{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WL3WMIXKBLVSHNCTJIWP2U4HKI","short_pith_number":"pith:WL3WMIXK","canonical_record":{"source":{"id":"1610.03958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-10-13T07:16:27Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"161302cfdb554b570df1d35a3e42b8e63a800c398af8c34f6c23ba9a92b93158","abstract_canon_sha256":"44819caf80040b5c511fe695d345f6b35ca05b9a36c4f76e252e8cc749e38bc7"},"schema_version":"1.0"},"canonical_sha256":"b2f76622ea0aeb23b4534a2cfd5387523f74d25326fce9e503356205a52b23ea","source":{"kind":"arxiv","id":"1610.03958","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03958","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03958v1","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03958","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"WL3WMIXKBLVS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WL3WMIXKBLVSHNCT","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WL3WMIXK","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WL3WMIXKBLVSHNCTJIWP2U4HKI","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-10-13T07:16:27Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"161302cfdb554b570df1d35a3e42b8e63a800c398af8c34f6c23ba9a92b93158","abstract_canon_sha256":"44819caf80040b5c511fe695d345f6b35ca05b9a36c4f76e252e8cc749e38bc7"},"schema_version":"1.0"},"canonical_sha256":"b2f76622ea0aeb23b4534a2cfd5387523f74d25326fce9e503356205a52b23ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:22.895740Z","signature_b64":"T1mruU4QUq78EcBHYC3JVgrWFL7r8rO0d4EbmMBM8zAFUcmGZ5izdYZBjHQQ3D+8uTdmZWHdd/k6CFfD4AjyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2f76622ea0aeb23b4534a2cfd5387523f74d25326fce9e503356205a52b23ea","last_reissued_at":"2026-05-18T01:02:22.895087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:22.895087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03958","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":"2026-05-18T01:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r50bvXAYtT5fcm0BKLAO+IqtbmvEVDR8MKWQAb09V6AbNTCML4E+gLg1onRlh6CUamw2gNPYf4A47+CLT5cADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:09:06.471184Z"},"content_sha256":"e86bfd8d2f2b432b72971b38816f4f633370cc986d3faad2d9182f493869dcdb","schema_version":"1.0","event_id":"sha256:e86bfd8d2f2b432b72971b38816f4f633370cc986d3faad2d9182f493869dcdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WL3WMIXKBLVSHNCTJIWP2U4HKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Consumption and Investment with Fixed and Proportional Transaction Costs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"q-fin.PM","authors_text":"Albert Altarovici, H. Mete Soner, Max Reppen","submitted_at":"2016-10-13T07:16:27Z","abstract_excerpt":"The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming is proved in the general setting and a comparison result for possibly discontinuous viscosity solutions of the dynamic programming equation is provided. Detailed numerical experiments illustrate several properties of the optimal investment strategies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03958","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":"2026-05-18T01:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBlBdInOOb3O6jgS0B4YLcdDYMIOWvW2ZQRy3CsBJeu0XLPYWzvzA1KdauQJoibNt3OlczYTIVsWGCUdThBaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:09:06.471551Z"},"content_sha256":"7bef7baf2cdb6853a92a1b16ee44fc3a199fa22ed0b500d8601ea8e6e4ffda87","schema_version":"1.0","event_id":"sha256:7bef7baf2cdb6853a92a1b16ee44fc3a199fa22ed0b500d8601ea8e6e4ffda87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/bundle.json","state_url":"https://pith.science/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/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":"2026-06-05T22:09:06Z","links":{"resolver":"https://pith.science/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI","bundle":"https://pith.science/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/bundle.json","state":"https://pith.science/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WL3WMIXKBLVSHNCTJIWP2U4HKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WL3WMIXKBLVSHNCTJIWP2U4HKI","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":"44819caf80040b5c511fe695d345f6b35ca05b9a36c4f76e252e8cc749e38bc7","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-10-13T07:16:27Z","title_canon_sha256":"161302cfdb554b570df1d35a3e42b8e63a800c398af8c34f6c23ba9a92b93158"},"schema_version":"1.0","source":{"id":"1610.03958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03958","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03958v1","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03958","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"WL3WMIXKBLVS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WL3WMIXKBLVSHNCT","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WL3WMIXK","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:7bef7baf2cdb6853a92a1b16ee44fc3a199fa22ed0b500d8601ea8e6e4ffda87","target":"graph","created_at":"2026-05-18T01:02:22Z","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":"The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming is proved in the general setting and a comparison result for possibly discontinuous viscosity solutions of the dynamic programming equation is provided. Detailed numerical experiments illustrate several properties of the optimal investment strategies.","authors_text":"Albert Altarovici, H. Mete Soner, Max Reppen","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-10-13T07:16:27Z","title":"Optimal Consumption and Investment with Fixed and Proportional Transaction Costs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03958","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:e86bfd8d2f2b432b72971b38816f4f633370cc986d3faad2d9182f493869dcdb","target":"record","created_at":"2026-05-18T01:02:22Z","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":"44819caf80040b5c511fe695d345f6b35ca05b9a36c4f76e252e8cc749e38bc7","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-10-13T07:16:27Z","title_canon_sha256":"161302cfdb554b570df1d35a3e42b8e63a800c398af8c34f6c23ba9a92b93158"},"schema_version":"1.0","source":{"id":"1610.03958","kind":"arxiv","version":1}},"canonical_sha256":"b2f76622ea0aeb23b4534a2cfd5387523f74d25326fce9e503356205a52b23ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2f76622ea0aeb23b4534a2cfd5387523f74d25326fce9e503356205a52b23ea","first_computed_at":"2026-05-18T01:02:22.895087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:22.895087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T1mruU4QUq78EcBHYC3JVgrWFL7r8rO0d4EbmMBM8zAFUcmGZ5izdYZBjHQQ3D+8uTdmZWHdd/k6CFfD4AjyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:22.895740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e86bfd8d2f2b432b72971b38816f4f633370cc986d3faad2d9182f493869dcdb","sha256:7bef7baf2cdb6853a92a1b16ee44fc3a199fa22ed0b500d8601ea8e6e4ffda87"],"state_sha256":"e92a35c16ee66f8dba42bf2bf3df846a26aaaf53920b439c71bcbf6cca4791bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSrgUvz4umwrbq8tCDuPudn0z051jntGRa/m4HLOSxwf83Zl/YDebLuB9aT2ev1m5RhE4PWa1uw81BQjjknOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:09:06.473721Z","bundle_sha256":"0e4d357323369e457a2ea7936c96bbb7b53b607f9d9a4be4206610bc9e7c9f92"}}