{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IKIED77AS7YHH5OEBWVGN3PW2V","short_pith_number":"pith:IKIED77A","canonical_record":{"source":{"id":"2505.13307","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-05-19T16:25:55Z","cross_cats_sorted":["cs.AI","cs.CV"],"title_canon_sha256":"abde1a505fb47c986b60b6ed9701fefb38d75e3d0294740798b60cda8ea08389","abstract_canon_sha256":"d00bdf14021b6cd5cf8f552574faa5ef30007ee577d8d398a7841be9ea2faf22"},"schema_version":"1.0"},"canonical_sha256":"429041ffe097f073f5c40daa66edf6d55358832024a957bcc712ce62f0e8f890","source":{"kind":"arxiv","id":"2505.13307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13307","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13307v1","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13307","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"IKIED77AS7YH","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"IKIED77AS7YHH5OE","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"IKIED77A","created_at":"2026-07-05T11:05:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IKIED77AS7YHH5OEBWVGN3PW2V","target":"record","payload":{"canonical_record":{"source":{"id":"2505.13307","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-05-19T16:25:55Z","cross_cats_sorted":["cs.AI","cs.CV"],"title_canon_sha256":"abde1a505fb47c986b60b6ed9701fefb38d75e3d0294740798b60cda8ea08389","abstract_canon_sha256":"d00bdf14021b6cd5cf8f552574faa5ef30007ee577d8d398a7841be9ea2faf22"},"schema_version":"1.0"},"canonical_sha256":"429041ffe097f073f5c40daa66edf6d55358832024a957bcc712ce62f0e8f890","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:28.285591Z","signature_b64":"rjZsC5NszDKC0X1cN1qmvys0vF01Cpa1BfLeNI1IzTDEzyIKypqOSI753o5xk+WHCJuE2RKuoJKpwqi7geE3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"429041ffe097f073f5c40daa66edf6d55358832024a957bcc712ce62f0e8f890","last_reissued_at":"2026-07-05T11:05:28.285086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:28.285086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.13307","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":"2026-07-05T11:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0Amul1UvO2J3pFs/uKUD1fA1y80b9eiYrLfmxpkI40+l3VdYlhs8C0TcOHFlK//Iym8nOiqLGqMrUJysTfLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:26:28.834316Z"},"content_sha256":"c636ba9b9a82d5377261519488a2d34062aad4c8e9d2e4c1b7600b73d0b726b7","schema_version":"1.0","event_id":"sha256:c636ba9b9a82d5377261519488a2d34062aad4c8e9d2e4c1b7600b73d0b726b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IKIED77AS7YHH5OEBWVGN3PW2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.AI","cs.CV"],"primary_cat":"cs.CL","authors_text":"Jiaqi Wang, Jingxuan Zhou, Jinhao Liu, Libo Qin, Qiguang Chen, Wanxiang Che, Yue Liao","submitted_at":"2025-05-19T16:25:55Z","abstract_excerpt":"Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models (LLMs) on complex tasks, spurring research into its underlying mechanisms. However, two primary challenges remain for real-world applications: (1) the lack of quantitative metrics and actionable guidelines for evaluating and optimizing measurable boundaries of CoT capability, and (2) the absence of methods to assess boundaries of unmeasurable CoT capability, such as multimodal perception. To address these gaps, we introduce the Reasoning Boundary Framework++ (RBF++). To tackle the first challenge, we defin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13307","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/2505.13307/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":"2026-07-05T11:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJsvCQhF0wsIjCfRXCnq5UgppBwhqPHWre4rCqbJ+l38sVuKRA8QEFfv6nEcgWPtSfrr3/X8skOEkeiisWXfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:26:28.834831Z"},"content_sha256":"a20fb2e2f252a6fafb02c03abe304eea4ca6ff9f0afa3d77ac9dcac092e74ebe","schema_version":"1.0","event_id":"sha256:a20fb2e2f252a6fafb02c03abe304eea4ca6ff9f0afa3d77ac9dcac092e74ebe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKIED77AS7YHH5OEBWVGN3PW2V/bundle.json","state_url":"https://pith.science/pith/IKIED77AS7YHH5OEBWVGN3PW2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKIED77AS7YHH5OEBWVGN3PW2V/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":"2026-08-16T05:26:28Z","links":{"resolver":"https://pith.science/pith/IKIED77AS7YHH5OEBWVGN3PW2V","bundle":"https://pith.science/pith/IKIED77AS7YHH5OEBWVGN3PW2V/bundle.json","state":"https://pith.science/pith/IKIED77AS7YHH5OEBWVGN3PW2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKIED77AS7YHH5OEBWVGN3PW2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IKIED77AS7YHH5OEBWVGN3PW2V","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":"d00bdf14021b6cd5cf8f552574faa5ef30007ee577d8d398a7841be9ea2faf22","cross_cats_sorted":["cs.AI","cs.CV"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-05-19T16:25:55Z","title_canon_sha256":"abde1a505fb47c986b60b6ed9701fefb38d75e3d0294740798b60cda8ea08389"},"schema_version":"1.0","source":{"id":"2505.13307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13307","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13307v1","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13307","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"IKIED77AS7YH","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"IKIED77AS7YHH5OE","created_at":"2026-07-05T11:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"IKIED77A","created_at":"2026-07-05T11:05:28Z"}],"graph_snapshots":[{"event_id":"sha256:a20fb2e2f252a6fafb02c03abe304eea4ca6ff9f0afa3d77ac9dcac092e74ebe","target":"graph","created_at":"2026-07-05T11:05:28Z","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/2505.13307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models (LLMs) on complex tasks, spurring research into its underlying mechanisms. However, two primary challenges remain for real-world applications: (1) the lack of quantitative metrics and actionable guidelines for evaluating and optimizing measurable boundaries of CoT capability, and (2) the absence of methods to assess boundaries of unmeasurable CoT capability, such as multimodal perception. To address these gaps, we introduce the Reasoning Boundary Framework++ (RBF++). To tackle the first challenge, we defin","authors_text":"Jiaqi Wang, Jingxuan Zhou, Jinhao Liu, Libo Qin, Qiguang Chen, Wanxiang Che, Yue Liao","cross_cats":["cs.AI","cs.CV"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-05-19T16:25:55Z","title":"RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13307","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:c636ba9b9a82d5377261519488a2d34062aad4c8e9d2e4c1b7600b73d0b726b7","target":"record","created_at":"2026-07-05T11:05:28Z","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":"d00bdf14021b6cd5cf8f552574faa5ef30007ee577d8d398a7841be9ea2faf22","cross_cats_sorted":["cs.AI","cs.CV"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-05-19T16:25:55Z","title_canon_sha256":"abde1a505fb47c986b60b6ed9701fefb38d75e3d0294740798b60cda8ea08389"},"schema_version":"1.0","source":{"id":"2505.13307","kind":"arxiv","version":1}},"canonical_sha256":"429041ffe097f073f5c40daa66edf6d55358832024a957bcc712ce62f0e8f890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"429041ffe097f073f5c40daa66edf6d55358832024a957bcc712ce62f0e8f890","first_computed_at":"2026-07-05T11:05:28.285086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:28.285086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rjZsC5NszDKC0X1cN1qmvys0vF01Cpa1BfLeNI1IzTDEzyIKypqOSI753o5xk+WHCJuE2RKuoJKpwqi7geE3Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:28.285591Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c636ba9b9a82d5377261519488a2d34062aad4c8e9d2e4c1b7600b73d0b726b7","sha256:a20fb2e2f252a6fafb02c03abe304eea4ca6ff9f0afa3d77ac9dcac092e74ebe"],"state_sha256":"b272aff97d76f8af46bb366a81e3e5ea8a8979f5073823d8c78d94bf1915a92a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkPyiqM56vQY88vHZbFrOHXpAqTaUDZkv8cwpAZiWPTHq/u1tFclvj0bvYz4+/eYtDl1nPWUmZ+7uE34G5iFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:26:28.838951Z","bundle_sha256":"34ddee29348b47b73a6e20e66254459c834cfef041f4b15be9c7d601e0c48a3b"}}