{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SEA2ZNMK4MBSZGZ2VQXFMADHOA","short_pith_number":"pith:SEA2ZNMK","schema_version":"1.0","canonical_sha256":"9101acb58ae3032c9b3aac2e560067701e08c4e48769895e7ed9a4ffe6644f7c","source":{"kind":"arxiv","id":"2501.11110","version":4},"attestation_state":"computed","paper":{"title":"Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Dongdong Zhang, Furu Wei, Hany Awadalla, Hengyuan Zhang, Junjie Wang, Mahmoud Khademi, Xiao Liang, Xingxing Zhang, Yiyao Yu, Yujiu Yang, Yuxiang Zhang, Ziyi Yang","submitted_at":"2025-01-19T16:53:26Z","abstract_excerpt":"Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet often rely on single-paradigm reasoning, limiting their effectiveness across diverse tasks. We introduce Chain-of-Reasoning (CoR), a novel unified framework integrating multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers via different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.11110","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-01-19T16:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"5fc37ff3454e63f6296ccb4cef32d12d43060bc841b4e3d5d42705cb2e8909ce","abstract_canon_sha256":"ea42903219e3c2d23c6b4dd7274e66afe77e1810f01041f65c83729f26d5b9a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:30.271623Z","signature_b64":"P5TSO+RP7qUQSTH9I25+tl8koRCpJscgttZBtxZ0zZR+VCR1lPx7ZGzf58jKShCl+YWEs1pkkQ9rFNNaLzNvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9101acb58ae3032c9b3aac2e560067701e08c4e48769895e7ed9a4ffe6644f7c","last_reissued_at":"2026-07-05T12:04:30.271137Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:30.271137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Dongdong Zhang, Furu Wei, Hany Awadalla, Hengyuan Zhang, Junjie Wang, Mahmoud Khademi, Xiao Liang, Xingxing Zhang, Yiyao Yu, Yujiu Yang, Yuxiang Zhang, Ziyi Yang","submitted_at":"2025-01-19T16:53:26Z","abstract_excerpt":"Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet often rely on single-paradigm reasoning, limiting their effectiveness across diverse tasks. We introduce Chain-of-Reasoning (CoR), a novel unified framework integrating multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers via different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11110","kind":"arxiv","version":4},"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/2501.11110/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.11110","created_at":"2026-07-05T12:04:30.271194+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.11110v4","created_at":"2026-07-05T12:04:30.271194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.11110","created_at":"2026-07-05T12:04:30.271194+00:00"},{"alias_kind":"pith_short_12","alias_value":"SEA2ZNMK4MBS","created_at":"2026-07-05T12:04:30.271194+00:00"},{"alias_kind":"pith_short_16","alias_value":"SEA2ZNMK4MBSZGZ2","created_at":"2026-07-05T12:04:30.271194+00:00"},{"alias_kind":"pith_short_8","alias_value":"SEA2ZNMK","created_at":"2026-07-05T12:04:30.271194+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.22389","citing_title":"Unified Data Selection for LLM Reasoning","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2502.17419","citing_title":"From System 1 to System 2: A Survey of Reasoning Large Language Models","ref_index":243,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA","json":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA.json","graph_json":"https://pith.science/api/pith-number/SEA2ZNMK4MBSZGZ2VQXFMADHOA/graph.json","events_json":"https://pith.science/api/pith-number/SEA2ZNMK4MBSZGZ2VQXFMADHOA/events.json","paper":"https://pith.science/paper/SEA2ZNMK"},"agent_actions":{"view_html":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA","download_json":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA.json","view_paper":"https://pith.science/paper/SEA2ZNMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.11110&json=true","fetch_graph":"https://pith.science/api/pith-number/SEA2ZNMK4MBSZGZ2VQXFMADHOA/graph.json","fetch_events":"https://pith.science/api/pith-number/SEA2ZNMK4MBSZGZ2VQXFMADHOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA/action/storage_attestation","attest_author":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA/action/author_attestation","sign_citation":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA/action/citation_signature","submit_replication":"https://pith.science/pith/SEA2ZNMK4MBSZGZ2VQXFMADHOA/action/replication_record"}},"created_at":"2026-07-05T12:04:30.271194+00:00","updated_at":"2026-07-05T12:04:30.271194+00:00"}