{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FLX6QP2QO5OHJQFSI76U4KWKV5","short_pith_number":"pith:FLX6QP2Q","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"},"canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","source":{"kind":"arxiv","id":"2410.17885","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17885","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17885v4","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17885","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_12","alias_value":"FLX6QP2QO5OH","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_16","alias_value":"FLX6QP2QO5OHJQFS","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_8","alias_value":"FLX6QP2Q","created_at":"2026-07-05T11:12:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FLX6QP2QO5OHJQFSI76U4KWKV5","target":"record","payload":{"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"},"canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","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"},"source_kind":"arxiv","source_id":"2410.17885","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:12:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEqc8hDg+ACLFgTBUWQC3HDRSIXQtjaczo0RdTkn5zP3M9nDFk7NXUlXMAK55vXe3mhlZoFIFRxORFnKLu7/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T19:09:13.074666Z"},"content_sha256":"7203c0f4834eb4646c7601bc70336b8d6636c5834010d69b86353be83d8f3ae1","schema_version":"1.0","event_id":"sha256:7203c0f4834eb4646c7601bc70336b8d6636c5834010d69b86353be83d8f3ae1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FLX6QP2QO5OHJQFSI76U4KWKV5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:12:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyCSz6gh3TezkMKf4vBAkXyO5j1HeSb8p/8gkSlzOhZjc1ZfPUMJ57ZT7UN+vy4nwts3WjbzkrPix/JP575GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T19:09:13.075395Z"},"content_sha256":"dc0c91fbb5a7de56dc2aefa07fd68110aabf63670bc2d8c4164d40656d23e004","schema_version":"1.0","event_id":"sha256:dc0c91fbb5a7de56dc2aefa07fd68110aabf63670bc2d8c4164d40656d23e004"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/bundle.json","state_url":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/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":"2026-08-06T19:09:13Z","links":{"resolver":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5","bundle":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/bundle.json","state":"https://pith.science/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLX6QP2QO5OHJQFSI76U4KWKV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FLX6QP2QO5OHJQFSI76U4KWKV5","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":"8ae056cbf452ca55623852b26a169c34bc328241215e701b701dd5776684ad29","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-10-23T13:58:39Z","title_canon_sha256":"97706810d996080071df5104895b19ff194a3063aa170d00e85f5fe0fbfe9d5b"},"schema_version":"1.0","source":{"id":"2410.17885","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17885","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17885v4","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17885","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_12","alias_value":"FLX6QP2QO5OH","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_16","alias_value":"FLX6QP2QO5OHJQFS","created_at":"2026-07-05T11:12:21Z"},{"alias_kind":"pith_short_8","alias_value":"FLX6QP2Q","created_at":"2026-07-05T11:12:21Z"}],"graph_snapshots":[{"event_id":"sha256:dc0c91fbb5a7de56dc2aefa07fd68110aabf63670bc2d8c4164d40656d23e004","target":"graph","created_at":"2026-07-05T11:12:21Z","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/2410.17885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Gang Zhang, Jingjing Wu, Linger Deng, Linghao Zhu, Qunyi Xie, Xiang Bai, Yingying Zhu, Yuliang Liu, Yu Wang","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-10-23T13:58:39Z","title":"Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17885","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":"sha256:7203c0f4834eb4646c7601bc70336b8d6636c5834010d69b86353be83d8f3ae1","target":"record","created_at":"2026-07-05T11:12:21Z","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":"8ae056cbf452ca55623852b26a169c34bc328241215e701b701dd5776684ad29","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-10-23T13:58:39Z","title_canon_sha256":"97706810d996080071df5104895b19ff194a3063aa170d00e85f5fe0fbfe9d5b"},"schema_version":"1.0","source":{"id":"2410.17885","kind":"arxiv","version":4}},"canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2aefe83f50775c74c0b247fd4e2acaaf6ca34e2716ce7d986563499542d90574","first_computed_at":"2026-07-05T11:12:21.605834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:21.605834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vpu8hEw3HLjlJyEG7Jk7Q3JhliPxpHi8es4irhNCi6ju6dH/qy8khwrbzl7B6HH8LDa5JYJELc2aUee4InMqCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:21.606343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.17885","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7203c0f4834eb4646c7601bc70336b8d6636c5834010d69b86353be83d8f3ae1","sha256:dc0c91fbb5a7de56dc2aefa07fd68110aabf63670bc2d8c4164d40656d23e004"],"state_sha256":"d11c267d5905d75fad2477269aeda850cb9829fae04d4b804a2555b25fb92df6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oy+6jVRwLQHQKZr63aXEm+KP4JWQ36f/DN/5D55HswJLgael4mz+N6+i0DjD6RU+I6dEMQwnPdg6GVrxcFkAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T19:09:13.079912Z","bundle_sha256":"7cd00724d160d37ba5e8d133c6e13dcef474de88fe60e4c714146f8951fe35a4"}}