Pith Number

pith:Z27CM5GR

pith:2026:Z27CM5GRXW5ENEY2D6RLNRPIX2

not attested not anchored not stored refs pending

On colorful generalizations of the Goodman--Pollack transversal problem

Nikola Sadovek

A colorful and matroidal generalization solves the Goodman-Pollack problem on the existence of affine transversals to families of convex sets.

arxiv:2604.19644 v2 · 2026-04-21 · math.CO · math.GT · math.MG

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\pithnumber{Z27CM5GRXW5ENEY2D6RLNRPIX2}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations 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

We establish a colorful, and more generally matroidal, solution to the problem of Goodman and Pollack on the existence of an F-affine k-dimensional transversal to a family of convex sets in F^d, where 0 ≤ k ≤ d-1 and F in {R, C}.

C2weakest assumption

The connectivity estimates for matroidal joins (defined as homotopy colimits of diagrams indexed by face posets of matroidal complexes) and the adaptations of nonexistence results for equivariant maps from Stiefel manifolds to spheres hold in the stated settings.

C3one line summary

A colorful and matroidal solution to the Goodman-Pollack transversal problem is established via new matroidal joins and equivariant map techniques, unifying several prior theorems.

Receipt and verification

First computed	2026-05-20T00:05:45.057842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cebe2674d1bdba46931a1fa2b6c5e8beba2d999f40d99a5ced0f881a0e485517

Aliases

arxiv: 2604.19644 · arxiv_version: 2604.19644v2 · doi: 10.48550/arxiv.2604.19644 · pith_short_12: Z27CM5GRXW5E · pith_short_16: Z27CM5GRXW5ENEY2 · pith_short_8: Z27CM5GR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z27CM5GRXW5ENEY2D6RLNRPIX2 \
  | 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: cebe2674d1bdba46931a1fa2b6c5e8beba2d999f40d99a5ced0f881a0e485517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23f5e8ff38f6d3134906c3b74cf59825e584d3c08d8884efae135237bf17c7d1",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-21T16:33:20Z",
    "title_canon_sha256": "07d2e842923bcf3edfc261c075fdd3d7b376f5120720f5a840945cb2aff8a4ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19644",
    "kind": "arxiv",
    "version": 2
  }
}