{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MRQJSW6F4WX632M6PV4K5CHKCG","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":"cbfad3a2647814514d93e42263adbd40d281ab95dbe86db667098efe6e960c41","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-01-26T17:05:16Z","title_canon_sha256":"f709daf9eee7dc39281d7bfc207529c998fedc19683ee51cfff714860f9d6d4b"},"schema_version":"1.0","source":{"id":"2501.15602","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15602","created_at":"2026-07-05T11:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15602v3","created_at":"2026-07-05T11:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15602","created_at":"2026-07-05T11:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"MRQJSW6F4WX6","created_at":"2026-07-05T11:24:13Z"},{"alias_kind":"pith_short_16","alias_value":"MRQJSW6F4WX632M6","created_at":"2026-07-05T11:24:13Z"},{"alias_kind":"pith_short_8","alias_value":"MRQJSW6F","created_at":"2026-07-05T11:24:13Z"}],"graph_snapshots":[{"event_id":"sha256:5882139f760611491b0e2142d309d34e956bf780573ac4953adb73a928c69540","target":"graph","created_at":"2026-07-05T11:24:13Z","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/2501.15602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Test-time scaling, which is also often referred to as slow-thinking, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be int","authors_text":"Yong Liu, Yun Liao, Zeyu Gan","cross_cats":["cs.CL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-01-26T17:05:16Z","title":"Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15602","kind":"arxiv","version":3},"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":"sha256:336b495a5572a93287ab76243eab453ebfe70b241be72fe9624d0fdcc9d9d38b","target":"record","created_at":"2026-07-05T11:24:13Z","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":"cbfad3a2647814514d93e42263adbd40d281ab95dbe86db667098efe6e960c41","cross_cats_sorted":["cs.CL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-01-26T17:05:16Z","title_canon_sha256":"f709daf9eee7dc39281d7bfc207529c998fedc19683ee51cfff714860f9d6d4b"},"schema_version":"1.0","source":{"id":"2501.15602","kind":"arxiv","version":3}},"canonical_sha256":"6460995bc5e5afede99e7d78ae88ea11985e40e8c3fdb625d89afc145d967c9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6460995bc5e5afede99e7d78ae88ea11985e40e8c3fdb625d89afc145d967c9b","first_computed_at":"2026-07-05T11:24:13.220618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:13.220618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3/sx9tSvzel9aY9ajumsff2jIqd/JKH+0RGf5t80CqF+d1Me3d2qxTm8O1624zekdYFq7JnnkGqLkUTe7llAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:13.221128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15602","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:336b495a5572a93287ab76243eab453ebfe70b241be72fe9624d0fdcc9d9d38b","sha256:5882139f760611491b0e2142d309d34e956bf780573ac4953adb73a928c69540"],"state_sha256":"6cbaf4fe86e7d4bb866b1ba7790faa8ac7ee97afdca62e0f49de39a2defceef0"}