{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PXLL6ECPCW4ICTRNHABRKKHPBR","short_pith_number":"pith:PXLL6ECP","canonical_record":{"source":{"id":"2607.01719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-02T05:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"529fd90bd538777fb6bf485225e3663dc560668b3446166119c85b09583e0ea2","abstract_canon_sha256":"3f160b70001a0da946d2fc937d9e0de8e95cfa75ff11ee0b734ff6424d62ebb4"},"schema_version":"1.0"},"canonical_sha256":"7dd6bf104f15b8814e2d38031528ef0c432fab7e9c0943be7cff06d906d52315","source":{"kind":"arxiv","id":"2607.01719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01719","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01719v1","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01719","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"PXLL6ECPCW4I","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"PXLL6ECPCW4ICTRN","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"PXLL6ECP","created_at":"2026-07-03T01:17:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PXLL6ECPCW4ICTRNHABRKKHPBR","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-02T05:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"529fd90bd538777fb6bf485225e3663dc560668b3446166119c85b09583e0ea2","abstract_canon_sha256":"3f160b70001a0da946d2fc937d9e0de8e95cfa75ff11ee0b734ff6424d62ebb4"},"schema_version":"1.0"},"canonical_sha256":"7dd6bf104f15b8814e2d38031528ef0c432fab7e9c0943be7cff06d906d52315","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:27.737596Z","signature_b64":"TAOK/8ANVrU9NkzOGG71/6xDX2ahcgUN/tbKObP9YXWDFu5YrUs70WNX0LZ+MXiyMEakbdcHW5eU3izdOESuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dd6bf104f15b8814e2d38031528ef0c432fab7e9c0943be7cff06d906d52315","last_reissued_at":"2026-07-03T01:17:27.737187Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:27.737187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01719","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":"2026-07-03T01:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1zFOCF/jf7uCjyuD35Kup1faRxNDCJ7Fnaml5r7rwx8N9b96rksOdjQ5pwfJ7Ih2qKMtte69urB8E1SQhqHACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:24:29.445286Z"},"content_sha256":"8f8dce23b03174f8bf8c54ecae290921bd0cbf3ff405561d4303458690ace76c","schema_version":"1.0","event_id":"sha256:8f8dce23b03174f8bf8c54ecae290921bd0cbf3ff405561d4303458690ace76c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PXLL6ECPCW4ICTRNHABRKKHPBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypergraph Minority Game with Local Hyperedge Payoffs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Fanyuan Meng, Yihang Zhu","submitted_at":"2026-07-02T05:17:11Z","abstract_excerpt":"We provide a theoretical derivation of the Hypergraph Minority Game with Local Hyperedge Payoffs (HMG-L), in which $N$ adaptive agents compete simultaneously in multiple overlapping groups modeled as hyperedges of a static hypergraph $\\Hyper=(\\Vset,\\Eset)$. Each hyperedge constitutes an independent local minority game, and agents accumulate payoffs across all groups to which they belong. We derive the continuum-time limit of the score dynamics, from which we obtain a set of coupled nonlinear stochastic differential equations for the agents' strategy polarization variables. The deterministic dr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01719","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/2607.01719/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":"2026-07-03T01:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imXpVnkxUw9jsgHe2QlG3rlSOrpDJ8B2Q937d5wwdVciw9EWy7hB7MAMKFDfjTNr+YMuu4BG6+0T80Qe/u2MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:24:29.445704Z"},"content_sha256":"cc03708c59232c729637316ce39f2d579c11992cd3c7c2119eef6ab68cd8a8ed","schema_version":"1.0","event_id":"sha256:cc03708c59232c729637316ce39f2d579c11992cd3c7c2119eef6ab68cd8a8ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/bundle.json","state_url":"https://pith.science/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/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":"2026-07-07T09:24:29Z","links":{"resolver":"https://pith.science/pith/PXLL6ECPCW4ICTRNHABRKKHPBR","bundle":"https://pith.science/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/bundle.json","state":"https://pith.science/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXLL6ECPCW4ICTRNHABRKKHPBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PXLL6ECPCW4ICTRNHABRKKHPBR","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":"3f160b70001a0da946d2fc937d9e0de8e95cfa75ff11ee0b734ff6424d62ebb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-02T05:17:11Z","title_canon_sha256":"529fd90bd538777fb6bf485225e3663dc560668b3446166119c85b09583e0ea2"},"schema_version":"1.0","source":{"id":"2607.01719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01719","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01719v1","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01719","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"PXLL6ECPCW4I","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"PXLL6ECPCW4ICTRN","created_at":"2026-07-03T01:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"PXLL6ECP","created_at":"2026-07-03T01:17:27Z"}],"graph_snapshots":[{"event_id":"sha256:cc03708c59232c729637316ce39f2d579c11992cd3c7c2119eef6ab68cd8a8ed","target":"graph","created_at":"2026-07-03T01:17:27Z","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/2607.01719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a theoretical derivation of the Hypergraph Minority Game with Local Hyperedge Payoffs (HMG-L), in which $N$ adaptive agents compete simultaneously in multiple overlapping groups modeled as hyperedges of a static hypergraph $\\Hyper=(\\Vset,\\Eset)$. Each hyperedge constitutes an independent local minority game, and agents accumulate payoffs across all groups to which they belong. We derive the continuum-time limit of the score dynamics, from which we obtain a set of coupled nonlinear stochastic differential equations for the agents' strategy polarization variables. The deterministic dr","authors_text":"Fanyuan Meng, Yihang Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-02T05:17:11Z","title":"Hypergraph Minority Game with Local Hyperedge Payoffs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01719","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":"sha256:8f8dce23b03174f8bf8c54ecae290921bd0cbf3ff405561d4303458690ace76c","target":"record","created_at":"2026-07-03T01:17:27Z","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":"3f160b70001a0da946d2fc937d9e0de8e95cfa75ff11ee0b734ff6424d62ebb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2026-07-02T05:17:11Z","title_canon_sha256":"529fd90bd538777fb6bf485225e3663dc560668b3446166119c85b09583e0ea2"},"schema_version":"1.0","source":{"id":"2607.01719","kind":"arxiv","version":1}},"canonical_sha256":"7dd6bf104f15b8814e2d38031528ef0c432fab7e9c0943be7cff06d906d52315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dd6bf104f15b8814e2d38031528ef0c432fab7e9c0943be7cff06d906d52315","first_computed_at":"2026-07-03T01:17:27.737187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:27.737187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TAOK/8ANVrU9NkzOGG71/6xDX2ahcgUN/tbKObP9YXWDFu5YrUs70WNX0LZ+MXiyMEakbdcHW5eU3izdOESuDA==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:27.737596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f8dce23b03174f8bf8c54ecae290921bd0cbf3ff405561d4303458690ace76c","sha256:cc03708c59232c729637316ce39f2d579c11992cd3c7c2119eef6ab68cd8a8ed"],"state_sha256":"f98b576670d72106d658fcfba5efec71a19103028d1e3a965c8b823019df0509"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D8MY9F13UorfdHx6bsQdd0NxtqWRa4e6R4kWNg8u6TUn5Hgs78FRSpti5HdvHQicvNUGYepZSD9RQyscMSlNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:24:29.447670Z","bundle_sha256":"aea9d80a57256fb98328018bf3414d4c64d4c8d926cf0ccff7b4e4d733cd02b8"}}