{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SEA2ZNMK4MBSZGZ2VQXFMADHOA","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":"ea42903219e3c2d23c6b4dd7274e66afe77e1810f01041f65c83729f26d5b9a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-01-19T16:53:26Z","title_canon_sha256":"5fc37ff3454e63f6296ccb4cef32d12d43060bc841b4e3d5d42705cb2e8909ce"},"schema_version":"1.0","source":{"id":"2501.11110","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.11110","created_at":"2026-07-05T12:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"2501.11110v4","created_at":"2026-07-05T12:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.11110","created_at":"2026-07-05T12:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"SEA2ZNMK4MBS","created_at":"2026-07-05T12:04:30Z"},{"alias_kind":"pith_short_16","alias_value":"SEA2ZNMK4MBSZGZ2","created_at":"2026-07-05T12:04:30Z"},{"alias_kind":"pith_short_8","alias_value":"SEA2ZNMK","created_at":"2026-07-05T12:04:30Z"}],"graph_snapshots":[{"event_id":"sha256:2b4698ba2ea381a169a685fea5b1134f31c0a19066073cdc2985a4d1821e2f52","target":"graph","created_at":"2026-07-05T12:04:30Z","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/2501.11110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","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","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-01-19T16:53:26Z","title":"Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11110","kind":"arxiv","version":4},"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":"sha256:073de778ad6ea89e9239ea35ea6d545f0254e9237413bbf08951e32e0f20d67e","target":"record","created_at":"2026-07-05T12:04:30Z","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":"ea42903219e3c2d23c6b4dd7274e66afe77e1810f01041f65c83729f26d5b9a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2025-01-19T16:53:26Z","title_canon_sha256":"5fc37ff3454e63f6296ccb4cef32d12d43060bc841b4e3d5d42705cb2e8909ce"},"schema_version":"1.0","source":{"id":"2501.11110","kind":"arxiv","version":4}},"canonical_sha256":"9101acb58ae3032c9b3aac2e560067701e08c4e48769895e7ed9a4ffe6644f7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9101acb58ae3032c9b3aac2e560067701e08c4e48769895e7ed9a4ffe6644f7c","first_computed_at":"2026-07-05T12:04:30.271137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:30.271137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P5TSO+RP7qUQSTH9I25+tl8koRCpJscgttZBtxZ0zZR+VCR1lPx7ZGzf58jKShCl+YWEs1pkkQ9rFNNaLzNvAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:30.271623Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.11110","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:073de778ad6ea89e9239ea35ea6d545f0254e9237413bbf08951e32e0f20d67e","sha256:2b4698ba2ea381a169a685fea5b1134f31c0a19066073cdc2985a4d1821e2f52"],"state_sha256":"7fae6d59203fe2275270c6e776a710ae5a970772c34d59c1631c535586956006"}