{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LRO7YNDB6KZMAJI6TKVB6XVTIS","short_pith_number":"pith:LRO7YNDB","canonical_record":{"source":{"id":"1609.07419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T16:21:04Z","cross_cats_sorted":[],"title_canon_sha256":"9bc8e0c8c5802772737b47c9c86e543acd912853bd1ae682a4a32d50b40850a9","abstract_canon_sha256":"f1b648aa26b9cd1522a67c115021ccd774ebc5d9745d49b149c82c87a68e0579"},"schema_version":"1.0"},"canonical_sha256":"5c5dfc3461f2b2c0251e9aaa1f5eb3448190bfc9f97ccdb238ea79bf844134fc","source":{"kind":"arxiv","id":"1609.07419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07419","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07419v1","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07419","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"LRO7YNDB6KZM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRO7YNDB6KZMAJI6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRO7YNDB","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LRO7YNDB6KZMAJI6TKVB6XVTIS","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T16:21:04Z","cross_cats_sorted":[],"title_canon_sha256":"9bc8e0c8c5802772737b47c9c86e543acd912853bd1ae682a4a32d50b40850a9","abstract_canon_sha256":"f1b648aa26b9cd1522a67c115021ccd774ebc5d9745d49b149c82c87a68e0579"},"schema_version":"1.0"},"canonical_sha256":"5c5dfc3461f2b2c0251e9aaa1f5eb3448190bfc9f97ccdb238ea79bf844134fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.908433Z","signature_b64":"2SON7aQLpP5qEYVwU56FLPv8MQUoG5bxfMAffmeONBk/tKb7lQuMFfp8ZpdUsob7esVLLP1EmJ0WbiUyl+vhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c5dfc3461f2b2c0251e9aaa1f5eb3448190bfc9f97ccdb238ea79bf844134fc","last_reissued_at":"2026-05-18T01:04:00.907755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.907755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07419","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":"2026-05-18T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRsQ0LumIYRNJ6uTee3mlIRzCiGa3wU8uWEaHIqdfU9tTFszV5Ef4A/OoNEqar9R0n2r6QwKSxSP+Um4iRecDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:33:49.339214Z"},"content_sha256":"5206e36f8018b48f56f8559608e9f9cdbd0b613b6cc1c9c68dd96cf13dce1089","schema_version":"1.0","event_id":"sha256:5206e36f8018b48f56f8559608e9f9cdbd0b613b6cc1c9c68dd96cf13dce1089"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LRO7YNDB6KZMAJI6TKVB6XVTIS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Watermark Options","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mihail Zervos, Neofytos Rodosthenous","submitted_at":"2016-09-23T16:21:04Z","abstract_excerpt":"We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly non-linear first order ODEs that have the characteristics of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07419","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":""},"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":"2026-05-18T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOX41kFVFMDM2QrytfWM61ynhV2M5S4ahy4GbA/L+IEHBrdYcbSnnzfqe7ilw1CfadNJp2ijmJ45snMR9H8IAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:33:49.339573Z"},"content_sha256":"a64479a26c78386c71d1a3c49e18f8f5fef9eed5a0fdee9a0edf80de61783abe","schema_version":"1.0","event_id":"sha256:a64479a26c78386c71d1a3c49e18f8f5fef9eed5a0fdee9a0edf80de61783abe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/bundle.json","state_url":"https://pith.science/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/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":"2026-06-24T14:33:49Z","links":{"resolver":"https://pith.science/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS","bundle":"https://pith.science/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/bundle.json","state":"https://pith.science/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRO7YNDB6KZMAJI6TKVB6XVTIS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LRO7YNDB6KZMAJI6TKVB6XVTIS","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":"f1b648aa26b9cd1522a67c115021ccd774ebc5d9745d49b149c82c87a68e0579","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T16:21:04Z","title_canon_sha256":"9bc8e0c8c5802772737b47c9c86e543acd912853bd1ae682a4a32d50b40850a9"},"schema_version":"1.0","source":{"id":"1609.07419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07419","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07419v1","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07419","created_at":"2026-05-18T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"LRO7YNDB6KZM","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LRO7YNDB6KZMAJI6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LRO7YNDB","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:a64479a26c78386c71d1a3c49e18f8f5fef9eed5a0fdee9a0edf80de61783abe","target":"graph","created_at":"2026-05-18T01:04:00Z","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 consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly non-linear first order ODEs that have the characteristics of a","authors_text":"Mihail Zervos, Neofytos Rodosthenous","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T16:21:04Z","title":"Watermark Options"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07419","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":"sha256:5206e36f8018b48f56f8559608e9f9cdbd0b613b6cc1c9c68dd96cf13dce1089","target":"record","created_at":"2026-05-18T01:04:00Z","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":"f1b648aa26b9cd1522a67c115021ccd774ebc5d9745d49b149c82c87a68e0579","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T16:21:04Z","title_canon_sha256":"9bc8e0c8c5802772737b47c9c86e543acd912853bd1ae682a4a32d50b40850a9"},"schema_version":"1.0","source":{"id":"1609.07419","kind":"arxiv","version":1}},"canonical_sha256":"5c5dfc3461f2b2c0251e9aaa1f5eb3448190bfc9f97ccdb238ea79bf844134fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c5dfc3461f2b2c0251e9aaa1f5eb3448190bfc9f97ccdb238ea79bf844134fc","first_computed_at":"2026-05-18T01:04:00.907755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:00.907755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2SON7aQLpP5qEYVwU56FLPv8MQUoG5bxfMAffmeONBk/tKb7lQuMFfp8ZpdUsob7esVLLP1EmJ0WbiUyl+vhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:00.908433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5206e36f8018b48f56f8559608e9f9cdbd0b613b6cc1c9c68dd96cf13dce1089","sha256:a64479a26c78386c71d1a3c49e18f8f5fef9eed5a0fdee9a0edf80de61783abe"],"state_sha256":"b88f0300efeb301ebc2fff1f12c388ee73b6b0f446e56e96fc6bba2fd57e2cd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXjOlmkPWJVXvMfr6vMPZGYByDqn42Cic1JCuwhuvJfyCl6Xny5+LIas+Rqu2QrN9I2N7pznk4NFZXtyGA3VDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:33:49.341525Z","bundle_sha256":"917113558281fc0ef0bc88d9efd6a120ea363dd7aa77c831123bf32096dcd719"}}