Pith Number

pith:U2GPRN34

pith:2026:U2GPRN34O2GYARZJ26TNK44DDO

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CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves

Amirreza Mohseni, Mona Mohammadi, Morteza Saghafian, Naser Talebizadeh Saradari

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.

arxiv:2605.14068 v1 · 2026-05-13 · cs.CV · cs.LG

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\pithnumber{U2GPRN34O2GYARZJ26TNK44DDO}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

44 extracted · 44 resolved · 10 Pith anchors

[1] Topographic Map Symbols , year =

[2] Jordan Theorem , year =

[3] Journal of Visual Languages and Computing , volume = 2014

[4] Findings of the Association for Computational Linguistics: ACL 2022 , pages = 2022

[5] 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 = 2021

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:12.452745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68cf8b77c768d804729d7a6d573831b8f3f6eae26abd474e5d76efecae0380b

Aliases

arxiv: 2605.14068 · arxiv_version: 2605.14068v1 · doi: 10.48550/arxiv.2605.14068 · pith_short_12: U2GPRN34O2GY · pith_short_16: U2GPRN34O2GYARZJ · pith_short_8: U2GPRN34

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U2GPRN34O2GYARZJ26TNK44DDO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a68cf8b77c768d804729d7a6d573831b8f3f6eae26abd474e5d76efecae0380b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dd9faab3424e6d7b65351d4013f730184889dac501b2a3eec4572b170e7b9b8",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-13T19:46:22Z",
    "title_canon_sha256": "0d9c0595ceb9bb930acd406796590d6f7502ec2fc2934690b5f53833a1b18430"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14068",
    "kind": "arxiv",
    "version": 1
  }
}