{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BZ5TYZEUULXEPRPIR3JUVDBPUH","short_pith_number":"pith:BZ5TYZEU","schema_version":"1.0","canonical_sha256":"0e7b3c6494a2ee47c5e88ed34a8c2fa1c2f3356a481e9c96a009dacf1a44734d","source":{"kind":"arxiv","id":"2603.12140","version":4},"attestation_state":"computed","paper":{"title":"Forecasting and Manipulating the Forecasts of Others","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH","q-fin.MF"],"primary_cat":"math.OC","authors_text":"Sam Babichenko","submitted_at":"2026-03-12T16:43:21Z","abstract_excerpt":"Finite-player dynamic games with dispersed private information are difficult because actions both move payoffs and reshape what opponents learn, generating hierarchies of beliefs about beliefs. This paper provides a recursive representation for this problem. The noise state records agents' beliefs about the underlying shocks that generate histories, so higher-order beliefs are generated by composition rather than tracked as separate state variables. In the canonical continuous-time LQG benchmark, the representation becomes explicit: beliefs, value gradients, and policy rules are deterministic "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.12140","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-03-12T16:43:21Z","cross_cats_sorted":["econ.TH","q-fin.MF"],"title_canon_sha256":"90b873266e552d33439b770da6516ceed4f87abcf9168efbc5a85433221d7190","abstract_canon_sha256":"3bddb3af6339a8a7d1f5897e97d77dbfe05195cfbb32a810ce34329a06267b08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:24.545095Z","signature_b64":"Lz8cCr2aqwE7jmud0cYMOH/l1mKHuCpgEK8SUxsFALzmB6dPWkEjceUnkhfFZ7YvrbAeSZCEXygviizGC7BDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e7b3c6494a2ee47c5e88ed34a8c2fa1c2f3356a481e9c96a009dacf1a44734d","last_reissued_at":"2026-05-21T01:04:24.544169Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:24.544169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forecasting and Manipulating the Forecasts of Others","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH","q-fin.MF"],"primary_cat":"math.OC","authors_text":"Sam Babichenko","submitted_at":"2026-03-12T16:43:21Z","abstract_excerpt":"Finite-player dynamic games with dispersed private information are difficult because actions both move payoffs and reshape what opponents learn, generating hierarchies of beliefs about beliefs. This paper provides a recursive representation for this problem. The noise state records agents' beliefs about the underlying shocks that generate histories, so higher-order beliefs are generated by composition rather than tracked as separate state variables. In the canonical continuous-time LQG benchmark, the representation becomes explicit: beliefs, value gradients, and policy rules are deterministic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.12140","kind":"arxiv","version":4},"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/2603.12140/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.12140","created_at":"2026-05-21T01:04:24.544302+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.12140v4","created_at":"2026-05-21T01:04:24.544302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.12140","created_at":"2026-05-21T01:04:24.544302+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ5TYZEUULXE","created_at":"2026-05-21T01:04:24.544302+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ5TYZEUULXEPRPI","created_at":"2026-05-21T01:04:24.544302+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ5TYZEU","created_at":"2026-05-21T01:04:24.544302+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.05545","citing_title":"Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2605.05545","citing_title":"Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH","json":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH.json","graph_json":"https://pith.science/api/pith-number/BZ5TYZEUULXEPRPIR3JUVDBPUH/graph.json","events_json":"https://pith.science/api/pith-number/BZ5TYZEUULXEPRPIR3JUVDBPUH/events.json","paper":"https://pith.science/paper/BZ5TYZEU"},"agent_actions":{"view_html":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH","download_json":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH.json","view_paper":"https://pith.science/paper/BZ5TYZEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.12140&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ5TYZEUULXEPRPIR3JUVDBPUH/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ5TYZEUULXEPRPIR3JUVDBPUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH/action/storage_attestation","attest_author":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH/action/author_attestation","sign_citation":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH/action/citation_signature","submit_replication":"https://pith.science/pith/BZ5TYZEUULXEPRPIR3JUVDBPUH/action/replication_record"}},"created_at":"2026-05-21T01:04:24.544302+00:00","updated_at":"2026-05-21T01:04:24.544302+00:00"}