{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KM7AT5KSFSOIORDAPJ3IPXDN2I","short_pith_number":"pith:KM7AT5KS","canonical_record":{"source":{"id":"1304.0368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-01T14:44:38Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"79cc6b245540f3aed64d4cc843abd57640b2a6a467a0a702afd522ba9c48b7ae","abstract_canon_sha256":"0c565ed423e44fb0be71657298e31238265c7966b55e568090367c28fd488b61"},"schema_version":"1.0"},"canonical_sha256":"533e09f5522c9c8744607a7687dc6dd2198e872805708a609f51057c69f496a5","source":{"kind":"arxiv","id":"1304.0368","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0368","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0368v2","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0368","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"KM7AT5KSFSOI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KM7AT5KSFSOIORDA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KM7AT5KS","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KM7AT5KSFSOIORDAPJ3IPXDN2I","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-01T14:44:38Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"79cc6b245540f3aed64d4cc843abd57640b2a6a467a0a702afd522ba9c48b7ae","abstract_canon_sha256":"0c565ed423e44fb0be71657298e31238265c7966b55e568090367c28fd488b61"},"schema_version":"1.0"},"canonical_sha256":"533e09f5522c9c8744607a7687dc6dd2198e872805708a609f51057c69f496a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:21.061424Z","signature_b64":"yBzYQgQa2lzYqM889KTl13031JdBFbv11ORfdI1twpATSMxUovDPvIBxdSZfy9Y0gNdKSGd1JIbeg/MYc3cSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"533e09f5522c9c8744607a7687dc6dd2198e872805708a609f51057c69f496a5","last_reissued_at":"2026-05-18T03:03:21.060701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:21.060701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0368","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":"2026-05-18T03:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SUbRE2zUwuVEytCf0GX+srnqFmz83nwViCcKwteSU0bPo5YTQF4modSyghuZiWkDHmxNOQ5HqODbyVv9Dc2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:57:29.371575Z"},"content_sha256":"177f155ff5c530a0fc8fdd03bdf5c07ce1a36f29820c91f872f469bc1e6e133e","schema_version":"1.0","event_id":"sha256:177f155ff5c530a0fc8fdd03bdf5c07ce1a36f29820c91f872f469bc1e6e133e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KM7AT5KSFSOIORDAPJ3IPXDN2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Iterated Az\\'{e}ma-Yor Type Embedding for Finitely Many Marginals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"math.PR","authors_text":"Jan Ob{\\l}\\'oj, Peter Spoida","submitted_at":"2013-04-01T14:44:38Z","abstract_excerpt":"We solve the $n$-marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures $\\mu_1,...,\\mu_n$ which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalisation of the Azema and Yor (1979) solution. In particular, we recover the stopping boundaries obtained by Brown et al. (2001) and Madan and Yor (2002). Our technical assumption is necessary for the explicit embedding, as demonstrated with a counterexample. We discuss extensions to the general case giving details wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0368","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":"2026-05-18T03:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/xRCNxwkOOsTg7F2iOzgeJXazVBpAJ9Ul0wMn+zjmM01xiqjtskePMD7V3Y1F9NjGuP9bglMpFFSAp1ZESeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:57:29.371919Z"},"content_sha256":"71ac9e061d09498edd1a7acf13fce984db644e336c99827aca420047f5a3b588","schema_version":"1.0","event_id":"sha256:71ac9e061d09498edd1a7acf13fce984db644e336c99827aca420047f5a3b588"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/bundle.json","state_url":"https://pith.science/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/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":"2026-06-05T15:57:29Z","links":{"resolver":"https://pith.science/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I","bundle":"https://pith.science/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/bundle.json","state":"https://pith.science/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KM7AT5KSFSOIORDAPJ3IPXDN2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KM7AT5KSFSOIORDAPJ3IPXDN2I","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":"0c565ed423e44fb0be71657298e31238265c7966b55e568090367c28fd488b61","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-01T14:44:38Z","title_canon_sha256":"79cc6b245540f3aed64d4cc843abd57640b2a6a467a0a702afd522ba9c48b7ae"},"schema_version":"1.0","source":{"id":"1304.0368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0368","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0368v2","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0368","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"KM7AT5KSFSOI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KM7AT5KSFSOIORDA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KM7AT5KS","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:71ac9e061d09498edd1a7acf13fce984db644e336c99827aca420047f5a3b588","target":"graph","created_at":"2026-05-18T03:03:21Z","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 solve the $n$-marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures $\\mu_1,...,\\mu_n$ which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalisation of the Azema and Yor (1979) solution. In particular, we recover the stopping boundaries obtained by Brown et al. (2001) and Madan and Yor (2002). Our technical assumption is necessary for the explicit embedding, as demonstrated with a counterexample. We discuss extensions to the general case giving details wh","authors_text":"Jan Ob{\\l}\\'oj, Peter Spoida","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-01T14:44:38Z","title":"An Iterated Az\\'{e}ma-Yor Type Embedding for Finitely Many Marginals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0368","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":"sha256:177f155ff5c530a0fc8fdd03bdf5c07ce1a36f29820c91f872f469bc1e6e133e","target":"record","created_at":"2026-05-18T03:03:21Z","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":"0c565ed423e44fb0be71657298e31238265c7966b55e568090367c28fd488b61","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-01T14:44:38Z","title_canon_sha256":"79cc6b245540f3aed64d4cc843abd57640b2a6a467a0a702afd522ba9c48b7ae"},"schema_version":"1.0","source":{"id":"1304.0368","kind":"arxiv","version":2}},"canonical_sha256":"533e09f5522c9c8744607a7687dc6dd2198e872805708a609f51057c69f496a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"533e09f5522c9c8744607a7687dc6dd2198e872805708a609f51057c69f496a5","first_computed_at":"2026-05-18T03:03:21.060701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:21.060701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBzYQgQa2lzYqM889KTl13031JdBFbv11ORfdI1twpATSMxUovDPvIBxdSZfy9Y0gNdKSGd1JIbeg/MYc3cSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:21.061424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:177f155ff5c530a0fc8fdd03bdf5c07ce1a36f29820c91f872f469bc1e6e133e","sha256:71ac9e061d09498edd1a7acf13fce984db644e336c99827aca420047f5a3b588"],"state_sha256":"9c8cd3c735f134bc9a841dd1b9fc306411e1798539fecc93d209ca3c9aecb51a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOW+a2GYMh9RaulsqCyHL2pZktc0q1rxt5wr2OBUeeUfND6TA6QH0Hz5Vem7fek9fDU7dcWXkbVv3AGhqcslDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:57:29.373947Z","bundle_sha256":"95433a492221a1181f3136158f309eba9fcf9214ceea18fbb48c1a3042c41500"}}