{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:G3RYTQA3RIGKPNF7Y3ID6SOUZU","short_pith_number":"pith:G3RYTQA3","canonical_record":{"source":{"id":"cs/0302035","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.CE","submitted_at":"2003-02-25T03:09:11Z","cross_cats_sorted":[],"title_canon_sha256":"742093b0f18ff30c00d1033860551df8c2def936f604628cce402265f8ab30ce","abstract_canon_sha256":"16a24af715b7cdcdd1c30d1755e915af45d1601059c9988bdeaeaeb8a0cc2371"},"schema_version":"1.0"},"canonical_sha256":"36e389c01b8a0ca7b4bfc6d03f49d4cd2f68cf5b2035b0092ad5fbe39a9d37bf","source":{"kind":"arxiv","id":"cs/0302035","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0302035","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0302035v2","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0302035","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_12","alias_value":"G3RYTQA3RIGK","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_16","alias_value":"G3RYTQA3RIGKPNF7","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_8","alias_value":"G3RYTQA3","created_at":"2026-07-04T14:47:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:G3RYTQA3RIGKPNF7Y3ID6SOUZU","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0302035","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.CE","submitted_at":"2003-02-25T03:09:11Z","cross_cats_sorted":[],"title_canon_sha256":"742093b0f18ff30c00d1033860551df8c2def936f604628cce402265f8ab30ce","abstract_canon_sha256":"16a24af715b7cdcdd1c30d1755e915af45d1601059c9988bdeaeaeb8a0cc2371"},"schema_version":"1.0"},"canonical_sha256":"36e389c01b8a0ca7b4bfc6d03f49d4cd2f68cf5b2035b0092ad5fbe39a9d37bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:47:56.010951Z","signature_b64":"w/Dr9XAGFv4dA8+RzhZk9jHmOb7ID/YxmjFixfJ8ps4AZ3IH893lMy8YjNNxq9wjfa3K6e4wcUOLEj8jcVvGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36e389c01b8a0ca7b4bfc6d03f49d4cd2f68cf5b2035b0092ad5fbe39a9d37bf","last_reissued_at":"2026-07-04T14:47:56.010611Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:47:56.010611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0302035","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":"2026-07-04T14:47:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GX1OThMXid7r2tdPMOiiL4faGMzOXTErCFZXbXyL57JGmeIlEwCULWN435qr+VEv+TeflFZG4xdRWDMI11lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T05:47:37.784488Z"},"content_sha256":"9e0307f5c3eb4e84fc17a05526b26ccd4eb46ffce503ca35282c0e0c281b7b3c","schema_version":"1.0","event_id":"sha256:9e0307f5c3eb4e84fc17a05526b26ccd4eb46ffce503ca35282c0e0c281b7b3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:G3RYTQA3RIGKPNF7Y3ID6SOUZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Risk-Management Methods for the Libor Market Model Using Semidefinite Programming","license":"","headline":"","cross_cats":[],"primary_cat":"cs.CE","authors_text":"Alexandre d'Aspremont","submitted_at":"2003-02-25T03:09:11Z","abstract_excerpt":"When interest rate dynamics are described by the Libor Market Model as in BGM97, we show how some essential risk-management results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption's price, we show that the optimal dual variables describe a hedging portfolio in the sense of \\cite{Avel96}. In the general case, the local sensitivity of the covariance matrix to all market movement scenarios can be directly computed from the optimal dual solution. We also show how semidefinite programming can be used to manage the Gamma exposu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0302035","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cs/0302035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:47:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uVieiCRheuoMbFDviiPpVYnOyziefYlVOBdG+Z3WplYjDHplLxafTGSe+x12mHd5hsdtW8oHrDwE+ieV9VUIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T05:47:37.785408Z"},"content_sha256":"ad3cf713576981141622d329d3d215e3c8d1d6fb3abf7b6fa0220d7572bad613","schema_version":"1.0","event_id":"sha256:ad3cf713576981141622d329d3d215e3c8d1d6fb3abf7b6fa0220d7572bad613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/bundle.json","state_url":"https://pith.science/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/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":"2026-08-06T05:47:37Z","links":{"resolver":"https://pith.science/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU","bundle":"https://pith.science/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/bundle.json","state":"https://pith.science/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3RYTQA3RIGKPNF7Y3ID6SOUZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:G3RYTQA3RIGKPNF7Y3ID6SOUZU","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":"16a24af715b7cdcdd1c30d1755e915af45d1601059c9988bdeaeaeb8a0cc2371","cross_cats_sorted":[],"license":"","primary_cat":"cs.CE","submitted_at":"2003-02-25T03:09:11Z","title_canon_sha256":"742093b0f18ff30c00d1033860551df8c2def936f604628cce402265f8ab30ce"},"schema_version":"1.0","source":{"id":"cs/0302035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0302035","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0302035v2","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0302035","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_12","alias_value":"G3RYTQA3RIGK","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_16","alias_value":"G3RYTQA3RIGKPNF7","created_at":"2026-07-04T14:47:56Z"},{"alias_kind":"pith_short_8","alias_value":"G3RYTQA3","created_at":"2026-07-04T14:47:56Z"}],"graph_snapshots":[{"event_id":"sha256:ad3cf713576981141622d329d3d215e3c8d1d6fb3abf7b6fa0220d7572bad613","target":"graph","created_at":"2026-07-04T14:47:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cs/0302035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When interest rate dynamics are described by the Libor Market Model as in BGM97, we show how some essential risk-management results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption's price, we show that the optimal dual variables describe a hedging portfolio in the sense of \\cite{Avel96}. In the general case, the local sensitivity of the covariance matrix to all market movement scenarios can be directly computed from the optimal dual solution. We also show how semidefinite programming can be used to manage the Gamma exposu","authors_text":"Alexandre d'Aspremont","cross_cats":[],"headline":"","license":"","primary_cat":"cs.CE","submitted_at":"2003-02-25T03:09:11Z","title":"Risk-Management Methods for the Libor Market Model Using Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0302035","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":"sha256:9e0307f5c3eb4e84fc17a05526b26ccd4eb46ffce503ca35282c0e0c281b7b3c","target":"record","created_at":"2026-07-04T14:47:56Z","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":"16a24af715b7cdcdd1c30d1755e915af45d1601059c9988bdeaeaeb8a0cc2371","cross_cats_sorted":[],"license":"","primary_cat":"cs.CE","submitted_at":"2003-02-25T03:09:11Z","title_canon_sha256":"742093b0f18ff30c00d1033860551df8c2def936f604628cce402265f8ab30ce"},"schema_version":"1.0","source":{"id":"cs/0302035","kind":"arxiv","version":2}},"canonical_sha256":"36e389c01b8a0ca7b4bfc6d03f49d4cd2f68cf5b2035b0092ad5fbe39a9d37bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36e389c01b8a0ca7b4bfc6d03f49d4cd2f68cf5b2035b0092ad5fbe39a9d37bf","first_computed_at":"2026-07-04T14:47:56.010611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:47:56.010611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w/Dr9XAGFv4dA8+RzhZk9jHmOb7ID/YxmjFixfJ8ps4AZ3IH893lMy8YjNNxq9wjfa3K6e4wcUOLEj8jcVvGBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:47:56.010951Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0302035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e0307f5c3eb4e84fc17a05526b26ccd4eb46ffce503ca35282c0e0c281b7b3c","sha256:ad3cf713576981141622d329d3d215e3c8d1d6fb3abf7b6fa0220d7572bad613"],"state_sha256":"d2afcf424badf7c01832874037dc52218eed07118b004e595476162c3af73b8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0CYx1chSBfcVPKStMtHnodrcpOwjx41equSohycRNR8H9BrWQ8T2yHrpWGRmFdf26qbqq/zq4AmvukBUh3moAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T05:47:37.790539Z","bundle_sha256":"0c9303085b81f2e90fd9c01fd13b31b4bdda69bbd3878dd3929260eadb5d816a"}}