Pith Number

pith:N4E2BH7L

pith:2026:N4E2BH7LRGSTUTOBQU2DSINNOT

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Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions

Oleg R. Musin

A Borsuk-Ulam theorem generalized to Stiefel manifolds yields bounds on d guaranteeing k mutually orthogonal hyperplanes whose any n subset equally partitions each of m given measures in R^d.

arxiv:2603.18550 v3 · 2026-03-19 · math.AT · math.CO · math.MG

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\pithnumber{N4E2BH7LRGSTUTOBQU2DSINNOT}

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Claims

C1strongest claim

A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on d that guarantee-for a given set of m measures in R^d-the existence of k mutually orthogonal hyperplanes, any n of which partition each of the measures into 2^n equal parts.

C2weakest assumption

The measures are continuous (or absolutely continuous) probability measures on R^d so that the topological configuration space and test maps satisfy the conditions needed for the generalized Borsuk-Ulam theorem to apply.

C3one line summary

A Borsuk-Ulam type theorem for Stiefel manifolds yields bounds on d guaranteeing k mutually orthogonal hyperplanes that partition m measures into equal parts.

Receipt and verification

First computed	2026-05-26T01:03:28.406872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f09a09feb89a53a4dc185343921ad74daaae90f974423e40629ab5e5715a836

Aliases

arxiv: 2603.18550 · arxiv_version: 2603.18550v3 · doi: 10.48550/arxiv.2603.18550 · pith_short_12: N4E2BH7LRGST · pith_short_16: N4E2BH7LRGSTUTOB · pith_short_8: N4E2BH7L

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N4E2BH7LRGSTUTOBQU2DSINNOT \
  | 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: 6f09a09feb89a53a4dc185343921ad74daaae90f974423e40629ab5e5715a836

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d7e283b0be92d2c7d2163e14d926b201b21c83dc074338a9436f21108a97445",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-03-19T07:07:43Z",
    "title_canon_sha256": "da2040816b20eb95651a2a3a04e995c54e15dc037c7235d690d6c56ae4847bc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.18550",
    "kind": "arxiv",
    "version": 3
  }
}