Pith Number

pith:TRWYRIOG

pith:2026:TRWYRIOG74K7N2XWXQBYPERVC5

not attested not anchored not stored refs pending

Sloan's Analytical G\"omb\"oc at Published $\beta$: A Strict-Convexity-Constrained Reanalysis

Vincent Wesley Couey

Sloan's analytical Gömböc equations produce no mono-monostatic bodies, but Fourier and radial extensions yield a catalog of thirteen verified examples.

arxiv:2604.17120 v2 · 2026-04-18 · cs.CE · cs.CG

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\pithnumber{TRWYRIOG74K7N2XWXQBYPERVC5}

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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

No tested parameter value produces a mono-monostatic body under Sloan's parameterization, but extensions with Fourier terms and radial perturbations produce thirteen verified mono-monostatic bodies with ECS=1 confirmed across merge thresholds 0.5-10%.

C2weakest assumption

That the ECS oracle, which counts stable equilibria via drainage basin analysis on the COM height landscape, accurately captures all equilibria and that differential evolution optimization finds parameters satisfying the mono-monostatic condition without overlooking additional minima.

C3one line summary

Sloan's parameterization fails to produce mono-monostatic bodies, but extensions yield thirteen verified examples with open data showing a near-perfect robustness-gentleness trade-off.

Receipt and verification

First computed	2026-05-26T01:03:30.349399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c6d88a1c6ff15f6eaf6bc038792351771e7d5ebd5da155fb962e05156891be3

Aliases

arxiv: 2604.17120 · arxiv_version: 2604.17120v2 · doi: 10.48550/arxiv.2604.17120 · pith_short_12: TRWYRIOG74K7 · pith_short_16: TRWYRIOG74K7N2XW · pith_short_8: TRWYRIOG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TRWYRIOG74K7N2XWXQBYPERVC5 \
  | 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: 9c6d88a1c6ff15f6eaf6bc038792351771e7d5ebd5da155fb962e05156891be3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ee13689ff584e80bc301dc77d85be65c690658216c44791e42d85d21823d6b7",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CE",
    "submitted_at": "2026-04-18T19:41:10Z",
    "title_canon_sha256": "0325e6d28f2cb171a6f69ab037111e16666bd1d1f3cd30da0cc3bee67d453c48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17120",
    "kind": "arxiv",
    "version": 2
  }
}