{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:543YZBV2A35WXJLYBV4P6HHDB7","short_pith_number":"pith:543YZBV2","canonical_record":{"source":{"id":"2606.07950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T02:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"0f0fe91cd44bb9ebe4d41a15bb8ea9831861b7b027908e05adf296154cf2f812","abstract_canon_sha256":"1912052ea5060ab564d94c103244a9f46cdce57b514abd137e7c7783d9e62fad"},"schema_version":"1.0"},"canonical_sha256":"ef378c86ba06fb6ba5780d78ff1ce30fd4ed14b9e962b08f1ac3b851778014ee","source":{"kind":"arxiv","id":"2606.07950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07950","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07950v1","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07950","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"543YZBV2A35W","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"543YZBV2A35WXJLY","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"543YZBV2","created_at":"2026-06-09T01:04:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:543YZBV2A35WXJLYBV4P6HHDB7","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T02:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"0f0fe91cd44bb9ebe4d41a15bb8ea9831861b7b027908e05adf296154cf2f812","abstract_canon_sha256":"1912052ea5060ab564d94c103244a9f46cdce57b514abd137e7c7783d9e62fad"},"schema_version":"1.0"},"canonical_sha256":"ef378c86ba06fb6ba5780d78ff1ce30fd4ed14b9e962b08f1ac3b851778014ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:56.217024Z","signature_b64":"+hNHhJq3+xb+xRWxboHgk9Y0P6jyu+uWvboRbjddU6MgSR6QPtFdTkq+zdtyoIFgshXdzFPivVHrklQ1B1dCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef378c86ba06fb6ba5780d78ff1ce30fd4ed14b9e962b08f1ac3b851778014ee","last_reissued_at":"2026-06-09T01:04:56.216595Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:56.216595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07950","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":"2026-06-09T01:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jlkPztr/WDhrAvcikJAmrgTLB2wbLMrW+6GVZkGnol1VV51hB/9xVTlfb6Oo+KFWU/p6UMUUm9viyH0qcCsQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:23:24.060136Z"},"content_sha256":"a27d4344c3873e308ef0712c30d39bcb48f07400af0d2d9197d249b7dd4830e3","schema_version":"1.0","event_id":"sha256:a27d4344c3873e308ef0712c30d39bcb48f07400af0d2d9197d249b7dd4830e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:543YZBV2A35WXJLYBV4P6HHDB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bo Han, Brando Miranda, Chentao Cao, Sanmi Koyejo, Tongliang Liu, Xiangyu Lu, Zhanke Zhou","submitted_at":"2026-06-06T02:51:33Z","abstract_excerpt":"RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07950","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/2606.07950/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":"2026-06-09T01:04:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7cAkZoSKQjFsq0DA0ly4AY2uyMmT9S1kdaqSFXIqJisAZI3oM1doY0hpFJtQbMhngnVp2iaxWhzGXwKlt/w/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:23:24.060527Z"},"content_sha256":"45752c617bc9027d4b5927952f8251f0db70ddb57abfa93f6817259fd12965c3","schema_version":"1.0","event_id":"sha256:45752c617bc9027d4b5927952f8251f0db70ddb57abfa93f6817259fd12965c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/543YZBV2A35WXJLYBV4P6HHDB7/bundle.json","state_url":"https://pith.science/pith/543YZBV2A35WXJLYBV4P6HHDB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/543YZBV2A35WXJLYBV4P6HHDB7/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":"2026-06-11T09:23:24Z","links":{"resolver":"https://pith.science/pith/543YZBV2A35WXJLYBV4P6HHDB7","bundle":"https://pith.science/pith/543YZBV2A35WXJLYBV4P6HHDB7/bundle.json","state":"https://pith.science/pith/543YZBV2A35WXJLYBV4P6HHDB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/543YZBV2A35WXJLYBV4P6HHDB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:543YZBV2A35WXJLYBV4P6HHDB7","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":"1912052ea5060ab564d94c103244a9f46cdce57b514abd137e7c7783d9e62fad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T02:51:33Z","title_canon_sha256":"0f0fe91cd44bb9ebe4d41a15bb8ea9831861b7b027908e05adf296154cf2f812"},"schema_version":"1.0","source":{"id":"2606.07950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07950","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07950v1","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07950","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_12","alias_value":"543YZBV2A35W","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_16","alias_value":"543YZBV2A35WXJLY","created_at":"2026-06-09T01:04:56Z"},{"alias_kind":"pith_short_8","alias_value":"543YZBV2","created_at":"2026-06-09T01:04:56Z"}],"graph_snapshots":[{"event_id":"sha256:45752c617bc9027d4b5927952f8251f0db70ddb57abfa93f6817259fd12965c3","target":"graph","created_at":"2026-06-09T01:04:56Z","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/2606.07950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question d","authors_text":"Bo Han, Brando Miranda, Chentao Cao, Sanmi Koyejo, Tongliang Liu, Xiangyu Lu, Zhanke Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T02:51:33Z","title":"The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07950","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:a27d4344c3873e308ef0712c30d39bcb48f07400af0d2d9197d249b7dd4830e3","target":"record","created_at":"2026-06-09T01:04:56Z","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":"1912052ea5060ab564d94c103244a9f46cdce57b514abd137e7c7783d9e62fad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-06T02:51:33Z","title_canon_sha256":"0f0fe91cd44bb9ebe4d41a15bb8ea9831861b7b027908e05adf296154cf2f812"},"schema_version":"1.0","source":{"id":"2606.07950","kind":"arxiv","version":1}},"canonical_sha256":"ef378c86ba06fb6ba5780d78ff1ce30fd4ed14b9e962b08f1ac3b851778014ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef378c86ba06fb6ba5780d78ff1ce30fd4ed14b9e962b08f1ac3b851778014ee","first_computed_at":"2026-06-09T01:04:56.216595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:56.216595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hNHhJq3+xb+xRWxboHgk9Y0P6jyu+uWvboRbjddU6MgSR6QPtFdTkq+zdtyoIFgshXdzFPivVHrklQ1B1dCDg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:56.217024Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a27d4344c3873e308ef0712c30d39bcb48f07400af0d2d9197d249b7dd4830e3","sha256:45752c617bc9027d4b5927952f8251f0db70ddb57abfa93f6817259fd12965c3"],"state_sha256":"35a7a6d272e1f5a7ed5f5adedf69029a0fa0cb511720201b5bb58a983f2b1304"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unrDTWNunOM0HEUXCnAMRnB9IWEz15vtPvPoMXsz3MIyjI/0tOqg/jyNqaFpatdWOCuTuepvp04APAva2aHGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:23:24.062480Z","bundle_sha256":"e2960090b1ac859345aa5d88b920b5dbd456f3249c689a60c3c7cc3347ccf206"}}