Pith Number

pith:XTHE4LPD

pith:2025:XTHE4LPDDFCYSWM3EX62U2LW57

not attested not anchored not stored refs resolved

Sensitivity Analysis on the Sphere and a Spherical ANOVA Decomposition

Laura Weidensager

A function on the sphere decomposes into a sum of terms each depending on a coordinate subset and a parity vector.

arxiv:2512.23476 v2 · 2025-12-29 · math.NA · cs.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XTHE4LPDDFCYSWM3EX62U2LW57}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We present formulas that allow us to decompose a function f : S^d → R into a sum of terms f_{u,ξ}. The index u is a subset of {1,2,…,d+1}, where each term f_{u,ξ} depends only on the variables with indices in u.

C2weakest assumption

The natural geometry on the sphere naturally leads to the dependencies between the input variables, and suitable orthogonal basis functions exist that permit the decomposition and approximation.

C3one line summary

A parity-augmented ANOVA decomposition is established for functions on the sphere using orthogonal bases to capture geometry-induced variable dependencies.

References

36 extracted · 36 resolved · 0 Pith anchors

[1] M. Abramowitz and I. A. Stegun.Handbook of Mathematical Functions, With Formulas, Graphs, and Mathe- matical Tables. National Bureau of Standards, 1964 1964

[2] H.-J. Bungartz and M. Griebel. Sparse grids.Acta Numer., 13:147–269, 2004.doi:10.1017/ S0962492904000182 2004

[3] R. Caflisch, W. Morokoff, and A. Owen. Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension.J. Comput. Finance, 1(1):27–46, 1997.doi:10.21314/jcf.1997.005 1997 · doi:10.21314/jcf.1997.005

[4] M. Chu, N. Del Buono, L. Lopez, and T. Politi. On the low-rank approximation of data on the unit sphere.SIAM Journal on Matrix Analysis and Applications, 27(1):46–60, Jan. 2005.doi:10.1137/s0895479803 2005 · doi:10.1137/s0895479803433295

[5] S. da Veiga. Kernel-based ANOV A decomposition and shapley effects – application to global sensitivity analysis, 2021.arXiv:2101.05487,doi:10.48550/ARXIV.2101.05487. 24 Sensitivity Analysis on the Sph 2021 · doi:10.48550/arxiv.2101.05487

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:16.776268Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcce4e2de3194589599b25fdaa6976efdd6d6c515e866b2d89a8efc67f9948b9

Aliases

arxiv: 2512.23476 · arxiv_version: 2512.23476v2 · doi: 10.48550/arxiv.2512.23476 · pith_short_12: XTHE4LPDDFCY · pith_short_16: XTHE4LPDDFCYSWM3 · pith_short_8: XTHE4LPD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XTHE4LPDDFCYSWM3EX62U2LW57 \
  | 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: bcce4e2de3194589599b25fdaa6976efdd6d6c515e866b2d89a8efc67f9948b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45a0de1cab9456946bbedc781278695e00cd1e9d7493f582bf4e274cf41f9e77",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-12-29T13:59:36Z",
    "title_canon_sha256": "dde61ceec236665529df38ade39125d36d7d4f36b2c74d6cd8acd55e55f82f7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.23476",
    "kind": "arxiv",
    "version": 2
  }
}