{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CFKVLJFGKU4BC6W73XJRMW55PG","short_pith_number":"pith:CFKVLJFG","canonical_record":{"source":{"id":"2606.30789","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T18:19:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"582931b4e21e1bc0c184ca56e1ab3ad200b769ba6d90250b3923699bc2c83bf2","abstract_canon_sha256":"eae770a13e2720a171be55a78ede261936dbc0773fee79b835aa7cd23289cae0"},"schema_version":"1.0"},"canonical_sha256":"115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30","source":{"kind":"arxiv","id":"2606.30789","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30789","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30789v1","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30789","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_12","alias_value":"CFKVLJFGKU4B","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_16","alias_value":"CFKVLJFGKU4BC6W7","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_8","alias_value":"CFKVLJFG","created_at":"2026-07-01T00:17:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CFKVLJFGKU4BC6W73XJRMW55PG","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30789","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T18:19:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"582931b4e21e1bc0c184ca56e1ab3ad200b769ba6d90250b3923699bc2c83bf2","abstract_canon_sha256":"eae770a13e2720a171be55a78ede261936dbc0773fee79b835aa7cd23289cae0"},"schema_version":"1.0"},"canonical_sha256":"115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T00:17:17.011568Z","signature_b64":"6eSsVQDFSsy5AdBpIWI2Y48JhAiJOM7aU2VRK+N5bbo0pO3+sKNncjdHfFgKQM0IRPnhTFTectOpPfbhb7MMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30","last_reissued_at":"2026-07-01T00:17:17.011111Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T00:17:17.011111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30789","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":"2026-07-01T00:17:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RDBfSNKGxbxPQy7dni8NCZzXQMcelKCVoTvkYOfDKT8sfNoms0h7rYZ1rJtS9iIstKsupilWMn70PDCjG8LkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:17:18.204904Z"},"content_sha256":"34326445aa59702271c2864a6905abf6d1e15ccea977b34721e185cdc8ac93d6","schema_version":"1.0","event_id":"sha256:34326445aa59702271c2864a6905abf6d1e15ccea977b34721e185cdc8ac93d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CFKVLJFGKU4BC6W73XJRMW55PG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Predictable GRPO: A Closed-Form Model of Training Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aryan Singhal, Datta Nimmaturi, Debojyoti Dutta, Henry Wong, Johnu George, Rajat Ghosh, Vaishnavi Bhargava","submitted_at":"2026-06-29T18:19:09Z","abstract_excerpt":"Group Relative Policy Optimization (GRPO) has become a standard tool for improving the reasoning ability of large language models, yet its training dynamics are still described empirically: reward trajectories are fit with low-parameter functional forms whose constants carry no mechanistic meaning, and hyperparameter choices remain a matter of trial and error.  We develop a first-principles reduced-order model of these dynamics. The reduction has three consequences. First, it subsumes the empirical single-exponential saturation law as its overdamped limit, recasting the fitted plateau, timesca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30789","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/2606.30789/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":"2026-07-01T00:17:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAMXUE5AsbPIdw80mlti9OLUdGM0se8P6Sr3is13FpXy3xiecZvelMKPzUFRRoJ1hV4pVH4Hsd1Y3XctQpFgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:17:18.205625Z"},"content_sha256":"8fc052f79273cafcab6f94263b655990825807d626bd6965d25ce60cf74013f6","schema_version":"1.0","event_id":"sha256:8fc052f79273cafcab6f94263b655990825807d626bd6965d25ce60cf74013f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFKVLJFGKU4BC6W73XJRMW55PG/bundle.json","state_url":"https://pith.science/pith/CFKVLJFGKU4BC6W73XJRMW55PG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFKVLJFGKU4BC6W73XJRMW55PG/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":"2026-07-01T12:17:18Z","links":{"resolver":"https://pith.science/pith/CFKVLJFGKU4BC6W73XJRMW55PG","bundle":"https://pith.science/pith/CFKVLJFGKU4BC6W73XJRMW55PG/bundle.json","state":"https://pith.science/pith/CFKVLJFGKU4BC6W73XJRMW55PG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFKVLJFGKU4BC6W73XJRMW55PG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CFKVLJFGKU4BC6W73XJRMW55PG","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":"eae770a13e2720a171be55a78ede261936dbc0773fee79b835aa7cd23289cae0","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T18:19:09Z","title_canon_sha256":"582931b4e21e1bc0c184ca56e1ab3ad200b769ba6d90250b3923699bc2c83bf2"},"schema_version":"1.0","source":{"id":"2606.30789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30789","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30789v1","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30789","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_12","alias_value":"CFKVLJFGKU4B","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_16","alias_value":"CFKVLJFGKU4BC6W7","created_at":"2026-07-01T00:17:17Z"},{"alias_kind":"pith_short_8","alias_value":"CFKVLJFG","created_at":"2026-07-01T00:17:17Z"}],"graph_snapshots":[{"event_id":"sha256:8fc052f79273cafcab6f94263b655990825807d626bd6965d25ce60cf74013f6","target":"graph","created_at":"2026-07-01T00:17:17Z","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/2606.30789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Group Relative Policy Optimization (GRPO) has become a standard tool for improving the reasoning ability of large language models, yet its training dynamics are still described empirically: reward trajectories are fit with low-parameter functional forms whose constants carry no mechanistic meaning, and hyperparameter choices remain a matter of trial and error.  We develop a first-principles reduced-order model of these dynamics. The reduction has three consequences. First, it subsumes the empirical single-exponential saturation law as its overdamped limit, recasting the fitted plateau, timesca","authors_text":"Aryan Singhal, Datta Nimmaturi, Debojyoti Dutta, Henry Wong, Johnu George, Rajat Ghosh, Vaishnavi Bhargava","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T18:19:09Z","title":"Predictable GRPO: A Closed-Form Model of Training Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30789","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":"sha256:34326445aa59702271c2864a6905abf6d1e15ccea977b34721e185cdc8ac93d6","target":"record","created_at":"2026-07-01T00:17:17Z","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":"eae770a13e2720a171be55a78ede261936dbc0773fee79b835aa7cd23289cae0","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T18:19:09Z","title_canon_sha256":"582931b4e21e1bc0c184ca56e1ab3ad200b769ba6d90250b3923699bc2c83bf2"},"schema_version":"1.0","source":{"id":"2606.30789","kind":"arxiv","version":1}},"canonical_sha256":"115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"115555a4a65538117adfddd3165bbd79acedf758ea8e302e0b6359a6a899ae30","first_computed_at":"2026-07-01T00:17:17.011111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T00:17:17.011111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6eSsVQDFSsy5AdBpIWI2Y48JhAiJOM7aU2VRK+N5bbo0pO3+sKNncjdHfFgKQM0IRPnhTFTectOpPfbhb7MMAw==","signature_status":"signed_v1","signed_at":"2026-07-01T00:17:17.011568Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34326445aa59702271c2864a6905abf6d1e15ccea977b34721e185cdc8ac93d6","sha256:8fc052f79273cafcab6f94263b655990825807d626bd6965d25ce60cf74013f6"],"state_sha256":"bbb25d8f640bf9692be51906bd6c19913eb1776d61f31f3e6176b33aebda638c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kqprn9XofHXeyHC/ImCPNq5oJb1jofH82yN75QBP0TlmGO+f6Q5rK71tn3zBiJwCw6AxElMnfOMNaXyghn2BDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:17:18.208704Z","bundle_sha256":"b2de5fc8c0b712ac18414fa32a772bbd9e1c21b9f9053c7a2a72103ccfeedc83"}}