{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:V7OYE3NLG7KLZ76IWYZUJUWNLT","short_pith_number":"pith:V7OYE3NL","canonical_record":{"source":{"id":"2606.28891","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-fin.MF","submitted_at":"2026-06-27T12:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"40867e619bbf4b04dcecda1a0e163710ba82619e808c6aea04942526aad7a6f6","abstract_canon_sha256":"f2c9fd967dc2ead1e96bc20c6cabcf31cd68a9c41e1f62a280de8770caefa007"},"schema_version":"1.0"},"canonical_sha256":"afdd826dab37d4bcffc8b63344d2cd5cc395e17e653446d320647343622a8878","source":{"kind":"arxiv","id":"2606.28891","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28891","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28891v1","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28891","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"V7OYE3NLG7KL","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"V7OYE3NLG7KLZ76I","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"V7OYE3NL","created_at":"2026-06-30T01:17:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:V7OYE3NLG7KLZ76IWYZUJUWNLT","target":"record","payload":{"canonical_record":{"source":{"id":"2606.28891","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-fin.MF","submitted_at":"2026-06-27T12:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"40867e619bbf4b04dcecda1a0e163710ba82619e808c6aea04942526aad7a6f6","abstract_canon_sha256":"f2c9fd967dc2ead1e96bc20c6cabcf31cd68a9c41e1f62a280de8770caefa007"},"schema_version":"1.0"},"canonical_sha256":"afdd826dab37d4bcffc8b63344d2cd5cc395e17e653446d320647343622a8878","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:43.939130Z","signature_b64":"RNa6NBU9b7iOG3hpuloC3DvqHXQPm6a2dYkp18FBqJtNdjIEolyckyBqBu/X9gjnGH7OOTxeWea1HyH6ruuiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afdd826dab37d4bcffc8b63344d2cd5cc395e17e653446d320647343622a8878","last_reissued_at":"2026-06-30T01:17:43.937775Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:43.937775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.28891","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":"2026-06-30T01:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JdQqxaBCtMXEeXug85c8jh7A17J58fqbA33zg1sht+jKtFOX1rCyFZmPFkLkbrxuQ7cCbFnjTgpHpeXaOFRUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:34:26.500219Z"},"content_sha256":"6edc9b9c6c14ba56425d8fc0f4c782130b7ce3e8ca3ec45e984c74bcab28e2e3","schema_version":"1.0","event_id":"sha256:6edc9b9c6c14ba56425d8fc0f4c782130b7ce3e8ca3ec45e984c74bcab28e2e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:V7OYE3NLG7KLZ76IWYZUJUWNLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hedging Maturity-Specific Risk in Forward Curve Derivatives under Stochastic Volatility","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Riccardo Alberti, Sven Karbach","submitted_at":"2026-06-27T12:35:26Z","abstract_excerpt":"We study the variance-optimal hedging of European contingent claims written on forwards. We assume that the dynamics of the underlying forward curves follow a Heath--Jarrow--Morton--Musiela stochastic partial differential equation modulated by an infinite-rank stochastic covariance component. The variance-optimal hedge is then given by the Galtchouk--Kunita--Watanabe projection with respect to some covariance-norm quotient generated by the forward curve martingale. We show density of finite-maturity and delivery-window strategies, convergence of spectral finite-rank hedge projections and an ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28891","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28891/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":"2026-06-30T01:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJD//zby8e7v+bSNKxuhTAiXe0V4tyl7frme753bx0Oy14vtv3igSzSrfsqhiOwa2v8VqocjzH7V12Eq6IA6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:34:26.500615Z"},"content_sha256":"bc286414469012485380827ab1069cec471b0d82beae622cdb6aa211c03a810d","schema_version":"1.0","event_id":"sha256:bc286414469012485380827ab1069cec471b0d82beae622cdb6aa211c03a810d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/bundle.json","state_url":"https://pith.science/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/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":"2026-07-04T13:34:26Z","links":{"resolver":"https://pith.science/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT","bundle":"https://pith.science/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/bundle.json","state":"https://pith.science/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7OYE3NLG7KLZ76IWYZUJUWNLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:V7OYE3NLG7KLZ76IWYZUJUWNLT","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":"f2c9fd967dc2ead1e96bc20c6cabcf31cd68a9c41e1f62a280de8770caefa007","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-fin.MF","submitted_at":"2026-06-27T12:35:26Z","title_canon_sha256":"40867e619bbf4b04dcecda1a0e163710ba82619e808c6aea04942526aad7a6f6"},"schema_version":"1.0","source":{"id":"2606.28891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28891","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28891v1","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28891","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"V7OYE3NLG7KL","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"V7OYE3NLG7KLZ76I","created_at":"2026-06-30T01:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"V7OYE3NL","created_at":"2026-06-30T01:17:43Z"}],"graph_snapshots":[{"event_id":"sha256:bc286414469012485380827ab1069cec471b0d82beae622cdb6aa211c03a810d","target":"graph","created_at":"2026-06-30T01:17:43Z","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/2606.28891/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the variance-optimal hedging of European contingent claims written on forwards. We assume that the dynamics of the underlying forward curves follow a Heath--Jarrow--Morton--Musiela stochastic partial differential equation modulated by an infinite-rank stochastic covariance component. The variance-optimal hedge is then given by the Galtchouk--Kunita--Watanabe projection with respect to some covariance-norm quotient generated by the forward curve martingale. We show density of finite-maturity and delivery-window strategies, convergence of spectral finite-rank hedge projections and an ex","authors_text":"Riccardo Alberti, Sven Karbach","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-fin.MF","submitted_at":"2026-06-27T12:35:26Z","title":"Hedging Maturity-Specific Risk in Forward Curve Derivatives under Stochastic Volatility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28891","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":"sha256:6edc9b9c6c14ba56425d8fc0f4c782130b7ce3e8ca3ec45e984c74bcab28e2e3","target":"record","created_at":"2026-06-30T01:17:43Z","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":"f2c9fd967dc2ead1e96bc20c6cabcf31cd68a9c41e1f62a280de8770caefa007","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-fin.MF","submitted_at":"2026-06-27T12:35:26Z","title_canon_sha256":"40867e619bbf4b04dcecda1a0e163710ba82619e808c6aea04942526aad7a6f6"},"schema_version":"1.0","source":{"id":"2606.28891","kind":"arxiv","version":1}},"canonical_sha256":"afdd826dab37d4bcffc8b63344d2cd5cc395e17e653446d320647343622a8878","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afdd826dab37d4bcffc8b63344d2cd5cc395e17e653446d320647343622a8878","first_computed_at":"2026-06-30T01:17:43.937775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:43.937775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RNa6NBU9b7iOG3hpuloC3DvqHXQPm6a2dYkp18FBqJtNdjIEolyckyBqBu/X9gjnGH7OOTxeWea1HyH6ruuiDg==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:43.939130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6edc9b9c6c14ba56425d8fc0f4c782130b7ce3e8ca3ec45e984c74bcab28e2e3","sha256:bc286414469012485380827ab1069cec471b0d82beae622cdb6aa211c03a810d"],"state_sha256":"9ef5bcc9d56e674268a2080f5c4335a1b2bb0ab02211fc4ccdd14e65fa4458b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSgwiLMd2CTAQkD1a+C6FnZxPNTULm9qBbE1uQMZ19LpJoH0cLQeRSD1d9Ha/g+6R+a5di7ZBT2VYwER10K1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:34:26.502670Z","bundle_sha256":"5591f5d37d87c62f1a8e32954c204a42a3fe4911f19f0e414c64a48532a1015a"}}