{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:C47ZSD3UOTVYIXLM5G3UCSLCCO","short_pith_number":"pith:C47ZSD3U","canonical_record":{"source":{"id":"2506.09820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-06-11T14:59:02Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"83050e75f748be3edc391f7b26a12e042615edf56fafd6dd4ef7ecdcd5d5ce5d","abstract_canon_sha256":"44f67eaf632991244dea693dec069f1ccb775c2f5799899fd9552848c423bcc3"},"schema_version":"1.0"},"canonical_sha256":"173f990f7474eb845d6ce9b74149621382ec63954ac0f21e5a98ddab5fe62d92","source":{"kind":"arxiv","id":"2506.09820","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09820","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09820v2","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09820","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"C47ZSD3UOTVY","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"C47ZSD3UOTVYIXLM","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"C47ZSD3U","created_at":"2026-07-05T11:20:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:C47ZSD3UOTVYIXLM5G3UCSLCCO","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-06-11T14:59:02Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"83050e75f748be3edc391f7b26a12e042615edf56fafd6dd4ef7ecdcd5d5ce5d","abstract_canon_sha256":"44f67eaf632991244dea693dec069f1ccb775c2f5799899fd9552848c423bcc3"},"schema_version":"1.0"},"canonical_sha256":"173f990f7474eb845d6ce9b74149621382ec63954ac0f21e5a98ddab5fe62d92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:14.857438Z","signature_b64":"/4ssCE2+djZ7EtRHVrzw/NsFo9ioVhWzAnwJUskSaJZ/d7sgjx5KrYfRO8dL+tmvV6fQGCgL7HSXjYmgRCfRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"173f990f7474eb845d6ce9b74149621382ec63954ac0f21e5a98ddab5fe62d92","last_reissued_at":"2026-07-05T11:20:14.856975Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:14.856975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09820","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nS/KNgaDSi07HDg4Hd+Nz1E9/A9rZybfU2f174VsXug5MIOQJ4sCQB63vGA1v0vS24HwrY+IC+g0bFZilixyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T13:02:45.293393Z"},"content_sha256":"5823f6cd0fa8df2bd29e10803e68f790b6e156a9e2aca34de401cfef2f006ee6","schema_version":"1.0","event_id":"sha256:5823f6cd0fa8df2bd29e10803e68f790b6e156a9e2aca34de401cfef2f006ee6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:C47ZSD3UOTVYIXLM5G3UCSLCCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CoRT: Code-integrated Reasoning within Thinking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.CL","authors_text":"Benyou Wang, Chengpeng Li, Dayiheng Liu, Junyang Lin, Keqin Bao, Mingfeng Xue, Ruoyu Sun, Tian Ding, Xiang Wang, Zhengyang Tang, Ziniu Li","submitted_at":"2025-06-11T14:59:02Z","abstract_excerpt":"Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09820","kind":"arxiv","version":2},"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/2506.09820/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":"2026-07-05T11:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKJbDrGpBmLw8ofSTGf18LRsLKP/YjsgxyBQcLO4b+lEEd88NIW14TNqgSUVouoVXTDKBWDU0/rv+SnmBu9bAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T13:02:45.293772Z"},"content_sha256":"7dbbf46152c40dd8830bace21ea83136512bece391ae29e2b59211a5182e138a","schema_version":"1.0","event_id":"sha256:7dbbf46152c40dd8830bace21ea83136512bece391ae29e2b59211a5182e138a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/bundle.json","state_url":"https://pith.science/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/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":"2026-07-27T13:02:45Z","links":{"resolver":"https://pith.science/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO","bundle":"https://pith.science/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/bundle.json","state":"https://pith.science/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C47ZSD3UOTVYIXLM5G3UCSLCCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:C47ZSD3UOTVYIXLM5G3UCSLCCO","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":"44f67eaf632991244dea693dec069f1ccb775c2f5799899fd9552848c423bcc3","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-06-11T14:59:02Z","title_canon_sha256":"83050e75f748be3edc391f7b26a12e042615edf56fafd6dd4ef7ecdcd5d5ce5d"},"schema_version":"1.0","source":{"id":"2506.09820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09820","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09820v2","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09820","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"C47ZSD3UOTVY","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"C47ZSD3UOTVYIXLM","created_at":"2026-07-05T11:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"C47ZSD3U","created_at":"2026-07-05T11:20:14Z"}],"graph_snapshots":[{"event_id":"sha256:7dbbf46152c40dd8830bace21ea83136512bece391ae29e2b59211a5182e138a","target":"graph","created_at":"2026-07-05T11:20:14Z","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/2506.09820/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework f","authors_text":"Benyou Wang, Chengpeng Li, Dayiheng Liu, Junyang Lin, Keqin Bao, Mingfeng Xue, Ruoyu Sun, Tian Ding, Xiang Wang, Zhengyang Tang, Ziniu Li","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-06-11T14:59:02Z","title":"CoRT: Code-integrated Reasoning within Thinking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09820","kind":"arxiv","version":2},"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":"sha256:5823f6cd0fa8df2bd29e10803e68f790b6e156a9e2aca34de401cfef2f006ee6","target":"record","created_at":"2026-07-05T11:20:14Z","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":"44f67eaf632991244dea693dec069f1ccb775c2f5799899fd9552848c423bcc3","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-06-11T14:59:02Z","title_canon_sha256":"83050e75f748be3edc391f7b26a12e042615edf56fafd6dd4ef7ecdcd5d5ce5d"},"schema_version":"1.0","source":{"id":"2506.09820","kind":"arxiv","version":2}},"canonical_sha256":"173f990f7474eb845d6ce9b74149621382ec63954ac0f21e5a98ddab5fe62d92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"173f990f7474eb845d6ce9b74149621382ec63954ac0f21e5a98ddab5fe62d92","first_computed_at":"2026-07-05T11:20:14.856975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:14.856975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/4ssCE2+djZ7EtRHVrzw/NsFo9ioVhWzAnwJUskSaJZ/d7sgjx5KrYfRO8dL+tmvV6fQGCgL7HSXjYmgRCfRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:14.857438Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5823f6cd0fa8df2bd29e10803e68f790b6e156a9e2aca34de401cfef2f006ee6","sha256:7dbbf46152c40dd8830bace21ea83136512bece391ae29e2b59211a5182e138a"],"state_sha256":"0380b9a86ad4444068b5efd68f890c99ffe7d303739f8106088497870673de73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gqp+2przrcUtzSU6USKdDzRqkIHGDPq6ReEATN76eoFXZpAA2Rizs1ghfYsk0iQz478oGyfWjy7F2rwOaJMUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-27T13:02:45.296279Z","bundle_sha256":"95c0686d063ead5a2e53fc238fe74c51fccc6e91bb277e0c536e9d8cc297432a"}}