{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CWSPPKZJPGM7WEBVVV4SSJVKAU","short_pith_number":"pith:CWSPPKZJ","canonical_record":{"source":{"id":"1608.05585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-08-19T12:46:21Z","cross_cats_sorted":[],"title_canon_sha256":"89d115d50097ece60fc739799dbd2edcb02b3e72cc975b45fe7e2d2bc694866c","abstract_canon_sha256":"ae14e372c8fe0abc2ebb3133dec94cbfc2f0e0649506fe4ef8086d1c621b9748"},"schema_version":"1.0"},"canonical_sha256":"15a4f7ab297999fb1035ad792926aa051e7ed1af2283d6375d2e5d8e9bec54e3","source":{"kind":"arxiv","id":"1608.05585","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05585","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05585v2","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05585","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"pith_short_12","alias_value":"CWSPPKZJPGM7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWSPPKZJPGM7WEBV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWSPPKZJ","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CWSPPKZJPGM7WEBVVV4SSJVKAU","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-08-19T12:46:21Z","cross_cats_sorted":[],"title_canon_sha256":"89d115d50097ece60fc739799dbd2edcb02b3e72cc975b45fe7e2d2bc694866c","abstract_canon_sha256":"ae14e372c8fe0abc2ebb3133dec94cbfc2f0e0649506fe4ef8086d1c621b9748"},"schema_version":"1.0"},"canonical_sha256":"15a4f7ab297999fb1035ad792926aa051e7ed1af2283d6375d2e5d8e9bec54e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:36.876101Z","signature_b64":"rNvVf8r7tXVzilXj8lCnFisRKu8+FxgvL4PLsiYxEnsFVlsIAAkboSfNuOqWYqlbNXZkew/xymizYaEn9VksBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15a4f7ab297999fb1035ad792926aa051e7ed1af2283d6375d2e5d8e9bec54e3","last_reissued_at":"2026-05-17T23:40:36.875477Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:36.875477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05585","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":"2026-05-17T23:40:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOYgBnxaOVFPgzhA3xKh8+BZ4HMWXc3jg43FAYEOKQknFgvtRMt6aTn695+Msxp+X06UZzkpcRWEO1Cr+f6pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:37:33.783707Z"},"content_sha256":"d1c1ed98e57c568e782394e28ab0647cd5940c80705f14f0270055116b209ef2","schema_version":"1.0","event_id":"sha256:d1c1ed98e57c568e782394e28ab0647cd5940c80705f14f0270055116b209ef2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CWSPPKZJPGM7WEBVVV4SSJVKAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consistency of option prices under bid-ask spreads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"I. Cetin G\\\"ul\\\"um, Stefan Gerhold","submitted_at":"2016-08-19T12:46:21Z","abstract_excerpt":"Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. The main question then is how large (in terms of a deterministic bound) this spread must be to explain the given prices. We fully solve this problem in the case of a single maturity, and give several partial results for multiple maturities. For the latter, our main mathematical tool is a recent result on approximation by peacocks [S. Gerhold,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05585","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":"2026-05-17T23:40:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAJiru0oYDSPTQxAw6tv8ccQQ97z7ukfjpDuQ71HbS4LcAHAhfRSGNyOaGB889jmMtH1u2kRC2qgXI2OPJO5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:37:33.784060Z"},"content_sha256":"cd7d3a54319799dea57726202197ac6b901cfc74cd46a244d9733ef46693db25","schema_version":"1.0","event_id":"sha256:cd7d3a54319799dea57726202197ac6b901cfc74cd46a244d9733ef46693db25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/bundle.json","state_url":"https://pith.science/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/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":"2026-06-03T06:37:33Z","links":{"resolver":"https://pith.science/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU","bundle":"https://pith.science/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/bundle.json","state":"https://pith.science/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWSPPKZJPGM7WEBVVV4SSJVKAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CWSPPKZJPGM7WEBVVV4SSJVKAU","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":"ae14e372c8fe0abc2ebb3133dec94cbfc2f0e0649506fe4ef8086d1c621b9748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-08-19T12:46:21Z","title_canon_sha256":"89d115d50097ece60fc739799dbd2edcb02b3e72cc975b45fe7e2d2bc694866c"},"schema_version":"1.0","source":{"id":"1608.05585","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05585","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05585v2","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05585","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"pith_short_12","alias_value":"CWSPPKZJPGM7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWSPPKZJPGM7WEBV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWSPPKZJ","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:cd7d3a54319799dea57726202197ac6b901cfc74cd46a244d9733ef46693db25","target":"graph","created_at":"2026-05-17T23:40:36Z","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":"Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. The main question then is how large (in terms of a deterministic bound) this spread must be to explain the given prices. We fully solve this problem in the case of a single maturity, and give several partial results for multiple maturities. For the latter, our main mathematical tool is a recent result on approximation by peacocks [S. Gerhold,","authors_text":"I. Cetin G\\\"ul\\\"um, Stefan Gerhold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-08-19T12:46:21Z","title":"Consistency of option prices under bid-ask spreads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05585","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:d1c1ed98e57c568e782394e28ab0647cd5940c80705f14f0270055116b209ef2","target":"record","created_at":"2026-05-17T23:40:36Z","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":"ae14e372c8fe0abc2ebb3133dec94cbfc2f0e0649506fe4ef8086d1c621b9748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-08-19T12:46:21Z","title_canon_sha256":"89d115d50097ece60fc739799dbd2edcb02b3e72cc975b45fe7e2d2bc694866c"},"schema_version":"1.0","source":{"id":"1608.05585","kind":"arxiv","version":2}},"canonical_sha256":"15a4f7ab297999fb1035ad792926aa051e7ed1af2283d6375d2e5d8e9bec54e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15a4f7ab297999fb1035ad792926aa051e7ed1af2283d6375d2e5d8e9bec54e3","first_computed_at":"2026-05-17T23:40:36.875477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:36.875477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rNvVf8r7tXVzilXj8lCnFisRKu8+FxgvL4PLsiYxEnsFVlsIAAkboSfNuOqWYqlbNXZkew/xymizYaEn9VksBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:36.876101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05585","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c1ed98e57c568e782394e28ab0647cd5940c80705f14f0270055116b209ef2","sha256:cd7d3a54319799dea57726202197ac6b901cfc74cd46a244d9733ef46693db25"],"state_sha256":"9f7e49a99e18bd49a42f7871c7fe33d145722e9c570aa333226a731b9abb230f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGTpm/EwYqVBzkxFYdDSLJpUghKFMHFJYibsw0bC9XyVgcUuq4+XH5Uj3XzIqM6C+If5z4sC9VSNidcx4QO8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:37:33.786105Z","bundle_sha256":"111707c2c5590d2feef12157697fdeaa31ef1f8c83a829e8d5747c01e78fbed3"}}