{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SHM2AOV3OUH73RSL546NP2PM7N","short_pith_number":"pith:SHM2AOV3","canonical_record":{"source":{"id":"1404.4225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-16T12:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"c96dfcb38b7fcae550a8d1b1bd2bee9c38ae3e0712c4687ffdb8d395f0422318","abstract_canon_sha256":"4ae3e53a623c623285d1357f0b45dbd25a3f99fa86c99043f21599b7133a9e64"},"schema_version":"1.0"},"canonical_sha256":"91d9a03abb750ffdc64bef3cd7e9ecfb6b89bb2fc640bdf79561f742fcbe226b","source":{"kind":"arxiv","id":"1404.4225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4225","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4225v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4225","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"SHM2AOV3OUH7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SHM2AOV3OUH73RSL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SHM2AOV3","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SHM2AOV3OUH73RSL546NP2PM7N","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-16T12:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"c96dfcb38b7fcae550a8d1b1bd2bee9c38ae3e0712c4687ffdb8d395f0422318","abstract_canon_sha256":"4ae3e53a623c623285d1357f0b45dbd25a3f99fa86c99043f21599b7133a9e64"},"schema_version":"1.0"},"canonical_sha256":"91d9a03abb750ffdc64bef3cd7e9ecfb6b89bb2fc640bdf79561f742fcbe226b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.877663Z","signature_b64":"CbvXAJN97VzA5rZdQ8IzQ64VZIU9wvlltoILLhKrx9MHGuWqYQdiRMfABHi7ctrJeJ6Issy9YrAj18RsbjQkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91d9a03abb750ffdc64bef3cd7e9ecfb6b89bb2fc640bdf79561f742fcbe226b","last_reissued_at":"2026-05-18T02:54:05.876946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.876946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4225","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5GpKLnEi9AQ+vVkkdQjqDh4v711kG7TVhyvSmGJ8h57Fs6m5n8p8TsgzQc73iDdVeKrax/eOMLLB2u8nE1ABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:21:19.799962Z"},"content_sha256":"557dee588ffc0fc23500785f6fae3e2235cbee02b3044a67b2c3b58f41864e3d","schema_version":"1.0","event_id":"sha256:557dee588ffc0fc23500785f6fae3e2235cbee02b3044a67b2c3b58f41864e3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SHM2AOV3OUH73RSL546NP2PM7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient rare event simulation for failure problems in random media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jianfeng Lu, Jingchen Liu, Xiang Zhou","submitted_at":"2014-04-16T12:46:53Z","abstract_excerpt":"In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian process. This model is employed to study the failure problem of elastic materials in random media in which the failure is characterized by that the strain field exceeds a high threshold. We propose an efficient importance sampling scheme to compute small failure probabilities in the high threshold limit. The change of measure in our scheme is parametrized by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4225","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4psV04rYcfCf60ZEtJe1F3cZUww7T6gy7QAQYallJpXLX9F8mR11tWc95HrxnnPo2tKcJu+gL3WxrCt81lBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:21:19.800640Z"},"content_sha256":"54d248296fd1a257d9ac002cfd06cc7aeb067470328bc3f1f842e8234252b5a9","schema_version":"1.0","event_id":"sha256:54d248296fd1a257d9ac002cfd06cc7aeb067470328bc3f1f842e8234252b5a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHM2AOV3OUH73RSL546NP2PM7N/bundle.json","state_url":"https://pith.science/pith/SHM2AOV3OUH73RSL546NP2PM7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHM2AOV3OUH73RSL546NP2PM7N/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":"2026-05-25T10:21:19Z","links":{"resolver":"https://pith.science/pith/SHM2AOV3OUH73RSL546NP2PM7N","bundle":"https://pith.science/pith/SHM2AOV3OUH73RSL546NP2PM7N/bundle.json","state":"https://pith.science/pith/SHM2AOV3OUH73RSL546NP2PM7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHM2AOV3OUH73RSL546NP2PM7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SHM2AOV3OUH73RSL546NP2PM7N","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":"4ae3e53a623c623285d1357f0b45dbd25a3f99fa86c99043f21599b7133a9e64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-16T12:46:53Z","title_canon_sha256":"c96dfcb38b7fcae550a8d1b1bd2bee9c38ae3e0712c4687ffdb8d395f0422318"},"schema_version":"1.0","source":{"id":"1404.4225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4225","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4225v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4225","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"SHM2AOV3OUH7","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SHM2AOV3OUH73RSL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SHM2AOV3","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:54d248296fd1a257d9ac002cfd06cc7aeb067470328bc3f1f842e8234252b5a9","target":"graph","created_at":"2026-05-18T02:54:05Z","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":"In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian process. This model is employed to study the failure problem of elastic materials in random media in which the failure is characterized by that the strain field exceeds a high threshold. We propose an efficient importance sampling scheme to compute small failure probabilities in the high threshold limit. The change of measure in our scheme is parametrized by ","authors_text":"Jianfeng Lu, Jingchen Liu, Xiang Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-16T12:46:53Z","title":"Efficient rare event simulation for failure problems in random media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4225","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":"sha256:557dee588ffc0fc23500785f6fae3e2235cbee02b3044a67b2c3b58f41864e3d","target":"record","created_at":"2026-05-18T02:54:05Z","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":"4ae3e53a623c623285d1357f0b45dbd25a3f99fa86c99043f21599b7133a9e64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-16T12:46:53Z","title_canon_sha256":"c96dfcb38b7fcae550a8d1b1bd2bee9c38ae3e0712c4687ffdb8d395f0422318"},"schema_version":"1.0","source":{"id":"1404.4225","kind":"arxiv","version":1}},"canonical_sha256":"91d9a03abb750ffdc64bef3cd7e9ecfb6b89bb2fc640bdf79561f742fcbe226b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91d9a03abb750ffdc64bef3cd7e9ecfb6b89bb2fc640bdf79561f742fcbe226b","first_computed_at":"2026-05-18T02:54:05.876946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.876946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CbvXAJN97VzA5rZdQ8IzQ64VZIU9wvlltoILLhKrx9MHGuWqYQdiRMfABHi7ctrJeJ6Issy9YrAj18RsbjQkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.877663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557dee588ffc0fc23500785f6fae3e2235cbee02b3044a67b2c3b58f41864e3d","sha256:54d248296fd1a257d9ac002cfd06cc7aeb067470328bc3f1f842e8234252b5a9"],"state_sha256":"6e064825e74326273530b731b22ac8c7e43b5631cb70f6e62f9bfd5d03d38e58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O78vF7VyFIlT29wVJIoiFQbXgPfueWRa77y4Kni/PsEbErcWk+U/SqT+ng3MO8OuF+Pzun/7zkjIQuK+y9YFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T10:21:19.804699Z","bundle_sha256":"61516c7417444e7625ca3583f97d7efb173bfac08207699ae07b4f236d07a8a0"}}