{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7RRY4RV6SZSYNNXPVF7OME6JLA","short_pith_number":"pith:7RRY4RV6","canonical_record":{"source":{"id":"2602.02979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-02-03T01:38:53Z","cross_cats_sorted":[],"title_canon_sha256":"5600fecc22fcedcfa4335d03307271e53eceb287693b0c06d90137e6baf6dc9c","abstract_canon_sha256":"7f9bb2ed9390126133d2ea896d1f09dbc4f8d2226b8cb7e2deae47b864e9d2fb"},"schema_version":"1.0"},"canonical_sha256":"fc638e46be966586b6efa97ee613c958354bcdc76130b7ca3b67fd1b586cf3a0","source":{"kind":"arxiv","id":"2602.02979","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.02979","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"2602.02979v2","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.02979","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"7RRY4RV6SZSY","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"7RRY4RV6SZSYNNXP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"7RRY4RV6","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7RRY4RV6SZSYNNXPVF7OME6JLA","target":"record","payload":{"canonical_record":{"source":{"id":"2602.02979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-02-03T01:38:53Z","cross_cats_sorted":[],"title_canon_sha256":"5600fecc22fcedcfa4335d03307271e53eceb287693b0c06d90137e6baf6dc9c","abstract_canon_sha256":"7f9bb2ed9390126133d2ea896d1f09dbc4f8d2226b8cb7e2deae47b864e9d2fb"},"schema_version":"1.0"},"canonical_sha256":"fc638e46be966586b6efa97ee613c958354bcdc76130b7ca3b67fd1b586cf3a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:05.536982Z","signature_b64":"96carS1tTYIwwdIq7Iytgbr0paw3/PkoY0Yh5/ZU5KFU4kLTYkja1nLZ4sgBlPXLM4sTDQ4H9nerKhYpmCskBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc638e46be966586b6efa97ee613c958354bcdc76130b7ca3b67fd1b586cf3a0","last_reissued_at":"2026-05-18T02:45:05.536378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:05.536378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.02979","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"390mYdyYmRU5oWeYR3MHn6Y1oa7ZAPloNO6lF4Wh+tDTp2wbXKGpU8VX3+/kj4OaQ/ZsLH7m4cWUAeJAxfwMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:02:50.842395Z"},"content_sha256":"b521250aef5bc9a087f2ecdd3b97cc2f8ed6f90b164aa43ea3ed5143aa252cbe","schema_version":"1.0","event_id":"sha256:b521250aef5bc9a087f2ecdd3b97cc2f8ed6f90b164aa43ea3ed5143aa252cbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7RRY4RV6SZSYNNXPVF7OME6JLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CPMobius: Iterative Coach-Player Reasoning for Data-Free Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Bingxiang He, Jiarui Yuan, Jinyi Hu, Maosong Sun, Ran Li, Weize Chen, Yinghao Chen, Zeyuan Liu, Zhiyuan Liu, Zixuan Fu","submitted_at":"2026-02-03T01:38:53Z","abstract_excerpt":"Large Language Models (LLMs) have demonstrated strong potential in complex reasoning, yet their progress remains fundamentally constrained by reliance on massive high-quality human-curated tasks and labels, either through supervised fine-tuning (SFT) or reinforcement learning (RL) on reasoning-specific data. This dependence renders supervision-heavy training paradigms increasingly unsustainable, with signs of diminishing scalability already evident in practice. To overcome this limitation, we introduce CPM\\\"obius (CPMobius), a collaborative Coach-Player paradigm for data-free reinforcement lea"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"CPMobius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on Qwen2.5-Math-7B-Instruct, our method improves accuracy by an overall average of +4.9 and an out-of-distribution average of +5.4.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cooperative optimization loop between Coach and Player directly enhances the Player's mathematical reasoning ability without external data or labels.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CPMobius uses iterative coach-player reinforcement learning to improve mathematical reasoning in LLMs without external training data, yielding +4.9 average accuracy gains on Qwen2.5-Math-7B-Instruct.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"af00d8d37100c7ad6926b05a420da03b492af55976d775a2a8bc476119afbf0f"},"source":{"id":"2602.02979","kind":"arxiv","version":2},"verdict":{"id":"06ab818a-5768-49d1-a65f-26930b8497bf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T08:39:31.999161Z","strongest_claim":"CPMobius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on Qwen2.5-Math-7B-Instruct, our method improves accuracy by an overall average of +4.9 and an out-of-distribution average of +5.4.","one_line_summary":"CPMobius uses iterative coach-player reinforcement learning to improve mathematical reasoning in LLMs without external training data, yielding +4.9 average accuracy gains on Qwen2.5-Math-7B-Instruct.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cooperative optimization loop between Coach and Player directly enhances the Player's mathematical reasoning ability without external data or labels.","pith_extraction_headline":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6fb6c2b6460be6fc0ec4621098faece13313602a8189bbffeb68cb065a57e60a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"06ab818a-5768-49d1-a65f-26930b8497bf"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ox2+Hfl3b94hY7cjfscJVkSsWzvuJjiqbtvJuPb8KWI7QvQGuMFIkfAj91BElzWFehYaHsaBsOSU58P+Jgk0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:02:50.843251Z"},"content_sha256":"fad4ff5f46191a2a25ef8779afc5c559b2f3fe966103cb91d889c15c7da7a5e1","schema_version":"1.0","event_id":"sha256:fad4ff5f46191a2a25ef8779afc5c559b2f3fe966103cb91d889c15c7da7a5e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/bundle.json","state_url":"https://pith.science/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/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":"2026-05-25T15:02:50Z","links":{"resolver":"https://pith.science/pith/7RRY4RV6SZSYNNXPVF7OME6JLA","bundle":"https://pith.science/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/bundle.json","state":"https://pith.science/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RRY4RV6SZSYNNXPVF7OME6JLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7RRY4RV6SZSYNNXPVF7OME6JLA","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":"7f9bb2ed9390126133d2ea896d1f09dbc4f8d2226b8cb7e2deae47b864e9d2fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-02-03T01:38:53Z","title_canon_sha256":"5600fecc22fcedcfa4335d03307271e53eceb287693b0c06d90137e6baf6dc9c"},"schema_version":"1.0","source":{"id":"2602.02979","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.02979","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"2602.02979v2","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.02979","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"7RRY4RV6SZSY","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"7RRY4RV6SZSYNNXP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"7RRY4RV6","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:fad4ff5f46191a2a25ef8779afc5c559b2f3fe966103cb91d889c15c7da7a5e1","target":"graph","created_at":"2026-05-18T02:45:05Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"CPMobius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on Qwen2.5-Math-7B-Instruct, our method improves accuracy by an overall average of +4.9 and an out-of-distribution average of +5.4."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The cooperative optimization loop between Coach and Player directly enhances the Player's mathematical reasoning ability without external data or labels."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"CPMobius uses iterative coach-player reinforcement learning to improve mathematical reasoning in LLMs without external training data, yielding +4.9 average accuracy gains on Qwen2.5-Math-7B-Instruct."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data."}],"snapshot_sha256":"af00d8d37100c7ad6926b05a420da03b492af55976d775a2a8bc476119afbf0f"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6fb6c2b6460be6fc0ec4621098faece13313602a8189bbffeb68cb065a57e60a"},"paper":{"abstract_excerpt":"Large Language Models (LLMs) have demonstrated strong potential in complex reasoning, yet their progress remains fundamentally constrained by reliance on massive high-quality human-curated tasks and labels, either through supervised fine-tuning (SFT) or reinforcement learning (RL) on reasoning-specific data. This dependence renders supervision-heavy training paradigms increasingly unsustainable, with signs of diminishing scalability already evident in practice. To overcome this limitation, we introduce CPM\\\"obius (CPMobius), a collaborative Coach-Player paradigm for data-free reinforcement lea","authors_text":"Bingxiang He, Jiarui Yuan, Jinyi Hu, Maosong Sun, Ran Li, Weize Chen, Yinghao Chen, Zeyuan Liu, Zhiyuan Liu, Zixuan Fu","cross_cats":[],"headline":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-02-03T01:38:53Z","title":"CPMobius: Iterative Coach-Player Reasoning for Data-Free Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.02979","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-16T08:39:31.999161Z","id":"06ab818a-5768-49d1-a65f-26930b8497bf","model_set":{"reader":"grok-4.3"},"one_line_summary":"CPMobius uses iterative coach-player reinforcement learning to improve mathematical reasoning in LLMs without external training data, yielding +4.9 average accuracy gains on Qwen2.5-Math-7B-Instruct.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A Coach generates tasks and rewards a Player for solving them, improving LLM math reasoning without any external data.","strongest_claim":"CPMobius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on Qwen2.5-Math-7B-Instruct, our method improves accuracy by an overall average of +4.9 and an out-of-distribution average of +5.4.","weakest_assumption":"The cooperative optimization loop between Coach and Player directly enhances the Player's mathematical reasoning ability without external data or labels."}},"verdict_id":"06ab818a-5768-49d1-a65f-26930b8497bf"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b521250aef5bc9a087f2ecdd3b97cc2f8ed6f90b164aa43ea3ed5143aa252cbe","target":"record","created_at":"2026-05-18T02:45:05Z","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":"7f9bb2ed9390126133d2ea896d1f09dbc4f8d2226b8cb7e2deae47b864e9d2fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-02-03T01:38:53Z","title_canon_sha256":"5600fecc22fcedcfa4335d03307271e53eceb287693b0c06d90137e6baf6dc9c"},"schema_version":"1.0","source":{"id":"2602.02979","kind":"arxiv","version":2}},"canonical_sha256":"fc638e46be966586b6efa97ee613c958354bcdc76130b7ca3b67fd1b586cf3a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc638e46be966586b6efa97ee613c958354bcdc76130b7ca3b67fd1b586cf3a0","first_computed_at":"2026-05-18T02:45:05.536378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:05.536378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96carS1tTYIwwdIq7Iytgbr0paw3/PkoY0Yh5/ZU5KFU4kLTYkja1nLZ4sgBlPXLM4sTDQ4H9nerKhYpmCskBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:05.536982Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.02979","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b521250aef5bc9a087f2ecdd3b97cc2f8ed6f90b164aa43ea3ed5143aa252cbe","sha256:fad4ff5f46191a2a25ef8779afc5c559b2f3fe966103cb91d889c15c7da7a5e1"],"state_sha256":"deec2cd517b54efb49a686db2b3f119dbaf440705d345cb17040c85c54282949"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vu20oh8mI1mr+5lg6MjCpasFwqD4KFpO+gFduHQajznDsglwwxoOodN7Vwq/mYhmC6MYPjGRbHEzwK9pO5udAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:02:50.847339Z","bundle_sha256":"22ca8b6067870e47c6048d83f059de88562e8946b0693cf379a39e484f1596cd"}}