{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LYYPRCQKTXGEEIJAZ4ZNXTJOVE","short_pith_number":"pith:LYYPRCQK","canonical_record":{"source":{"id":"1609.05832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-09-19T17:18:01Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"12c87a53a4e3c88369b58d67e8624637176001fa5513213271323433f20c1a3d","abstract_canon_sha256":"99e1d4f6d5aafde55c123783d9477bf6bd259bf4ca5e9fc2154944923d684518"},"schema_version":"1.0"},"canonical_sha256":"5e30f88a0a9dcc422120cf32dbcd2ea931d7eea85797534d76c360eb53286ed6","source":{"kind":"arxiv","id":"1609.05832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05832","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05832v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05832","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"LYYPRCQKTXGE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYYPRCQKTXGEEIJA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYYPRCQK","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LYYPRCQKTXGEEIJAZ4ZNXTJOVE","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-09-19T17:18:01Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"12c87a53a4e3c88369b58d67e8624637176001fa5513213271323433f20c1a3d","abstract_canon_sha256":"99e1d4f6d5aafde55c123783d9477bf6bd259bf4ca5e9fc2154944923d684518"},"schema_version":"1.0"},"canonical_sha256":"5e30f88a0a9dcc422120cf32dbcd2ea931d7eea85797534d76c360eb53286ed6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:51.319091Z","signature_b64":"mhqyROws227FzeZqF/A7bKL6lk/YCZwLo/9vQ6oMirmkdLFcfHVbrVP2CVAkqhTGWpOiB9GfydBLs4DM1KtPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e30f88a0a9dcc422120cf32dbcd2ea931d7eea85797534d76c360eb53286ed6","last_reissued_at":"2026-05-18T00:41:51.318626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:51.318626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05832","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":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EfvaL8DsV5HrJpp+Ub26abhUqm4Ti/JJcOHqsXED1Q2rFt6il0S4l8e5vNQhN3aM1TRYi8egM79Qbcaeme7OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:07.210995Z"},"content_sha256":"17460d64b45dc5d53ca83d47db75a8f080c50623fb203ccb9d0552556de25340","schema_version":"1.0","event_id":"sha256:17460d64b45dc5d53ca83d47db75a8f080c50623fb203ccb9d0552556de25340"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LYYPRCQKTXGEEIJAZ4ZNXTJOVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for VIX Futures given S&P 500 Smiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"q-fin.PR","authors_text":"Julien Guyon, Marcel Nutz, Romain Menegaux","submitted_at":"2016-09-19T17:18:01Z","abstract_excerpt":"We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of minimizing/maximizing certain risk-neutral expectations is introduced and shown to yield the same value.\n  The classical bounds for VIX futures given the smiles only use a calendar spread of log-contracts on the S&P 500. We analyze for which smiles the classical bounds are sharp and how they can be improved when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05832","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":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s39OS1vqK95ci0Ln6zPmBj9b6+7LZlCl8hIvgAI7zObGq1o7zX68XhaxeW/V/8aK/WIismM+Cp8Rcdxxjra4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:17:07.211582Z"},"content_sha256":"a9f75ad81d449e08716d89edde4acc823811a5fe1e8f58c17337e5372b788eac","schema_version":"1.0","event_id":"sha256:a9f75ad81d449e08716d89edde4acc823811a5fe1e8f58c17337e5372b788eac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/bundle.json","state_url":"https://pith.science/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/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":"2026-06-02T13:17:07Z","links":{"resolver":"https://pith.science/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE","bundle":"https://pith.science/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/bundle.json","state":"https://pith.science/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYYPRCQKTXGEEIJAZ4ZNXTJOVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LYYPRCQKTXGEEIJAZ4ZNXTJOVE","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":"99e1d4f6d5aafde55c123783d9477bf6bd259bf4ca5e9fc2154944923d684518","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-09-19T17:18:01Z","title_canon_sha256":"12c87a53a4e3c88369b58d67e8624637176001fa5513213271323433f20c1a3d"},"schema_version":"1.0","source":{"id":"1609.05832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05832","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05832v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05832","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"LYYPRCQKTXGE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYYPRCQKTXGEEIJA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYYPRCQK","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:a9f75ad81d449e08716d89edde4acc823811a5fe1e8f58c17337e5372b788eac","target":"graph","created_at":"2026-05-18T00:41:51Z","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 derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of minimizing/maximizing certain risk-neutral expectations is introduced and shown to yield the same value.\n  The classical bounds for VIX futures given the smiles only use a calendar spread of log-contracts on the S&P 500. We analyze for which smiles the classical bounds are sharp and how they can be improved when","authors_text":"Julien Guyon, Marcel Nutz, Romain Menegaux","cross_cats":["math.OC","q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-09-19T17:18:01Z","title":"Bounds for VIX Futures given S&P 500 Smiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05832","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":"sha256:17460d64b45dc5d53ca83d47db75a8f080c50623fb203ccb9d0552556de25340","target":"record","created_at":"2026-05-18T00:41:51Z","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":"99e1d4f6d5aafde55c123783d9477bf6bd259bf4ca5e9fc2154944923d684518","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2016-09-19T17:18:01Z","title_canon_sha256":"12c87a53a4e3c88369b58d67e8624637176001fa5513213271323433f20c1a3d"},"schema_version":"1.0","source":{"id":"1609.05832","kind":"arxiv","version":2}},"canonical_sha256":"5e30f88a0a9dcc422120cf32dbcd2ea931d7eea85797534d76c360eb53286ed6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e30f88a0a9dcc422120cf32dbcd2ea931d7eea85797534d76c360eb53286ed6","first_computed_at":"2026-05-18T00:41:51.318626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:51.318626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhqyROws227FzeZqF/A7bKL6lk/YCZwLo/9vQ6oMirmkdLFcfHVbrVP2CVAkqhTGWpOiB9GfydBLs4DM1KtPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:51.319091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17460d64b45dc5d53ca83d47db75a8f080c50623fb203ccb9d0552556de25340","sha256:a9f75ad81d449e08716d89edde4acc823811a5fe1e8f58c17337e5372b788eac"],"state_sha256":"772912da0b261db0d3c5c64582d5e9b9de3eafdad873778cd3db821876c34134"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQ88U+GF8fzncQFznY0wDVGMQHyj5vbxbyWFBnlCvPXoqyZIoqK5rALcbPV24/0+GTHkgrhR3pXmkO0AOKAsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:17:07.213700Z","bundle_sha256":"ccc311c824a1221e8618ec79087d62e657574b7da5d2133128ec938d5684d117"}}