{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FLX6QP2QO5OHJQFSI76U4KWKV5","short_pith_number":"pith:FLX6QP2Q","schema_version":"1.0","canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","source":{"kind":"arxiv","id":"2410.17885","version":4},"attestation_state":"computed","paper":{"title":"Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.AI","authors_text":"Gang Zhang, Jingjing Wu, Linger Deng, Linghao Zhu, Qunyi Xie, Xiang Bai, Yingying Zhu, Yuliang Liu, Yu Wang","submitted_at":"2024-10-23T13:58:39Z","abstract_excerpt":"Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data creation, they often face challenges in achieving both diversity and precision. To bridge this gap, we introduce a two-stage Theorem-Validated Reverse Chain-of-Thought Reasoning Synthesis (TR-CoT) framework. The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties. The second stage, TR-Reasoner, emp"},"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":"2410.17885","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-10-23T13:58:39Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"97706810d996080071df5104895b19ff194a3063aa170d00e85f5fe0fbfe9d5b","abstract_canon_sha256":"8ae056cbf452ca55623852b26a169c34bc328241215e701b701dd5776684ad29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:21.606343Z","signature_b64":"Vpu8hEw3HLjlJyEG7Jk7Q3JhliPxpHi8es4irhNCi6ju6dH/qy8khwrbzl7B6HH8LDa5JYJELc2aUee4InMqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","last_reissued_at":"2026-07-05T11:12:21.605834Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:21.605834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.AI","authors_text":"Gang Zhang, Jingjing Wu, Linger Deng, Linghao Zhu, Qunyi Xie, Xiang Bai, Yingying Zhu, Yuliang Liu, Yu Wang","submitted_at":"2024-10-23T13:58:39Z","abstract_excerpt":"Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data creation, they often face challenges in achieving both diversity and precision. To bridge this gap, we introduce a two-stage Theorem-Validated Reverse Chain-of-Thought Reasoning Synthesis (TR-CoT) framework. The first stage, TR-Engine, synthesizes theorem-grounded geometric diagrams with structured descriptions and properties. The second stage, TR-Reasoner, emp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17885","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/2410.17885/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":"2410.17885","created_at":"2026-07-05T11:12:21.605895+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.17885v4","created_at":"2026-07-05T11:12:21.605895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17885","created_at":"2026-07-05T11:12:21.605895+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLX6QP2QO5OH","created_at":"2026-07-05T11:12:21.605895+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLX6QP2QO5OHJQFS","created_at":"2026-07-05T11:12:21.605895+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLX6QP2Q","created_at":"2026-07-05T11:12:21.605895+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17888","citing_title":"MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoning","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16371","citing_title":"GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2503.12605","citing_title":"Multimodal Chain-of-Thought Reasoning: A Comprehensive Survey","ref_index":88,"is_internal_anchor":false},{"citing_arxiv_id":"2509.18154","citing_title":"MiniCPM-V 4.5: Cooking Efficient MLLMs via Architecture, Data, and Training Recipe","ref_index":31,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5","json":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5.json","graph_json":"https://pith.science/api/pith-number/FLX6QP2QO5OHJQFSI76U4KWKV5/graph.json","events_json":"https://pith.science/api/pith-number/FLX6QP2QO5OHJQFSI76U4KWKV5/events.json","paper":"https://pith.science/paper/FLX6QP2Q"},"agent_actions":{"view_html":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5","download_json":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5.json","view_paper":"https://pith.science/paper/FLX6QP2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.17885&json=true","fetch_graph":"https://pith.science/api/pith-number/FLX6QP2QO5OHJQFSI76U4KWKV5/graph.json","fetch_events":"https://pith.science/api/pith-number/FLX6QP2QO5OHJQFSI76U4KWKV5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/action/storage_attestation","attest_author":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/action/author_attestation","sign_citation":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/action/citation_signature","submit_replication":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/action/replication_record"}},"created_at":"2026-07-05T11:12:21.605895+00:00","updated_at":"2026-07-05T11:12:21.605895+00:00"}