{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LDSAW5MH53Z2PYCSPR4KYWDVGE","short_pith_number":"pith:LDSAW5MH","canonical_record":{"source":{"id":"1603.08245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-03-27T19:10:38Z","cross_cats_sorted":["math.PR","q-fin.PM"],"title_canon_sha256":"cbd4bd1d5e7cfc37fd2181e5a4009cc9f54f179f4bb58588e05681dafa4016cd","abstract_canon_sha256":"8d98263a204dabd67f3e1d30906a5db906d407abbef66f751fae95a7be894da4"},"schema_version":"1.0"},"canonical_sha256":"58e40b7587eef3a7e0527c78ac5875311810a8639608e8312edd023b4bbad82d","source":{"kind":"arxiv","id":"1603.08245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08245","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08245v1","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08245","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"LDSAW5MH53Z2","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LDSAW5MH53Z2PYCS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LDSAW5MH","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LDSAW5MH53Z2PYCSPR4KYWDVGE","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-03-27T19:10:38Z","cross_cats_sorted":["math.PR","q-fin.PM"],"title_canon_sha256":"cbd4bd1d5e7cfc37fd2181e5a4009cc9f54f179f4bb58588e05681dafa4016cd","abstract_canon_sha256":"8d98263a204dabd67f3e1d30906a5db906d407abbef66f751fae95a7be894da4"},"schema_version":"1.0"},"canonical_sha256":"58e40b7587eef3a7e0527c78ac5875311810a8639608e8312edd023b4bbad82d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:12.785915Z","signature_b64":"jqRG+ba/ZdmSAfuYW+LdWzi57nK0+DjMgbAuWFbTCgG2mMNfXVQzhuxF03Xqv7uqi5HKv8iKyIHZ8Seyze0jDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58e40b7587eef3a7e0527c78ac5875311810a8639608e8312edd023b4bbad82d","last_reissued_at":"2026-05-18T01:18:12.785164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:12.785164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08245","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":"2026-05-18T01:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2U3WelRN52xQNqzRU/+aCgs6YFw8R00Gt0ins0uyUafqjE7ZZhQ6eh+qzOCP8rZqGPHN9Ye7QmoyWWRZpS3gDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:21:06.187723Z"},"content_sha256":"5b8088114aabe105165aab60211eabe077bd12555885450ebb1b7b1b5dc14c98","schema_version":"1.0","event_id":"sha256:5b8088114aabe105165aab60211eabe077bd12555885450ebb1b7b1b5dc14c98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LDSAW5MH53Z2PYCSPR4KYWDVGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trading Strategies Generated by Lyapunov Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.PM"],"primary_cat":"q-fin.MF","authors_text":"Ioannis Karatzas, Johannes Ruf","submitted_at":"2016-03-27T19:10:38Z","abstract_excerpt":"Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameters. In this paper, the corresponding generating functions $G$ are interpreted as Lyapunov functions for the vector process $\\mu(\\cdot)$ of market weights; that is, via the property that $G(\\mu(\\cdot))$ is a supermartingale under an appropriate change of measure. This point of view"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08245","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":"2026-05-18T01:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0RQtN03/IPOnmJdqM/GgKv2bN25tYxdN8hWUI/vSOuQYtPodeWYPwXwyY98zY2x4t5qBrKEGkA+OQ307SftZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:21:06.188359Z"},"content_sha256":"84f93d204e41f8b663e0b2be426b5152bd601946433c8ae1c91c8872288724f8","schema_version":"1.0","event_id":"sha256:84f93d204e41f8b663e0b2be426b5152bd601946433c8ae1c91c8872288724f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/bundle.json","state_url":"https://pith.science/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/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":"2026-05-26T01:21:06Z","links":{"resolver":"https://pith.science/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE","bundle":"https://pith.science/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/bundle.json","state":"https://pith.science/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDSAW5MH53Z2PYCSPR4KYWDVGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LDSAW5MH53Z2PYCSPR4KYWDVGE","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":"8d98263a204dabd67f3e1d30906a5db906d407abbef66f751fae95a7be894da4","cross_cats_sorted":["math.PR","q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-03-27T19:10:38Z","title_canon_sha256":"cbd4bd1d5e7cfc37fd2181e5a4009cc9f54f179f4bb58588e05681dafa4016cd"},"schema_version":"1.0","source":{"id":"1603.08245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08245","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08245v1","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08245","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"LDSAW5MH53Z2","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LDSAW5MH53Z2PYCS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LDSAW5MH","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:84f93d204e41f8b663e0b2be426b5152bd601946433c8ae1c91c8872288724f8","target":"graph","created_at":"2026-05-18T01:18:12Z","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":"Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameters. In this paper, the corresponding generating functions $G$ are interpreted as Lyapunov functions for the vector process $\\mu(\\cdot)$ of market weights; that is, via the property that $G(\\mu(\\cdot))$ is a supermartingale under an appropriate change of measure. This point of view","authors_text":"Ioannis Karatzas, Johannes Ruf","cross_cats":["math.PR","q-fin.PM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-03-27T19:10:38Z","title":"Trading Strategies Generated by Lyapunov Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08245","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":"sha256:5b8088114aabe105165aab60211eabe077bd12555885450ebb1b7b1b5dc14c98","target":"record","created_at":"2026-05-18T01:18:12Z","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":"8d98263a204dabd67f3e1d30906a5db906d407abbef66f751fae95a7be894da4","cross_cats_sorted":["math.PR","q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-03-27T19:10:38Z","title_canon_sha256":"cbd4bd1d5e7cfc37fd2181e5a4009cc9f54f179f4bb58588e05681dafa4016cd"},"schema_version":"1.0","source":{"id":"1603.08245","kind":"arxiv","version":1}},"canonical_sha256":"58e40b7587eef3a7e0527c78ac5875311810a8639608e8312edd023b4bbad82d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58e40b7587eef3a7e0527c78ac5875311810a8639608e8312edd023b4bbad82d","first_computed_at":"2026-05-18T01:18:12.785164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:12.785164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jqRG+ba/ZdmSAfuYW+LdWzi57nK0+DjMgbAuWFbTCgG2mMNfXVQzhuxF03Xqv7uqi5HKv8iKyIHZ8Seyze0jDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:12.785915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b8088114aabe105165aab60211eabe077bd12555885450ebb1b7b1b5dc14c98","sha256:84f93d204e41f8b663e0b2be426b5152bd601946433c8ae1c91c8872288724f8"],"state_sha256":"cfeadf7c264e733913132078c0050d956c3f335285898210ae916563e4c3da83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Py43djW4hVCKglRlBcx5KMXi1rEBa1nEJ9kU0TYWub23HkVppQyK+1UivzW8dK6l9nvU7CTkr5NuZykzm+aJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:21:06.191699Z","bundle_sha256":"efd3a4f2640cb9787dce9f87385300bf3f72f0bfaedf33f5bf7f5927055e64b4"}}