Pith Number

pith:GO7DQ5IB

pith:2026:GO7DQ5IBTY7CXCTNICV2VFT525

not attested not anchored not stored refs resolved

Meschers: Geometry Processing of Impossible Objects

Ana Dodik, Isabella Yu, Jonathan Ragan-Kelley, Joshua Tenenbaum, Justin Solomon, Kartik Chandra, Vincent Sitzmann

Meschers represent impossible objects as meshes that support standard geometry processing and inverse rendering.

arxiv:2605.14960 v1 · 2026-05-14 · cs.GR · cs.CG · cs.CV

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\pithnumber{GO7DQ5IBTY7CXCTNICV2VFT525}

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3 Author claim open · sign in to claim

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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

Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects.

C2weakest assumption

That discrete exterior calculus can be extended to meshes representing impossible objects while preserving the validity of standard geometry operations such as distance computation and smoothing without introducing new inconsistencies.

C3one line summary

Meschers are a new mesh representation for impossible geometric objects grounded in discrete exterior calculus that supports full discrete geometry processing including inverse rendering.

References

47 extracted · 47 resolved · 1 Pith anchors

[1] In ACM SIGGRAPH 2006 Papers 2006

[2] InRendering Techniques 2000: Proceedings of the Eurographics Workshop in Brno, Czech Republic, June 26–28, 2000 2000

[3] The Visual Computer19, 2 (2003), 105–114 2003

[4] Computer vision, graphics, and image processing32, 1 (1985), 29–73 1985 · doi:10.1145/3596711.3596740

[5] month = dec, year = 2023

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:38:55.297222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33be3875019e3e2b8a6d40abaa967dd76732becba41674bab2ab48a20e0c5c80

Aliases

arxiv: 2605.14960 · arxiv_version: 2605.14960v1 · doi: 10.48550/arxiv.2605.14960 · pith_short_12: GO7DQ5IBTY7C · pith_short_16: GO7DQ5IBTY7CXCTN · pith_short_8: GO7DQ5IB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GO7DQ5IBTY7CXCTNICV2VFT525 \
  | 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: 33be3875019e3e2b8a6d40abaa967dd76732becba41674bab2ab48a20e0c5c80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c63b209673f6d633696557300fca3cc3c03c8c75168196f231f2cb81ba30716f",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.CV"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.GR",
    "submitted_at": "2026-05-14T15:28:14Z",
    "title_canon_sha256": "3d41387c9a9b5be48af44e8a0ffb62fd34bd75c060344d02b1ac2630a624e03a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14960",
    "kind": "arxiv",
    "version": 1
  }
}