Pith Number

pith:P27JHOIO

pith:2026:P27JHOIO2YLGPV72LTDVNR6FPU

not attested not anchored not stored refs pending

Testing axial symmetry around an unspecified direction

Alejandro Cholaquidis, Juan Cuesta-Albertos, Manuel Hern\'andez-Banadik, Ricardo Fraiman

Axial symmetry about an unknown direction reduces to testing a finite set of eigenvector candidates using projected Kolmogorov-Smirnov statistics.

arxiv:2604.09317 v2 · 2026-04-10 · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{P27JHOIO2YLGPV72LTDVNR6FPU}

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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

This leads to a feasible testing procedure for axial symmetry when the symmetry direction is unspecified.

C2weakest assumption

Under a simple-spectrum assumption on the covariance matrix, any symmetry axis must coincide with an eigenvector of the covariance matrix.

C3one line summary

A Kolmogorov-Smirnov-type test for axial symmetry about an unspecified direction that reduces to testing a finite set of covariance eigenvectors under a simple-spectrum assumption, with derived asymptotics and bootstrap validity.

Receipt and verification

First computed	2026-06-10T01:10:00.710284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ebe93b90ed61667d7fa5cc756c7c57d3991a965398105cdfac7cff26b9e8f58

Aliases

arxiv: 2604.09317 · arxiv_version: 2604.09317v2 · doi: 10.48550/arxiv.2604.09317 · pith_short_12: P27JHOIO2YLG · pith_short_16: P27JHOIO2YLGPV72 · pith_short_8: P27JHOIO

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/P27JHOIO2YLGPV72LTDVNR6FPU \
  | 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: 7ebe93b90ed61667d7fa5cc756c7c57d3991a965398105cdfac7cff26b9e8f58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cac4e5dc2fb01838d8b4b835f31b9dcec424ea4ee515a4fd7b384c10d4a0cc17",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-04-10T13:37:10Z",
    "title_canon_sha256": "46cbb571cb7083a7eb774af6ad871fbad4b0bd6cfe3f8d2002041df2efb55af4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09317",
    "kind": "arxiv",
    "version": 2
  }
}