{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SYO4IKLPDCYI3SGGJMCPW2BBYN","short_pith_number":"pith:SYO4IKLP","canonical_record":{"source":{"id":"2605.21260","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T14:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"c5537c603f445efd9e508a5f8b165e8ee9e64d822b420c9599f0aab7be4ffb97","abstract_canon_sha256":"b3cece2b11642441650bd29b6b9d8dee41f07c2f776c6cd565edf211b61539c6"},"schema_version":"1.0"},"canonical_sha256":"961dc4296f18b08dc8c64b04fb6821c34da27f110cfed7545300b7e4ce1b1104","source":{"kind":"arxiv","id":"2605.21260","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21260","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21260v1","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21260","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"SYO4IKLPDCYI","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"SYO4IKLPDCYI3SGG","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"SYO4IKLP","created_at":"2026-05-21T02:05:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SYO4IKLPDCYI3SGGJMCPW2BBYN","target":"record","payload":{"canonical_record":{"source":{"id":"2605.21260","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T14:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"c5537c603f445efd9e508a5f8b165e8ee9e64d822b420c9599f0aab7be4ffb97","abstract_canon_sha256":"b3cece2b11642441650bd29b6b9d8dee41f07c2f776c6cd565edf211b61539c6"},"schema_version":"1.0"},"canonical_sha256":"961dc4296f18b08dc8c64b04fb6821c34da27f110cfed7545300b7e4ce1b1104","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:25.445453Z","signature_b64":"evIskf7QAHM/szVCRMyfzydPs5gT5x1hdOF8dUp16cxMKnsE3dg+PCaIOj+RToybmixIP25nAYGDO2KSYNq7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"961dc4296f18b08dc8c64b04fb6821c34da27f110cfed7545300b7e4ce1b1104","last_reissued_at":"2026-05-21T02:05:25.443817Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:25.443817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.21260","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":"2026-05-21T02:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JJZt3eJTUrRkKpGOX6iHomMX1C/0h9Ll441wDrTXLk+XqwBxaWvISk2G7XeNyDopxrlVYN0fUC/It/GMaB0MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:51:48.688366Z"},"content_sha256":"75a3177044f8b663ae9bb3fe2779cd62123b5911668a65f6b56c44152b76ddac","schema_version":"1.0","event_id":"sha256:75a3177044f8b663ae9bb3fe2779cd62123b5911668a65f6b56c44152b76ddac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SYO4IKLPDCYI3SGGJMCPW2BBYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Tommaso Cesari, Yongyi Mao, Yue Zhang, Zhiyi Dong","submitted_at":"2026-05-20T14:51:20Z","abstract_excerpt":"We develop a learning-theoretic framework for understanding Chain of Thought (CoT). We model CoT as the interaction between an answer map and a chain rule that generates intermediate questions autoregressively, and define the reasoning risk of a hypothesis under this interaction. Our first result is a tight canonical decomposition of this risk into two terms with opposing roles: an oracle-trajectory risk (OTR), which captures the benefit of CoT and reduces to a target-domain risk in a domain adaptation problem, and a trajectory-mismatch risk (TMR), which captures the cost of CoT through error "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21260","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/2605.21260/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":"2026-05-21T02:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNlMH+rwSssvEwHw6ZWSnghTioUs8J4j+qY3rSsxG9Vwvx2kr7xgwrhq018k81pmI9AS+VO+JDpmhLMijx6VCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:51:48.689065Z"},"content_sha256":"ef5de43887f6051cc6915b02a4545b77b5f11ae45ede94d0b384ff5a5754b100","schema_version":"1.0","event_id":"sha256:ef5de43887f6051cc6915b02a4545b77b5f11ae45ede94d0b384ff5a5754b100"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:SYO4IKLPDCYI3SGGJMCPW2BBYN","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1162/tacla) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"M. Hahn. Theoretical limitations of self-attention in neural sequence models.Transactions of the Association for Computational Linguistics, 8:156–171, 2020. doi: 10.1162/tacl a 00306","arxiv_id":"2605.21260","detector":"doi_compliance","evidence":{"ref_index":38,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"M. Hahn. Theoretical limitations of self-attention in neural sequence models.Transactions of the Association for Computational Linguistics, 8:156–171, 2020. doi: 10.1162/tacl a 00306","reconstructed_doi":"10.1162/tacla"},"severity":"advisory","ref_index":38,"audited_at":"2026-05-21T05:13:28.298678Z","event_type":"pith.integrity.v1","detected_doi":"10.1162/tacla","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"f40e2a2bd8fd0b8ae61b4b1c6f27eb43708ccd233deafbd4e7d70f80f5404801","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":5683,"payload_sha256":"7bd703035ec1e140482b8a36bb46ecfa8cd8426cdbf31595a9743e94fd27bee5","signature_b64":"1o+RtOhgf1Vx8PhQJdehV72RUhyXlQ1/Ati+pzYdFqh4O3wz2BoQDiJD5+xV6NqV/PPqFecC5lZ43+U3pDfNDQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T05:14:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgMrAdIwFbW0tCG9Dj1Np34iBTvHXnnz0qflC085L/9N3hUssw4t9Bz/84lOPGgshiKQu+LiD/UFO0m8uIuRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:51:48.690311Z"},"content_sha256":"a11b9ef641435ef86974a34215c57cadb7600289eb98b08740a4994b27f5d03a","schema_version":"1.0","event_id":"sha256:a11b9ef641435ef86974a34215c57cadb7600289eb98b08740a4994b27f5d03a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/bundle.json","state_url":"https://pith.science/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/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":"2026-05-21T18:51:48Z","links":{"resolver":"https://pith.science/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN","bundle":"https://pith.science/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/bundle.json","state":"https://pith.science/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYO4IKLPDCYI3SGGJMCPW2BBYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SYO4IKLPDCYI3SGGJMCPW2BBYN","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b3cece2b11642441650bd29b6b9d8dee41f07c2f776c6cd565edf211b61539c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T14:51:20Z","title_canon_sha256":"c5537c603f445efd9e508a5f8b165e8ee9e64d822b420c9599f0aab7be4ffb97"},"schema_version":"1.0","source":{"id":"2605.21260","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21260","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21260v1","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21260","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"SYO4IKLPDCYI","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"SYO4IKLPDCYI3SGG","created_at":"2026-05-21T02:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"SYO4IKLP","created_at":"2026-05-21T02:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:ef5de43887f6051cc6915b02a4545b77b5f11ae45ede94d0b384ff5a5754b100","target":"graph","created_at":"2026-05-21T02:05:25Z","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/2605.21260/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a learning-theoretic framework for understanding Chain of Thought (CoT). We model CoT as the interaction between an answer map and a chain rule that generates intermediate questions autoregressively, and define the reasoning risk of a hypothesis under this interaction. Our first result is a tight canonical decomposition of this risk into two terms with opposing roles: an oracle-trajectory risk (OTR), which captures the benefit of CoT and reduces to a target-domain risk in a domain adaptation problem, and a trajectory-mismatch risk (TMR), which captures the cost of CoT through error ","authors_text":"Tommaso Cesari, Yongyi Mao, Yue Zhang, Zhiyi Dong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T14:51:20Z","title":"On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21260","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":"sha256:75a3177044f8b663ae9bb3fe2779cd62123b5911668a65f6b56c44152b76ddac","target":"record","created_at":"2026-05-21T02:05:25Z","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":"b3cece2b11642441650bd29b6b9d8dee41f07c2f776c6cd565edf211b61539c6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T14:51:20Z","title_canon_sha256":"c5537c603f445efd9e508a5f8b165e8ee9e64d822b420c9599f0aab7be4ffb97"},"schema_version":"1.0","source":{"id":"2605.21260","kind":"arxiv","version":1}},"canonical_sha256":"961dc4296f18b08dc8c64b04fb6821c34da27f110cfed7545300b7e4ce1b1104","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"961dc4296f18b08dc8c64b04fb6821c34da27f110cfed7545300b7e4ce1b1104","first_computed_at":"2026-05-21T02:05:25.443817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T02:05:25.443817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"evIskf7QAHM/szVCRMyfzydPs5gT5x1hdOF8dUp16cxMKnsE3dg+PCaIOj+RToybmixIP25nAYGDO2KSYNq7DQ==","signature_status":"signed_v1","signed_at":"2026-05-21T02:05:25.445453Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21260","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75a3177044f8b663ae9bb3fe2779cd62123b5911668a65f6b56c44152b76ddac","sha256:ef5de43887f6051cc6915b02a4545b77b5f11ae45ede94d0b384ff5a5754b100","sha256:a11b9ef641435ef86974a34215c57cadb7600289eb98b08740a4994b27f5d03a"],"state_sha256":"9297b802f3529c01b1db6a3109be0991b73463596ccd3f8243600ff25c04c808"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EwLYQgotBVIn8tJ1F81mMgxs3p/mMXR4ODo/T/aBtPpVNZSPjN+DbyXioO0w/d6GJOUk+kkoRqpFlKSDGaPVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T18:51:48.693713Z","bundle_sha256":"3f42e91d4456428959f9ed2401c5b222ccfd513796c3e604d4e58b86647b359f"}}