{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:656DUZ7RGZFJUYAPXDQZFLINN6","short_pith_number":"pith:656DUZ7R","canonical_record":{"source":{"id":"1609.05475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-09-18T12:09:28Z","cross_cats_sorted":["cond-mat.dis-nn","math.OC","stat.AP"],"title_canon_sha256":"3a9491850b6907b55eb83e2e50b581765c5a64f7dcf669469ecfc7063182ac68","abstract_canon_sha256":"341c2c0dbbf9db826a22de2d24212af8a48f90b2c0b090c97cf111a9f196e751"},"schema_version":"1.0"},"canonical_sha256":"f77c3a67f1364a9a600fb8e192ad0d6fa86f5c2160ecc2b5d2ddcec423fac0e8","source":{"kind":"arxiv","id":"1609.05475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05475","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05475v1","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05475","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"656DUZ7RGZFJ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"656DUZ7RGZFJUYAP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"656DUZ7R","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:656DUZ7RGZFJUYAPXDQZFLINN6","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-09-18T12:09:28Z","cross_cats_sorted":["cond-mat.dis-nn","math.OC","stat.AP"],"title_canon_sha256":"3a9491850b6907b55eb83e2e50b581765c5a64f7dcf669469ecfc7063182ac68","abstract_canon_sha256":"341c2c0dbbf9db826a22de2d24212af8a48f90b2c0b090c97cf111a9f196e751"},"schema_version":"1.0"},"canonical_sha256":"f77c3a67f1364a9a600fb8e192ad0d6fa86f5c2160ecc2b5d2ddcec423fac0e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:47.372899Z","signature_b64":"35rsRu90mJHIEY5e5Mly+xyJ5HDnwYuRsQ1PXboU4RrpMll6B1Tqvb3Ol8KrVcGEE13D05K5fLl629lqvERvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f77c3a67f1364a9a600fb8e192ad0d6fa86f5c2160ecc2b5d2ddcec423fac0e8","last_reissued_at":"2026-05-18T00:54:47.372279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:47.372279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05475","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":"2026-05-18T00:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNCQ+3R2s8/Hbd2R4II4ixF5zd0jB7BnnLiMyNlUs1jSrELLH6e3ULl6v/XAzKfP2HORmbpw+zUWbHE1aLwhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:24:40.381130Z"},"content_sha256":"b9114ce43d7c78c5648d8b0660e742f87934aec1ea8a99e08ae5a3d4efd28ca2","schema_version":"1.0","event_id":"sha256:b9114ce43d7c78c5648d8b0660e742f87934aec1ea8a99e08ae5a3d4efd28ca2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:656DUZ7RGZFJUYAPXDQZFLINN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Replica Analysis for the Duality of the Portfolio Optimization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.OC","stat.AP"],"primary_cat":"q-fin.PM","authors_text":"Takashi Shinzato","submitted_at":"2016-09-18T12:09:28Z","abstract_excerpt":"In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05475","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":"2026-05-18T00:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nd5x0nP3wsIlUPrI+ZkMz8V8tMJ/bQkHsZLpNfGRymdLRDbPD5LEb7AFx3q90ZKAqFWrdOijd/tThZpq0IzfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:24:40.381511Z"},"content_sha256":"0a2fcba8efe408322fe8dbd0d4c0ddf95ffb8788061ab630d89f2e77cdbb39b9","schema_version":"1.0","event_id":"sha256:0a2fcba8efe408322fe8dbd0d4c0ddf95ffb8788061ab630d89f2e77cdbb39b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/656DUZ7RGZFJUYAPXDQZFLINN6/bundle.json","state_url":"https://pith.science/pith/656DUZ7RGZFJUYAPXDQZFLINN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/656DUZ7RGZFJUYAPXDQZFLINN6/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":"2026-06-24T22:24:40Z","links":{"resolver":"https://pith.science/pith/656DUZ7RGZFJUYAPXDQZFLINN6","bundle":"https://pith.science/pith/656DUZ7RGZFJUYAPXDQZFLINN6/bundle.json","state":"https://pith.science/pith/656DUZ7RGZFJUYAPXDQZFLINN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/656DUZ7RGZFJUYAPXDQZFLINN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:656DUZ7RGZFJUYAPXDQZFLINN6","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":"341c2c0dbbf9db826a22de2d24212af8a48f90b2c0b090c97cf111a9f196e751","cross_cats_sorted":["cond-mat.dis-nn","math.OC","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-09-18T12:09:28Z","title_canon_sha256":"3a9491850b6907b55eb83e2e50b581765c5a64f7dcf669469ecfc7063182ac68"},"schema_version":"1.0","source":{"id":"1609.05475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05475","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05475v1","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05475","created_at":"2026-05-18T00:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"656DUZ7RGZFJ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"656DUZ7RGZFJUYAP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"656DUZ7R","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:0a2fcba8efe408322fe8dbd0d4c0ddf95ffb8788061ab630d89f2e77cdbb39b9","target":"graph","created_at":"2026-05-18T00:54:47Z","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":"In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constra","authors_text":"Takashi Shinzato","cross_cats":["cond-mat.dis-nn","math.OC","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-09-18T12:09:28Z","title":"Replica Analysis for the Duality of the Portfolio Optimization Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05475","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:b9114ce43d7c78c5648d8b0660e742f87934aec1ea8a99e08ae5a3d4efd28ca2","target":"record","created_at":"2026-05-18T00:54:47Z","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":"341c2c0dbbf9db826a22de2d24212af8a48f90b2c0b090c97cf111a9f196e751","cross_cats_sorted":["cond-mat.dis-nn","math.OC","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2016-09-18T12:09:28Z","title_canon_sha256":"3a9491850b6907b55eb83e2e50b581765c5a64f7dcf669469ecfc7063182ac68"},"schema_version":"1.0","source":{"id":"1609.05475","kind":"arxiv","version":1}},"canonical_sha256":"f77c3a67f1364a9a600fb8e192ad0d6fa86f5c2160ecc2b5d2ddcec423fac0e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f77c3a67f1364a9a600fb8e192ad0d6fa86f5c2160ecc2b5d2ddcec423fac0e8","first_computed_at":"2026-05-18T00:54:47.372279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:47.372279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"35rsRu90mJHIEY5e5Mly+xyJ5HDnwYuRsQ1PXboU4RrpMll6B1Tqvb3Ol8KrVcGEE13D05K5fLl629lqvERvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:47.372899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9114ce43d7c78c5648d8b0660e742f87934aec1ea8a99e08ae5a3d4efd28ca2","sha256:0a2fcba8efe408322fe8dbd0d4c0ddf95ffb8788061ab630d89f2e77cdbb39b9"],"state_sha256":"1d062880e30730a5da33d8a248d8861ffe47a13edb5ae5f355b78b1b200ee372"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDJcsl1xxPTcc6sYbqY5AkHGSWV0Ox+vyS8wfLEhSk3oVsb2Dx8ncGrLv6CkrMl4pzBl5Nz8s2aVdh3twbMBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:24:40.383570Z","bundle_sha256":"226c8118be272790c4f1a13f09583fb683e5792a88a77aec61a55994cc7c398a"}}