{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YRQKGRQIFPZ65LY2BGML5LBPEY","short_pith_number":"pith:YRQKGRQI","canonical_record":{"source":{"id":"1612.09469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2016-12-30T12:05:06Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"7236e317c3945bc26138682f8c8737467abcfeda73833a36d8a34e1ab5030d76","abstract_canon_sha256":"16a02cc32fae36e6066a5900ac00c3d18ae1cf3710da8f39fbc6317e709642f4"},"schema_version":"1.0"},"canonical_sha256":"c460a346082bf3eeaf1a0998beac2f26265438192ac31a54e16ddcfb55eb61a6","source":{"kind":"arxiv","id":"1612.09469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09469","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09469v1","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09469","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"YRQKGRQIFPZ6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YRQKGRQIFPZ65LY2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YRQKGRQI","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YRQKGRQIFPZ65LY2BGML5LBPEY","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2016-12-30T12:05:06Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"7236e317c3945bc26138682f8c8737467abcfeda73833a36d8a34e1ab5030d76","abstract_canon_sha256":"16a02cc32fae36e6066a5900ac00c3d18ae1cf3710da8f39fbc6317e709642f4"},"schema_version":"1.0"},"canonical_sha256":"c460a346082bf3eeaf1a0998beac2f26265438192ac31a54e16ddcfb55eb61a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:06.862807Z","signature_b64":"+rm+uWeO9UKGlELJOCaeUpVIfvfAxX7KUv/UvkG/FKTie5TacnYiX4j8mPeN4/VsaegsBY78gehvl78sm7bHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c460a346082bf3eeaf1a0998beac2f26265438192ac31a54e16ddcfb55eb61a6","last_reissued_at":"2026-05-18T00:51:06.862266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:06.862266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09469","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":"2026-05-18T00:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZgyyuDm5VVBEmu/qx314wXogqQv0FkyvaUXfF5Q4ymApP1nkEwOOiD6mWBsjxvhuCm83BB+H15s+RWy3/lbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:50:07.734453Z"},"content_sha256":"36ae4eb43f2aa3f7abda6c635d964745558ff1e0c949b99d2b931820f1baeab1","schema_version":"1.0","event_id":"sha256:36ae4eb43f2aa3f7abda6c635d964745558ff1e0c949b99d2b931820f1baeab1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YRQKGRQIFPZ65LY2BGML5LBPEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A spectral method for an Optimal Investment problem with Transaction Costs under Potential Utility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"q-fin.CP","authors_text":"Javier de Frutos, Victor Gaton","submitted_at":"2016-12-30T12:05:06Z","abstract_excerpt":"This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem, Day-Yi, the problem is reformulated as a non-linear parabolic double obstacle problem posed in one spatial variable and defined in an unbounded domain where several explicit properties and formulas are obtained. The restatement of the problem in polar coordinates al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09469","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":"2026-05-18T00:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBExouRAMp0/L1d4SVD8aDZFJgqbYxMD+OfoFWLBC5IXAwELiX9Xjh+nqT7KYamI1S1e/dCeziNv5kaPcTJ0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:50:07.734802Z"},"content_sha256":"8ac4b9860237d9c329367cd4db9d9b8eb386a98cc5528456e3d0f63639f77487","schema_version":"1.0","event_id":"sha256:8ac4b9860237d9c329367cd4db9d9b8eb386a98cc5528456e3d0f63639f77487"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/bundle.json","state_url":"https://pith.science/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/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":"2026-06-02T23:50:07Z","links":{"resolver":"https://pith.science/pith/YRQKGRQIFPZ65LY2BGML5LBPEY","bundle":"https://pith.science/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/bundle.json","state":"https://pith.science/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YRQKGRQIFPZ65LY2BGML5LBPEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YRQKGRQIFPZ65LY2BGML5LBPEY","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":"16a02cc32fae36e6066a5900ac00c3d18ae1cf3710da8f39fbc6317e709642f4","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2016-12-30T12:05:06Z","title_canon_sha256":"7236e317c3945bc26138682f8c8737467abcfeda73833a36d8a34e1ab5030d76"},"schema_version":"1.0","source":{"id":"1612.09469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09469","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09469v1","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09469","created_at":"2026-05-18T00:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"YRQKGRQIFPZ6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YRQKGRQIFPZ65LY2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YRQKGRQI","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:8ac4b9860237d9c329367cd4db9d9b8eb386a98cc5528456e3d0f63639f77487","target":"graph","created_at":"2026-05-18T00:51:06Z","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":"This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem, Day-Yi, the problem is reformulated as a non-linear parabolic double obstacle problem posed in one spatial variable and defined in an unbounded domain where several explicit properties and formulas are obtained. The restatement of the problem in polar coordinates al","authors_text":"Javier de Frutos, Victor Gaton","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2016-12-30T12:05:06Z","title":"A spectral method for an Optimal Investment problem with Transaction Costs under Potential Utility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09469","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":"sha256:36ae4eb43f2aa3f7abda6c635d964745558ff1e0c949b99d2b931820f1baeab1","target":"record","created_at":"2026-05-18T00:51:06Z","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":"16a02cc32fae36e6066a5900ac00c3d18ae1cf3710da8f39fbc6317e709642f4","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2016-12-30T12:05:06Z","title_canon_sha256":"7236e317c3945bc26138682f8c8737467abcfeda73833a36d8a34e1ab5030d76"},"schema_version":"1.0","source":{"id":"1612.09469","kind":"arxiv","version":1}},"canonical_sha256":"c460a346082bf3eeaf1a0998beac2f26265438192ac31a54e16ddcfb55eb61a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c460a346082bf3eeaf1a0998beac2f26265438192ac31a54e16ddcfb55eb61a6","first_computed_at":"2026-05-18T00:51:06.862266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:06.862266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+rm+uWeO9UKGlELJOCaeUpVIfvfAxX7KUv/UvkG/FKTie5TacnYiX4j8mPeN4/VsaegsBY78gehvl78sm7bHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:06.862807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ae4eb43f2aa3f7abda6c635d964745558ff1e0c949b99d2b931820f1baeab1","sha256:8ac4b9860237d9c329367cd4db9d9b8eb386a98cc5528456e3d0f63639f77487"],"state_sha256":"7bee4e80709adf4390095a655af2a24d40e2126f813f2fe20a85343e019e691d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0qR3P4pBiiEZdlJuWLv+2LWYRI4rD1lij+S/p46V2QRWdnK/5LVV9+iHyU6618KTfLS3YTZd7/Fc/x1GCSmAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:50:07.736784Z","bundle_sha256":"4f85ae990d48aef6c948ffb0abb6e186502ddac2f60009f3f6ecf64e5f892d55"}}