{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:K2YEIR5XJT7MI2KBLW776BHW63","short_pith_number":"pith:K2YEIR5X","canonical_record":{"source":{"id":"2605.22764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-21T17:25:13Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"0adc4c6da30cff1810ad68736f058f7b0e9d971eba324d2cd12be5adce013828","abstract_canon_sha256":"68af82d44edb72c19948aa19015d5ea98ae7a67d4c77dbe00642d5d389068423"},"schema_version":"1.0"},"canonical_sha256":"56b04447b74cfec469415dbfff04f6f6d029baef59a18b30d253826ad76dcd63","source":{"kind":"arxiv","id":"2605.22764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22764","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22764v1","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22764","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"K2YEIR5XJT7M","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"K2YEIR5XJT7MI2KB","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"K2YEIR5X","created_at":"2026-05-22T02:04:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:K2YEIR5XJT7MI2KBLW776BHW63","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-21T17:25:13Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"0adc4c6da30cff1810ad68736f058f7b0e9d971eba324d2cd12be5adce013828","abstract_canon_sha256":"68af82d44edb72c19948aa19015d5ea98ae7a67d4c77dbe00642d5d389068423"},"schema_version":"1.0"},"canonical_sha256":"56b04447b74cfec469415dbfff04f6f6d029baef59a18b30d253826ad76dcd63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:53.997660Z","signature_b64":"8W4GoNhsi0to4bSSsSbanNiDJK1qQiMbZqemCi9tDkb3hW5U7C1WVd+8qQ2k86OTsicBzXVgEWB0WMzf9JOGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56b04447b74cfec469415dbfff04f6f6d029baef59a18b30d253826ad76dcd63","last_reissued_at":"2026-05-22T02:04:53.997166Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:53.997166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22764","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":"2026-05-22T02:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+XNiREQjTAo3o4XdpWfjoawWIqjmH/4wsuPCqDizzn8iW/fRWE2jIGP0yvf7TvTzS2YfHytaCImYklRdBaJ1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:00:40.702221Z"},"content_sha256":"bc0eeb50568ddb8c87c85476847a0553ea053074995dc6830efa23d29d2179c2","schema_version":"1.0","event_id":"sha256:bc0eeb50568ddb8c87c85476847a0553ea053074995dc6830efa23d29d2179c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:K2YEIR5XJT7MI2KBLW776BHW63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin Glass Mapping of the Parallel Minority Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Anirban Chakraborti, Aryan Tyagi, Soumyaditya Das, Soumyajyoti Biswas","submitted_at":"2026-05-21T17:25:13Z","abstract_excerpt":"The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22764","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/2605.22764/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":"2026-05-22T02:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FgbqUVNG0FBgDQ8ionAb0KIT9cJSiNoMHbXAprFq3gJKJEJdeReyzoVpjdcguRbLMj6GHVkLHfOrtfOb0tPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:00:40.702932Z"},"content_sha256":"a8d6b4956cdf113f684989d66cd7f122cefc6bfaa21b911135123b8eeae27253","schema_version":"1.0","event_id":"sha256:a8d6b4956cdf113f684989d66cd7f122cefc6bfaa21b911135123b8eeae27253"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2YEIR5XJT7MI2KBLW776BHW63/bundle.json","state_url":"https://pith.science/pith/K2YEIR5XJT7MI2KBLW776BHW63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2YEIR5XJT7MI2KBLW776BHW63/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":"2026-05-27T03:00:40Z","links":{"resolver":"https://pith.science/pith/K2YEIR5XJT7MI2KBLW776BHW63","bundle":"https://pith.science/pith/K2YEIR5XJT7MI2KBLW776BHW63/bundle.json","state":"https://pith.science/pith/K2YEIR5XJT7MI2KBLW776BHW63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2YEIR5XJT7MI2KBLW776BHW63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K2YEIR5XJT7MI2KBLW776BHW63","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":"68af82d44edb72c19948aa19015d5ea98ae7a67d4c77dbe00642d5d389068423","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-21T17:25:13Z","title_canon_sha256":"0adc4c6da30cff1810ad68736f058f7b0e9d971eba324d2cd12be5adce013828"},"schema_version":"1.0","source":{"id":"2605.22764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22764","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22764v1","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22764","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"K2YEIR5XJT7M","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"K2YEIR5XJT7MI2KB","created_at":"2026-05-22T02:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"K2YEIR5X","created_at":"2026-05-22T02:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:a8d6b4956cdf113f684989d66cd7f122cefc6bfaa21b911135123b8eeae27253","target":"graph","created_at":"2026-05-22T02:04:53Z","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/2605.22764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. T","authors_text":"Anirban Chakraborti, Aryan Tyagi, Soumyaditya Das, Soumyajyoti Biswas","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-21T17:25:13Z","title":"Spin Glass Mapping of the Parallel Minority Game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22764","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:bc0eeb50568ddb8c87c85476847a0553ea053074995dc6830efa23d29d2179c2","target":"record","created_at":"2026-05-22T02:04:53Z","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":"68af82d44edb72c19948aa19015d5ea98ae7a67d4c77dbe00642d5d389068423","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-05-21T17:25:13Z","title_canon_sha256":"0adc4c6da30cff1810ad68736f058f7b0e9d971eba324d2cd12be5adce013828"},"schema_version":"1.0","source":{"id":"2605.22764","kind":"arxiv","version":1}},"canonical_sha256":"56b04447b74cfec469415dbfff04f6f6d029baef59a18b30d253826ad76dcd63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56b04447b74cfec469415dbfff04f6f6d029baef59a18b30d253826ad76dcd63","first_computed_at":"2026-05-22T02:04:53.997166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:53.997166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8W4GoNhsi0to4bSSsSbanNiDJK1qQiMbZqemCi9tDkb3hW5U7C1WVd+8qQ2k86OTsicBzXVgEWB0WMzf9JOGBA==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:53.997660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0eeb50568ddb8c87c85476847a0553ea053074995dc6830efa23d29d2179c2","sha256:a8d6b4956cdf113f684989d66cd7f122cefc6bfaa21b911135123b8eeae27253"],"state_sha256":"845341e878f27814953f4f79d6895ccc9c0abe7c96eeddf8354a40ab1b2ce519"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBCpQmkEGwuUOnpH/+6nss5drHCfgGO+EmkZtIvf7Q3uAWSSgZSqxOWlqiPc1w/4nU5FUsAGQ7wCrtKbINDTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:00:40.706417Z","bundle_sha256":"d6f0cb58a706a5c6b7e907e8c3ebf692cf31562c3679910956c6ec908019a999"}}