Pith Number

pith:NRB7GPB6

pith:2026:NRB7GPB67JXWDWR5UTXOYFJVHN

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Transversality and Geometric Regularisation in Distributional Statistical Models

R. Labouriau

Generic kernels in rich families place distributional statistical models in transversal position to degeneracy loci.

arxiv:2605.04536 v2 · 2026-05-06 · math.ST · math.DG · stat.ME · stat.TH

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Claims

C1strongest claim

for a generic kernel in any sufficiently rich family, the kernel-induced feature map avoids degeneracy strata of sufficiently high codimension. We establish verifiable conditions -- formulated as rank conditions on the Jacobian of the joint feature map -- under which the transversality hypothesis can be checked.

C2weakest assumption

That the family of kernels is sufficiently rich for the transversality theorems to apply, and that the rank conditions on the Jacobian hold for the specific models (location families, log-normal, etc.) without post-hoc adjustments.

C3one line summary

Kernels serve as geometric regularizers ensuring generic transversality of kernel-induced feature maps to high-codimension degeneracy strata in parametric distributional models, via a weak transversality theorem from Whitney-Thom-Mather.

Cited by

2 papers in Pith

Inference Functionals and Observation Operators for Distributional Statistical Models

Notes on Transversality and Statistical Degeneracies in Distributional Models

Receipt and verification

First computed	2026-05-26T02:04:11.992039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c43f33c3efa6f61da3da4eeec15353b5279f3c6d23ba07813769c2737bb708e

Aliases

arxiv: 2605.04536 · arxiv_version: 2605.04536v2 · doi: 10.48550/arxiv.2605.04536 · pith_short_12: NRB7GPB67JXW · pith_short_16: NRB7GPB67JXWDWR5 · pith_short_8: NRB7GPB6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NRB7GPB67JXWDWR5UTXOYFJVHN \
  | 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: 6c43f33c3efa6f61da3da4eeec15353b5279f3c6d23ba07813769c2737bb708e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90fc75754e20a03597cb44bb3417aa80ee72e2c687b271a966b28c96eca0db92",
    "cross_cats_sorted": [
      "math.DG",
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-06T06:24:41Z",
    "title_canon_sha256": "3faabdc8d41f1941f929e3d2e65368c2fccf77999494fb11fb658ef3b6b5d5ae"
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  "source": {
    "id": "2605.04536",
    "kind": "arxiv",
    "version": 2
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}