{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DFESOLUSVSWS5L4ZW3CJ656RBA","short_pith_number":"pith:DFESOLUS","canonical_record":{"source":{"id":"1109.2557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-09-12T18:18:49Z","cross_cats_sorted":["math.NA","math.PR","q-fin.PR"],"title_canon_sha256":"fc7213c9d9b777c0731036c6e4ee10e579f1a06f8098bb7d8b6701ddcaa8f11a","abstract_canon_sha256":"11a5f46b0b90e7f42d342693dbcf04342aa52da94e08b849d24c4e84ec70731f"},"schema_version":"1.0"},"canonical_sha256":"1949272e92acad2eaf99b6c49f77d108241e38b88d4cec484789073eda095127","source":{"kind":"arxiv","id":"1109.2557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2557","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2557v1","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2557","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"DFESOLUSVSWS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFESOLUSVSWS5L4Z","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFESOLUS","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DFESOLUSVSWS5L4ZW3CJ656RBA","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-09-12T18:18:49Z","cross_cats_sorted":["math.NA","math.PR","q-fin.PR"],"title_canon_sha256":"fc7213c9d9b777c0731036c6e4ee10e579f1a06f8098bb7d8b6701ddcaa8f11a","abstract_canon_sha256":"11a5f46b0b90e7f42d342693dbcf04342aa52da94e08b849d24c4e84ec70731f"},"schema_version":"1.0"},"canonical_sha256":"1949272e92acad2eaf99b6c49f77d108241e38b88d4cec484789073eda095127","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:58.987583Z","signature_b64":"kgsYAi/9vRkzYRF2zg/HMDdQcHkpNUJbASrOFn0CkHg1jC6q9G8S1Oot1CaTpU6HQPFVwbw30PIDTR4SYNTUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1949272e92acad2eaf99b6c49f77d108241e38b88d4cec484789073eda095127","last_reissued_at":"2026-05-18T01:12:58.987020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:58.987020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2557","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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNyTsNDffkr6m80X4//pFFBRXs4JZUjf5OozjSm7TBcFendjXgMLyY0Q7PL3qqbTYhXsa/T/mJzzoHB6ehQRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:50:22.043530Z"},"content_sha256":"d17f13176d62162e95fbdb64270ec49f9129feb183e65b81c19084e719d91fea","schema_version":"1.0","event_id":"sha256:d17f13176d62162e95fbdb64270ec49f9129feb183e65b81c19084e719d91fea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DFESOLUSVSWS5L4ZW3CJ656RBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical integration of Heath-Jarrow-Morton model of interest rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.PR","q-fin.PR"],"primary_cat":"q-fin.CP","authors_text":"M. Krivko, M.V. Tretyakov","submitted_at":"2011-09-12T18:18:49Z","abstract_excerpt":"We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense using the general theory of numerical integration of SDEs. The proposed numerical algorithms are computationally highly efficient due to the use of high-order quadrature rules which allow us to take"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2557","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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hJdTIee9PBrs3PMtL56M1DARtIezI/RCpBTbyGAjP0cuwh0Oq2mi1FmEbH6gE6HSws654exwiy+XopjEZj5jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:50:22.043883Z"},"content_sha256":"db4f6d929a6c8ef9a2abe1a0ec02a1895a2a83f93c40d4e274243668445dd5ec","schema_version":"1.0","event_id":"sha256:db4f6d929a6c8ef9a2abe1a0ec02a1895a2a83f93c40d4e274243668445dd5ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/bundle.json","state_url":"https://pith.science/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/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":"2026-05-28T22:50:22Z","links":{"resolver":"https://pith.science/pith/DFESOLUSVSWS5L4ZW3CJ656RBA","bundle":"https://pith.science/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/bundle.json","state":"https://pith.science/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFESOLUSVSWS5L4ZW3CJ656RBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DFESOLUSVSWS5L4ZW3CJ656RBA","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":"11a5f46b0b90e7f42d342693dbcf04342aa52da94e08b849d24c4e84ec70731f","cross_cats_sorted":["math.NA","math.PR","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-09-12T18:18:49Z","title_canon_sha256":"fc7213c9d9b777c0731036c6e4ee10e579f1a06f8098bb7d8b6701ddcaa8f11a"},"schema_version":"1.0","source":{"id":"1109.2557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2557","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2557v1","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2557","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"DFESOLUSVSWS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFESOLUSVSWS5L4Z","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFESOLUS","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:db4f6d929a6c8ef9a2abe1a0ec02a1895a2a83f93c40d4e274243668445dd5ec","target":"graph","created_at":"2026-05-18T01:12:58Z","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 propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense using the general theory of numerical integration of SDEs. The proposed numerical algorithms are computationally highly efficient due to the use of high-order quadrature rules which allow us to take","authors_text":"M. Krivko, M.V. Tretyakov","cross_cats":["math.NA","math.PR","q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-09-12T18:18:49Z","title":"Numerical integration of Heath-Jarrow-Morton model of interest rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2557","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:d17f13176d62162e95fbdb64270ec49f9129feb183e65b81c19084e719d91fea","target":"record","created_at":"2026-05-18T01:12:58Z","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":"11a5f46b0b90e7f42d342693dbcf04342aa52da94e08b849d24c4e84ec70731f","cross_cats_sorted":["math.NA","math.PR","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-09-12T18:18:49Z","title_canon_sha256":"fc7213c9d9b777c0731036c6e4ee10e579f1a06f8098bb7d8b6701ddcaa8f11a"},"schema_version":"1.0","source":{"id":"1109.2557","kind":"arxiv","version":1}},"canonical_sha256":"1949272e92acad2eaf99b6c49f77d108241e38b88d4cec484789073eda095127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1949272e92acad2eaf99b6c49f77d108241e38b88d4cec484789073eda095127","first_computed_at":"2026-05-18T01:12:58.987020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.987020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgsYAi/9vRkzYRF2zg/HMDdQcHkpNUJbASrOFn0CkHg1jC6q9G8S1Oot1CaTpU6HQPFVwbw30PIDTR4SYNTUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.987583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d17f13176d62162e95fbdb64270ec49f9129feb183e65b81c19084e719d91fea","sha256:db4f6d929a6c8ef9a2abe1a0ec02a1895a2a83f93c40d4e274243668445dd5ec"],"state_sha256":"f8777d5093a67ff9591b13e84b87f01689136fc88308793bfb494de842aefa0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPTyhGgmZJudcTqk1I3k4jSogz+Cx+DDFOcs4Itf23Fiuxok67T8nRPmU0x+q/ElR6vMmEZOwMU0qeU5FXgUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:50:22.045877Z","bundle_sha256":"f5f30ea4b924e99966bc3f0bf1e5dabe0fbfb4125c89cd5bd84fd76464ff00b8"}}