{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J7UZJOUZTUH3EQHAOKCBXVN5BQ","short_pith_number":"pith:J7UZJOUZ","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"},"canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","source":{"kind":"arxiv","id":"2507.20150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20150","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20150v1","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20150","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"J7UZJOUZTUH3","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_16","alias_value":"J7UZJOUZTUH3EQHA","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_8","alias_value":"J7UZJOUZ","created_at":"2026-07-05T11:44:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J7UZJOUZTUH3EQHAOKCBXVN5BQ","target":"record","payload":{"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"},"canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","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"},"source_kind":"arxiv","source_id":"2507.20150","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":"2026-07-05T11:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ki3Zu3AZFLslpNWpC30MXWbrMOsMz+wWNmJEAkXAOUG+wlAY+czcVSfVgJpCPQMhWTCxDAxW0nNvzwkr6v9cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:10:36.846228Z"},"content_sha256":"77b6df05efc464e085cb32237bf2a5a6d0218776d58d3b470ced1dcdf1166389","schema_version":"1.0","event_id":"sha256:77b6df05efc464e085cb32237bf2a5a6d0218776d58d3b470ced1dcdf1166389"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J7UZJOUZTUH3EQHAOKCBXVN5BQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2bII9X9MmigPVld2QljnjNWYaS4FssWenXVAmtO3YVvAEwu2mScXMFG8mKaxvTRUIITzNefZQj7kYInSHVHbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:10:36.847193Z"},"content_sha256":"ed54bfd2482c22da6bd61df36cff238bd28a38856fbd92bb681e81b5d7a8ca0a","schema_version":"1.0","event_id":"sha256:ed54bfd2482c22da6bd61df36cff238bd28a38856fbd92bb681e81b5d7a8ca0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/bundle.json","state_url":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/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":"2026-08-16T15:10:36Z","links":{"resolver":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ","bundle":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/bundle.json","state":"https://pith.science/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7UZJOUZTUH3EQHAOKCBXVN5BQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J7UZJOUZTUH3EQHAOKCBXVN5BQ","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":"7c35d02f9befd33e21ae280eff10cf20dcd618496d4f0465b89fb8d8c888824e","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-07-27T06:56:10Z","title_canon_sha256":"d12c4e3e7c14fdeea43cf4ead7a85913d95576fe6b14eaf8ec11a1b32f8c4d11"},"schema_version":"1.0","source":{"id":"2507.20150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20150","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20150v1","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20150","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"J7UZJOUZTUH3","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_16","alias_value":"J7UZJOUZTUH3EQHA","created_at":"2026-07-05T11:44:14Z"},{"alias_kind":"pith_short_8","alias_value":"J7UZJOUZ","created_at":"2026-07-05T11:44:14Z"}],"graph_snapshots":[{"event_id":"sha256:ed54bfd2482c22da6bd61df36cff238bd28a38856fbd92bb681e81b5d7a8ca0a","target":"graph","created_at":"2026-07-05T11:44:14Z","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/2507.20150/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Xingcheng Xu","cross_cats":["cs.CL","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-07-27T06:56:10Z","title":"The Policy Cliff: A Theoretical Analysis of Reward-Policy Maps in Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20150","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":"sha256:77b6df05efc464e085cb32237bf2a5a6d0218776d58d3b470ced1dcdf1166389","target":"record","created_at":"2026-07-05T11:44:14Z","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":"7c35d02f9befd33e21ae280eff10cf20dcd618496d4f0465b89fb8d8c888824e","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-07-27T06:56:10Z","title_canon_sha256":"d12c4e3e7c14fdeea43cf4ead7a85913d95576fe6b14eaf8ec11a1b32f8c4d11"},"schema_version":"1.0","source":{"id":"2507.20150","kind":"arxiv","version":1}},"canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fe994ba999d0fb240e072841bd5bd0c09089edc40d158e27a4eb1e9b366e1c5","first_computed_at":"2026-07-05T11:44:14.168267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:14.168267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FMot4GnLE3EDODxs1f/CFC5WnzduhmYcHzXJhkjnrP9vhMsKUb/ohwfWds7nBq6vAw4YrmXZxAMcvLphFphODw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:14.168719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.20150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77b6df05efc464e085cb32237bf2a5a6d0218776d58d3b470ced1dcdf1166389","sha256:ed54bfd2482c22da6bd61df36cff238bd28a38856fbd92bb681e81b5d7a8ca0a"],"state_sha256":"7dba6cf19ece7c39c9bf29cd5bb16fe5dd5c101be280229796ec33a58000adfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWBtfJv5d/1qwsPWg7v3Lc9A+ZHVa+YOQ3k6STlKaZB+X++XK5M2xAqpTW/NGwdORcz2dF9xbIw/no1nR1BOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:10:36.853400Z","bundle_sha256":"af169ceb662485d19749b2f03958390d4a96195f1607e2a1ecbab8fc02646b2b"}}