{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:J7UZJOUZTUH3EQHAOKCBXVN5BQ","short_pith_number":"pith:J7UZJOUZ","schema_version":"1.0","canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","source":{"kind":"arxiv","id":"2507.20150","version":1},"attestation_state":"computed","paper":{"title":"The Policy Cliff: A Theoretical Analysis of Reward-Policy Maps in Large Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL","cs.LG"],"primary_cat":"cs.AI","authors_text":"Xingcheng Xu","submitted_at":"2025-07-27T06:56:10Z","abstract_excerpt":"Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal"},"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":"2507.20150","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-07-27T06:56:10Z","cross_cats_sorted":["cs.CL","cs.LG"],"title_canon_sha256":"d12c4e3e7c14fdeea43cf4ead7a85913d95576fe6b14eaf8ec11a1b32f8c4d11","abstract_canon_sha256":"7c35d02f9befd33e21ae280eff10cf20dcd618496d4f0465b89fb8d8c888824e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:14.168719Z","signature_b64":"FMot4GnLE3EDODxs1f/CFC5WnzduhmYcHzXJhkjnrP9vhMsKUb/ohwfWds7nBq6vAw4YrmXZxAMcvLphFphODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","last_reissued_at":"2026-07-05T11:44:14.168267Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:14.168267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Policy Cliff: A Theoretical Analysis of Reward-Policy Maps in Large Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL","cs.LG"],"primary_cat":"cs.AI","authors_text":"Xingcheng Xu","submitted_at":"2025-07-27T06:56:10Z","abstract_excerpt":"Reinforcement learning (RL) plays a crucial role in shaping the behavior of large language and reasoning models (LLMs/LRMs). However, it often produces brittle and unstable policies, leading to critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience that undermine the trustworthiness and safety of LLMs/LRMs. Currently, these issues lack a unified theoretical explanation and are typically addressed using ad-hoc heuristics. This paper presents a rigorous mathematical framework for analyzing the stability of the mapping from a reward function to the optimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20150","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/2507.20150/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":"2507.20150","created_at":"2026-07-05T11:44:14.168334+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20150v1","created_at":"2026-07-05T11:44:14.168334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20150","created_at":"2026-07-05T11:44:14.168334+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7UZJOUZTUH3","created_at":"2026-07-05T11:44:14.168334+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7UZJOUZTUH3EQHA","created_at":"2026-07-05T11:44:14.168334+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7UZJOUZ","created_at":"2026-07-05T11:44:14.168334+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ","json":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ.json","graph_json":"https://pith.science/api/pith-number/J7UZJOUZTUH3EQHAOKCBXVN5BQ/graph.json","events_json":"https://pith.science/api/pith-number/J7UZJOUZTUH3EQHAOKCBXVN5BQ/events.json","paper":"https://pith.science/paper/J7UZJOUZ"},"agent_actions":{"view_html":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ","download_json":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ.json","view_paper":"https://pith.science/paper/J7UZJOUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20150&json=true","fetch_graph":"https://pith.science/api/pith-number/J7UZJOUZTUH3EQHAOKCBXVN5BQ/graph.json","fetch_events":"https://pith.science/api/pith-number/J7UZJOUZTUH3EQHAOKCBXVN5BQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/action/storage_attestation","attest_author":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/action/author_attestation","sign_citation":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/action/citation_signature","submit_replication":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/action/replication_record"}},"created_at":"2026-07-05T11:44:14.168334+00:00","updated_at":"2026-07-05T11:44:14.168334+00:00"}