{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:U2GPRN34O2GYARZJ26TNK44DDO","short_pith_number":"pith:U2GPRN34","schema_version":"1.0","canonical_sha256":"a68cf8b77c768d804729d7a6d573831b8f3f6eae26abd474e5d76efecae0380b","source":{"kind":"arxiv","id":"2605.14068","version":1},"attestation_state":"computed","paper":{"title":"CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Vision-language models recover exact containment trees from nested Jordan curves at only 71 percent accuracy on easy cases and 19 percent on hard cases.","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Amirreza Mohseni, Mona Mohammadi, Morteza Saghafian, Naser Talebizadeh Saradari","submitted_at":"2026-05-13T19:46:22Z","abstract_excerpt":"We introduce CurveBench, a benchmark for hierarchical topological reasoning from visual input. CurveBench consists of \\textbf{756 images} of pairwise non-intersecting Jordan curves across easy, polygonal, topographic-inspired, maze-like, and dense counting configurations. Each image is annotated with a rooted tree encoding the containment relations between planar regions. We formulate the task as structured prediction: given an image, a model must recover the full rooted containment tree induced by the curves. Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T19:46:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0d9c0595ceb9bb930acd406796590d6f7502ec2fc2934690b5f53833a1b18430","abstract_canon_sha256":"4dd9faab3424e6d7b65351d4013f730184889dac501b2a3eec4572b170e7b9b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:12.453369Z","signature_b64":"g/0p3Y2LKwLz1cv8CiEUrQrxe+CKf05Z6YUS1AoU7IavQ1rljVvfJSHBv6UTo3NQaH3dao6/oJ4umkT3bC0dBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68cf8b77c768d804729d7a6d573831b8f3f6eae26abd474e5d76efecae0380b","last_reissued_at":"2026-05-17T23:39:12.452745Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:12.452745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Vision-language models recover exact containment trees from nested Jordan curves at only 71 percent accuracy on easy cases and 19 percent on hard cases.","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Amirreza Mohseni, Mona Mohammadi, Morteza Saghafian, Naser Talebizadeh Saradari","submitted_at":"2026-05-13T19:46:22Z","abstract_excerpt":"We introduce CurveBench, a benchmark for hierarchical topological reasoning from visual input. CurveBench consists of \\textbf{756 images} of pairwise non-intersecting Jordan curves across easy, polygonal, topographic-inspired, maze-like, and dense counting configurations. Each image is annotated with a rooted tree encoding the containment relations between planar regions. We formulate the task as structured prediction: given an image, a model must recover the full rooted containment tree induced by the curves. Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1 Pro, achieves only 71.1% tree-generation accuracy on CurveBench-Easy and 19.1% on CurveBench-Hard.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the generated images and their tree annotations faithfully isolate topological containment reasoning without providing unintended low-level visual shortcuts or dataset-specific biases that models could exploit.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CurveBench benchmark reveals that even leading VLMs like Gemini 3.1 Pro reach only 71.1% accuracy recovering containment trees on easy nested-curve images and 19.1% on hard versions, while fine-tuning lifts an open 8B model to 33.3% on easy cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Vision-language models recover exact containment trees from nested Jordan curves at only 71 percent accuracy on easy cases and 19 percent on hard cases.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8c959dfc07e0289e15e4f7997f90f45006c7d07fc7f9ea0745f0e98877071448"},"source":{"id":"2605.14068","kind":"arxiv","version":1},"verdict":{"id":"f70b9cb0-297f-4075-af14-507829a0b5bc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:30:49.710142Z","strongest_claim":"Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1 Pro, achieves only 71.1% tree-generation accuracy on CurveBench-Easy and 19.1% on CurveBench-Hard.","one_line_summary":"CurveBench benchmark reveals that even leading VLMs like Gemini 3.1 Pro reach only 71.1% accuracy recovering containment trees on easy nested-curve images and 19.1% on hard versions, while fine-tuning lifts an open 8B model to 33.3% on easy cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the generated images and their tree annotations faithfully isolate topological containment reasoning without providing unintended low-level visual shortcuts or dataset-specific biases that models could exploit.","pith_extraction_headline":"Vision-language models recover exact containment trees from nested Jordan curves at only 71 percent accuracy on easy cases and 19 percent on hard cases."},"references":{"count":44,"sample":[{"doi":"","year":null,"title":"Topographic Map Symbols , year =","work_id":"97537c87-e528-4e49-8aa6-c4a856a8e769","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Jordan Theorem , year =","work_id":"1b97f40c-b303-44f0-be1b-993511763d99","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Journal of Visual Languages and Computing , volume =","work_id":"9b902288-1e92-4908-a0e0-08556ec84269","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Findings of the Association for Computational Linguistics: ACL 2022 , pages =","work_id":"80430d48-4070-43de-b886-0d69668c33c3","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Mathew, Minesh and Karatzas, Dimosthenis and Jawahar, C. V. , title =. Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages =. 2021 , url =","work_id":"0289afd3-d25b-479c-a341-b704cb979319","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":44,"snapshot_sha256":"80adee1f36ded0afa842dac20456da112d1fe35319c75a9dde85151a0b83d11c","internal_anchors":10},"formal_canon":{"evidence_count":1,"snapshot_sha256":"977f3def4313ba2ec4124af84af93ea5a60e0a73a6b56c7952340acbff025b50"},"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":"2605.14068","created_at":"2026-05-17T23:39:12.452833+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14068v1","created_at":"2026-05-17T23:39:12.452833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14068","created_at":"2026-05-17T23:39:12.452833+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2GPRN34O2GY","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2GPRN34O2GYARZJ","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2GPRN34","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO","json":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO.json","graph_json":"https://pith.science/api/pith-number/U2GPRN34O2GYARZJ26TNK44DDO/graph.json","events_json":"https://pith.science/api/pith-number/U2GPRN34O2GYARZJ26TNK44DDO/events.json","paper":"https://pith.science/paper/U2GPRN34"},"agent_actions":{"view_html":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO","download_json":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO.json","view_paper":"https://pith.science/paper/U2GPRN34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14068&json=true","fetch_graph":"https://pith.science/api/pith-number/U2GPRN34O2GYARZJ26TNK44DDO/graph.json","fetch_events":"https://pith.science/api/pith-number/U2GPRN34O2GYARZJ26TNK44DDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO/action/storage_attestation","attest_author":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO/action/author_attestation","sign_citation":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO/action/citation_signature","submit_replication":"https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO/action/replication_record"}},"created_at":"2026-05-17T23:39:12.452833+00:00","updated_at":"2026-05-17T23:39:12.452833+00:00"}