{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RIS4ZPPS3G7LCNLV2LDPTFE26I","short_pith_number":"pith:RIS4ZPPS","canonical_record":{"source":{"id":"1307.0483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-01T19:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"741a86f5ff5d8a6582b94798e81670cbbcd1ebe263ae68ac2ba9289892be188a","abstract_canon_sha256":"35caf482aef1379c6b6020d50c4d748c16aa30be1e60721080ec5c63a8273210"},"schema_version":"1.0"},"canonical_sha256":"8a25ccbdf2d9beb13575d2c6f9949af23b329e64fea211c784487c9feb196bf2","source":{"kind":"arxiv","id":"1307.0483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0483","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0483v2","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0483","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"RIS4ZPPS3G7L","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RIS4ZPPS3G7LCNLV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RIS4ZPPS","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RIS4ZPPS3G7LCNLV2LDPTFE26I","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-01T19:00:29Z","cross_cats_sorted":[],"title_canon_sha256":"741a86f5ff5d8a6582b94798e81670cbbcd1ebe263ae68ac2ba9289892be188a","abstract_canon_sha256":"35caf482aef1379c6b6020d50c4d748c16aa30be1e60721080ec5c63a8273210"},"schema_version":"1.0"},"canonical_sha256":"8a25ccbdf2d9beb13575d2c6f9949af23b329e64fea211c784487c9feb196bf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:25.427136Z","signature_b64":"Nzqbkv7ik5nhDa3abGoO1s9ndPrM6lN3enPeezqMK3Rot+pzzIVVhUG7KCYswXHzJN1ndZTiSfOtdU50YxkmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a25ccbdf2d9beb13575d2c6f9949af23b329e64fea211c784487c9feb196bf2","last_reissued_at":"2026-05-18T03:19:25.426532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:25.426532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0483","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":"2026-05-18T03:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezwcsaAgUWGms5Z9sa1Di2paengfq1JXsPfMpjr8q7mJxAvjPmphsqmy8ITO87Lmxs9bDQBoODHY4zgFwR6nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:19:21.698956Z"},"content_sha256":"f5b007e9328395e3428bd1827eaffabb37e677f05e49ab0b9d9b51661aade1d3","schema_version":"1.0","event_id":"sha256:f5b007e9328395e3428bd1827eaffabb37e677f05e49ab0b9d9b51661aade1d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RIS4ZPPS3G7LCNLV2LDPTFE26I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Compressive Sampling Approach To Adaptive Multi-Resolution Approximation of Differential Equations With Random Inputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Behrooz Azarkhalili","submitted_at":"2013-07-01T19:00:29Z","abstract_excerpt":"In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse recovery with respect to multi-wavelet basis (MWB) from a small number of random samples to approximate the solution to problems. To illustrate the robustness of developed method, three benchmark problems are studied and main statistical features of solutions such as the variance and the mean of solutions obtained by proposed method are compared with the ones obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0483","kind":"arxiv","version":2},"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":"2026-05-18T03:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9QBgIYo1Ai8OE70mvDqPVAZHPfBHjKYS9alZcUNj+PHX/PgRgCiOEtRLgGaE5XaGcwAQXIavK+3PIfFQ9lMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:19:21.699301Z"},"content_sha256":"734e533be624b7e5530b033548cb7565b22eb5fc3e44323cd872bbe960258e96","schema_version":"1.0","event_id":"sha256:734e533be624b7e5530b033548cb7565b22eb5fc3e44323cd872bbe960258e96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/bundle.json","state_url":"https://pith.science/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/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":"2026-06-05T16:19:21Z","links":{"resolver":"https://pith.science/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I","bundle":"https://pith.science/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/bundle.json","state":"https://pith.science/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIS4ZPPS3G7LCNLV2LDPTFE26I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RIS4ZPPS3G7LCNLV2LDPTFE26I","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":"35caf482aef1379c6b6020d50c4d748c16aa30be1e60721080ec5c63a8273210","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-01T19:00:29Z","title_canon_sha256":"741a86f5ff5d8a6582b94798e81670cbbcd1ebe263ae68ac2ba9289892be188a"},"schema_version":"1.0","source":{"id":"1307.0483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0483","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0483v2","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0483","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"RIS4ZPPS3G7L","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RIS4ZPPS3G7LCNLV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RIS4ZPPS","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:734e533be624b7e5530b033548cb7565b22eb5fc3e44323cd872bbe960258e96","target":"graph","created_at":"2026-05-18T03:19:25Z","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, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse recovery with respect to multi-wavelet basis (MWB) from a small number of random samples to approximate the solution to problems. To illustrate the robustness of developed method, three benchmark problems are studied and main statistical features of solutions such as the variance and the mean of solutions obtained by proposed method are compared with the ones obtai","authors_text":"Behrooz Azarkhalili","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-01T19:00:29Z","title":"A Compressive Sampling Approach To Adaptive Multi-Resolution Approximation of Differential Equations With Random Inputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0483","kind":"arxiv","version":2},"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:f5b007e9328395e3428bd1827eaffabb37e677f05e49ab0b9d9b51661aade1d3","target":"record","created_at":"2026-05-18T03:19:25Z","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":"35caf482aef1379c6b6020d50c4d748c16aa30be1e60721080ec5c63a8273210","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-01T19:00:29Z","title_canon_sha256":"741a86f5ff5d8a6582b94798e81670cbbcd1ebe263ae68ac2ba9289892be188a"},"schema_version":"1.0","source":{"id":"1307.0483","kind":"arxiv","version":2}},"canonical_sha256":"8a25ccbdf2d9beb13575d2c6f9949af23b329e64fea211c784487c9feb196bf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a25ccbdf2d9beb13575d2c6f9949af23b329e64fea211c784487c9feb196bf2","first_computed_at":"2026-05-18T03:19:25.426532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:25.426532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nzqbkv7ik5nhDa3abGoO1s9ndPrM6lN3enPeezqMK3Rot+pzzIVVhUG7KCYswXHzJN1ndZTiSfOtdU50YxkmAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:25.427136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5b007e9328395e3428bd1827eaffabb37e677f05e49ab0b9d9b51661aade1d3","sha256:734e533be624b7e5530b033548cb7565b22eb5fc3e44323cd872bbe960258e96"],"state_sha256":"9ef36353d2b7bc32b14f4bb80626896762aaaee130cbfa569752671bd21b6f21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sh5asfHJds1/qpBZdnIQT+1rf89py/JrJISXxL3ioNMamrN2bqb79Ikpdn3Q7Y0s/0lYlGwj5M4rIiOo54mwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:19:21.701367Z","bundle_sha256":"9bc6ce311c71b4f40aa709d6e94647c68350b5f10d1873ebe45830497352178d"}}