{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6XQ2NJX3UP2YBFQYZCQRNWF4W4","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":"742253950980bf76e45f0195ec9d2f346b56393e10379fa5a4a365046e521427","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T13:49:54Z","title_canon_sha256":"a81b422e3b3278cd2abb8c31c35c1e0998d7ac4bcd5fcac89ab38b2a32455933"},"schema_version":"1.0","source":{"id":"2607.07423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07423","created_at":"2026-07-09T01:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07423v1","created_at":"2026-07-09T01:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07423","created_at":"2026-07-09T01:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"6XQ2NJX3UP2Y","created_at":"2026-07-09T01:20:24Z"},{"alias_kind":"pith_short_16","alias_value":"6XQ2NJX3UP2YBFQY","created_at":"2026-07-09T01:20:24Z"},{"alias_kind":"pith_short_8","alias_value":"6XQ2NJX3","created_at":"2026-07-09T01:20:24Z"}],"graph_snapshots":[{"event_id":"sha256:2c73b5e640ba4ff3877a493513d316ea3d838d657457967bffdc7371d8ea9180","target":"graph","created_at":"2026-07-09T01:20:24Z","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/2607.07423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, in the realizable PAC setting, the sample complexity of exact-trace learning for full autoregressive Chain-of-Thought traces is upper bounded by the standard multiclass rate of the local next-token class, where this rate is governed by the Daniely--Shalev-Shwartz dimension. Under exact-trace loss, one wrong action makes the whole trace incorrect; nevertheless, for every stopping rule $\\mathtt{halt}$ and every pointwise $\\mathtt{halt}$-halting local class $\\mathrm{H}$, $n_{\\mathrm{PAC}}^{\\varepsilon,\\delta}(\\operatorname{Roll}_{\\mathtt{halt}}(\\mathrm{H}))=O((\\operatorname{DSdim}(","authors_text":"Zhiyuan Li","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T13:49:54Z","title":"The Optimal Sample Complexity of Learning Autoregressive Chain-of-Thought"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07423","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:a113b4aabc815d825e6d867f55a735cbf524811c115f4f35fbcece5e302b6a6e","target":"record","created_at":"2026-07-09T01:20:24Z","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":"742253950980bf76e45f0195ec9d2f346b56393e10379fa5a4a365046e521427","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T13:49:54Z","title_canon_sha256":"a81b422e3b3278cd2abb8c31c35c1e0998d7ac4bcd5fcac89ab38b2a32455933"},"schema_version":"1.0","source":{"id":"2607.07423","kind":"arxiv","version":1}},"canonical_sha256":"f5e1a6a6fba3f5809618c8a116d8bcb7032afb2cef8406f2f312c8bb6c715d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5e1a6a6fba3f5809618c8a116d8bcb7032afb2cef8406f2f312c8bb6c715d2e","first_computed_at":"2026-07-09T01:20:24.545423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:24.545423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3m+Y7bUDmhURxrfgVH+DYRN/HiyD1yQFodyMFOUio541ZCtPdOek/f0BFT1HQjwv6gAdHIKs/zHnzzui2t6YBQ==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:24.545828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a113b4aabc815d825e6d867f55a735cbf524811c115f4f35fbcece5e302b6a6e","sha256:2c73b5e640ba4ff3877a493513d316ea3d838d657457967bffdc7371d8ea9180"],"state_sha256":"dde73779e2cbf001dbe07e7360ae11886c4ec0b3390f6fcb844404f985fda571"}