9816c193f0b4e22fd334b4e822b4c8da7a58b74fbc60190770084213","source":{"kind":"arxiv","id":"1208.5029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5029","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5029v1","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5029","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"LEQGWK4YC3AZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LEQGWK4YC3AZH4FU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LEQGWK4Y","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LEQGWK4YC3AZH4FU4IX5GNFU5A","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-24T18:21:17Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"135443bedde71ac3b77a7101927e613e54c24cb54ad9437825bf9538fb0aae75","abstract_canon_sha256":"d8001a1e9cc33400f11f159ac9270645ca77a7c9a81143fa4ce982f97de0fc8d"},"schema_version":"1.0"},"canonical_sha256":"59206b2b9816c193f0b4e22fd334b4e822b4c8da7a58b74fbc60190770084213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:52.068917Z","signature_b64":"MMJzrl8hlRkB8/GEv92ZXD/RUiWagjrrcKayxkzKhhES6F9xntIk9ChOkOpJDPsmbXla2+CzFc25R/Rsmt6iDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59206b2b9816c193f0b4e22fd334b4e822b4c8da7a58b74fbc60190770084213","last_reissued_at":"2026-05-18T03:47:52.068515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:52.068515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5029","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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feBVtCiDw8OkNO8wXjOSKMumwy2WbaBG+eGrp2pAJy1S3X0Gb7w3IXPusgwiIeQ5Nd1b/bULPtj4uUqDh8VgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:01:56.710223Z"},"content_sha256":"bf34fe6b2cecbc8850ba9302c0d71fbb5a6b3e4603bb1cce4c95e5a6a665b1e8","schema_version":"1.0","event_id":"sha256:bf34fe6b2cecbc8850ba9302c0d71fbb5a6b3e4603bb1cce4c95e5a6a665b1e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LEQGWK4YC3AZH4FU4IX5GNFU5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probability of Failure in Hypersonic Engines Using Large Deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"George Papanicolaou, Nicholas West, Tzu-Wei Yang","submitted_at":"2012-08-24T18:21:17Z","abstract_excerpt":"We consider a reduced order model of an air-breathing hypersonic engine with a time-dependent stochastic inflow that may cause the failure of the engine. The probability of failure is analyzed by the Freidlin-Wentzell theory, the large deviation principle for finite dimensional stochastic differential equations. We compute the asymptotic failure probability by numerically solving the constrained optimization related to the large deviation problem. A large-deviation-based importance sampling suggested by the most probable inflow perturbation is also implemented to compute the probability of fai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5029","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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDxxy1F7e/OCZDNDJSYHuI1l2FVwQir80zhUv0PuwtbSx9/e31XKP4AEX1pVNS1rAo75tA2H14T6P6OC7khBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:01:56.710807Z"},"content_sha256":"730f2e27515c0dc5502d9e230126956e0a486116d1a67691d64f099294f8d716","schema_version":"1.0","event_id":"sha256:730f2e27515c0dc5502d9e230126956e0a486116d1a67691d64f099294f8d716"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/bundle.json","state_url":"https://pith.science/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/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":"2026-06-11T02:01:56Z","links":{"resolver":"https://pith.science/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A","bundle":"https://pith.science/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/bundle.json","state":"https://pith.science/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEQGWK4YC3AZH4FU4IX5GNFU5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LEQGWK4YC3AZH4FU4IX5GNFU5A","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":"d8001a1e9cc33400f11f159ac9270645ca77a7c9a81143fa4ce982f97de0fc8d","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-24T18:21:17Z","title_canon_sha256":"135443bedde71ac3b77a7101927e613e54c24cb54ad9437825bf9538fb0aae75"},"schema_version":"1.0","source":{"id":"1208.5029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5029","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5029v1","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5029","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"LEQGWK4YC3AZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LEQGWK4YC3AZH4FU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LEQGWK4Y","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:730f2e27515c0dc5502d9e230126956e0a486116d1a67691d64f099294f8d716","target":"graph","created_at":"2026-05-18T03:47:52Z","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 consider a reduced order model of an air-breathing hypersonic engine with a time-dependent stochastic inflow that may cause the failure of the engine. The probability of failure is analyzed by the Freidlin-Wentzell theory, the large deviation principle for finite dimensional stochastic differential equations. We compute the asymptotic failure probability by numerically solving the constrained optimization related to the large deviation problem. A large-deviation-based importance sampling suggested by the most probable inflow perturbation is also implemented to compute the probability of fai","authors_text":"George Papanicolaou, Nicholas West, Tzu-Wei Yang","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-24T18:21:17Z","title":"Probability of Failure in Hypersonic Engines Using Large Deviations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5029","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:bf34fe6b2cecbc8850ba9302c0d71fbb5a6b3e4603bb1cce4c95e5a6a665b1e8","target":"record","created_at":"2026-05-18T03:47:52Z","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":"d8001a1e9cc33400f11f159ac9270645ca77a7c9a81143fa4ce982f97de0fc8d","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-24T18:21:17Z","title_canon_sha256":"135443bedde71ac3b77a7101927e613e54c24cb54ad9437825bf9538fb0aae75"},"schema_version":"1.0","source":{"id":"1208.5029","kind":"arxiv","version":1}},"canonical_sha256":"59206b2b9816c193f0b4e22fd334b4e822b4c8da7a58b74fbc60190770084213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59206b2b9816c193f0b4e22fd334b4e822b4c8da7a58b74fbc60190770084213","first_computed_at":"2026-05-18T03:47:52.068515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:52.068515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMJzrl8hlRkB8/GEv92ZXD/RUiWagjrrcKayxkzKhhES6F9xntIk9ChOkOpJDPsmbXla2+CzFc25R/Rsmt6iDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:52.068917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf34fe6b2cecbc8850ba9302c0d71fbb5a6b3e4603bb1cce4c95e5a6a665b1e8","sha256:730f2e27515c0dc5502d9e230126956e0a486116d1a67691d64f099294f8d716"],"state_sha256":"07f6954b5d1ee5f38317a1045ad641034b50f7c3b5676141bcb6b1f43c3b67a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQMRW6kgnk16SbnHkL50o9HwSwy0DzKwixnDFQbzsSOI9EBYDEKWmB3SGzlbFSflJhUUBFWSHCJlDPgXrg+wCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:01:56.714099Z","bundle_sha256":"23239e862a82eb7402b5077910189251980aa5dea31b4c105b62a7a83ea4ffa8"}}