{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YYDMACYLSHUX22FHH67UVHQL57","short_pith_number":"pith:YYDMACYL","canonical_record":{"source":{"id":"2605.25824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2026-05-25T13:21:30Z","cross_cats_sorted":[],"title_canon_sha256":"57db0ad61a2dc14606756d2c47ecccdfa6701f1b0e201354b9a288621ca7e3f0","abstract_canon_sha256":"df11f48b5e5e22e10fdcf73a89e8f4c2979b14ccb6f2b727aa18648e4c8226e7"},"schema_version":"1.0"},"canonical_sha256":"c606c00b0b91e97d68a73fbf4a9e0befdc08f9e0b640de9fb43ee0e70ae4e902","source":{"kind":"arxiv","id":"2605.25824","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25824","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25824v1","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25824","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"YYDMACYLSHUX","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_16","alias_value":"YYDMACYLSHUX22FH","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_8","alias_value":"YYDMACYL","created_at":"2026-05-26T02:05:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YYDMACYLSHUX22FHH67UVHQL57","target":"record","payload":{"canonical_record":{"source":{"id":"2605.25824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2026-05-25T13:21:30Z","cross_cats_sorted":[],"title_canon_sha256":"57db0ad61a2dc14606756d2c47ecccdfa6701f1b0e201354b9a288621ca7e3f0","abstract_canon_sha256":"df11f48b5e5e22e10fdcf73a89e8f4c2979b14ccb6f2b727aa18648e4c8226e7"},"schema_version":"1.0"},"canonical_sha256":"c606c00b0b91e97d68a73fbf4a9e0befdc08f9e0b640de9fb43ee0e70ae4e902","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:13.924670Z","signature_b64":"W7E5ltmPbEZT2pmWyfhtmRflV138mY/6QZwJAsicyBi9pT8lUt1uOmVynbR4p3WxpYkESVNeKleysKMJd2WuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c606c00b0b91e97d68a73fbf4a9e0befdc08f9e0b640de9fb43ee0e70ae4e902","last_reissued_at":"2026-05-26T02:05:13.923932Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:13.923932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.25824","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":"2026-05-26T02:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkDvN5m/8BhvUBDnvPKd7lhEY2PDGrDmWoEGW+gvsWh1wIiHeOr0+W/TG5LCGl5RSG6b7u9vpbEZRtFlgh5lDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:45:12.068871Z"},"content_sha256":"9c7221e9fb2b4325b7ba45daef619b0335e22900f642bf8a2ce1b46d91adbf83","schema_version":"1.0","event_id":"sha256:9c7221e9fb2b4325b7ba45daef619b0335e22900f642bf8a2ce1b46d91adbf83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YYDMACYLSHUX22FHH67UVHQL57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field game of mean-variance portfolio management with peer-based relative risk aversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Sheng Wang, Weilun Cheng, Xiang Yu, Zongxia Liang","submitted_at":"2026-05-25T13:21:30Z","abstract_excerpt":"This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average. Due to the inherent time-inconsistency in the MV criterion, together with the piecewise risk aversion, we encounter a class of time-inconsistent MFG, new to the literature. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25824","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25824/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-26T02:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9SA+lW77kuiA8O7sP8pxwbJTUuFSY0gqBPh1uv0L5HosVIt/ftkJzzNElZJ10+XabyeOWuCIUjcQPF3jcxeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:45:12.069464Z"},"content_sha256":"cdcc5d23dcfc0b057d7705fb17a6be9281902b6d2e1855fac2dd6b93b4829ca0","schema_version":"1.0","event_id":"sha256:cdcc5d23dcfc0b057d7705fb17a6be9281902b6d2e1855fac2dd6b93b4829ca0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYDMACYLSHUX22FHH67UVHQL57/bundle.json","state_url":"https://pith.science/pith/YYDMACYLSHUX22FHH67UVHQL57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYDMACYLSHUX22FHH67UVHQL57/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":"2026-06-02T06:45:12Z","links":{"resolver":"https://pith.science/pith/YYDMACYLSHUX22FHH67UVHQL57","bundle":"https://pith.science/pith/YYDMACYLSHUX22FHH67UVHQL57/bundle.json","state":"https://pith.science/pith/YYDMACYLSHUX22FHH67UVHQL57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYDMACYLSHUX22FHH67UVHQL57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YYDMACYLSHUX22FHH67UVHQL57","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":"df11f48b5e5e22e10fdcf73a89e8f4c2979b14ccb6f2b727aa18648e4c8226e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2026-05-25T13:21:30Z","title_canon_sha256":"57db0ad61a2dc14606756d2c47ecccdfa6701f1b0e201354b9a288621ca7e3f0"},"schema_version":"1.0","source":{"id":"2605.25824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25824","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25824v1","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25824","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"YYDMACYLSHUX","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_16","alias_value":"YYDMACYLSHUX22FH","created_at":"2026-05-26T02:05:13Z"},{"alias_kind":"pith_short_8","alias_value":"YYDMACYL","created_at":"2026-05-26T02:05:13Z"}],"graph_snapshots":[{"event_id":"sha256:cdcc5d23dcfc0b057d7705fb17a6be9281902b6d2e1855fac2dd6b93b4829ca0","target":"graph","created_at":"2026-05-26T02:05:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.25824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average. Due to the inherent time-inconsistency in the MV criterion, together with the piecewise risk aversion, we encounter a class of time-inconsistent MFG, new to the literature. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward","authors_text":"Sheng Wang, Weilun Cheng, Xiang Yu, Zongxia Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2026-05-25T13:21:30Z","title":"Mean-field game of mean-variance portfolio management with peer-based relative risk aversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25824","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":"sha256:9c7221e9fb2b4325b7ba45daef619b0335e22900f642bf8a2ce1b46d91adbf83","target":"record","created_at":"2026-05-26T02:05:13Z","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":"df11f48b5e5e22e10fdcf73a89e8f4c2979b14ccb6f2b727aa18648e4c8226e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2026-05-25T13:21:30Z","title_canon_sha256":"57db0ad61a2dc14606756d2c47ecccdfa6701f1b0e201354b9a288621ca7e3f0"},"schema_version":"1.0","source":{"id":"2605.25824","kind":"arxiv","version":1}},"canonical_sha256":"c606c00b0b91e97d68a73fbf4a9e0befdc08f9e0b640de9fb43ee0e70ae4e902","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c606c00b0b91e97d68a73fbf4a9e0befdc08f9e0b640de9fb43ee0e70ae4e902","first_computed_at":"2026-05-26T02:05:13.923932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:13.923932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W7E5ltmPbEZT2pmWyfhtmRflV138mY/6QZwJAsicyBi9pT8lUt1uOmVynbR4p3WxpYkESVNeKleysKMJd2WuCg==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:13.924670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c7221e9fb2b4325b7ba45daef619b0335e22900f642bf8a2ce1b46d91adbf83","sha256:cdcc5d23dcfc0b057d7705fb17a6be9281902b6d2e1855fac2dd6b93b4829ca0"],"state_sha256":"8cced46bcfba67f68bd130830d00006482a15b19a7d3f6a92b2e3047e9225940"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"quw8ruY3W1Ta3d8F4rnyyGs967eAdlWx8sOi0aVxqyfQKVK1ibhtIMyiGTekzMzUMqlaoE0Yn6nZnwgrEwmvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:45:12.073091Z","bundle_sha256":"a0cb9b640aa40a40a26489673edbd904dce98d027bbd4ea34110d1dae509ed2d"}}