Pith Number

pith:KXUYQT7B

pith:2026:KXUYQT7BYGQXEDLHEECTYMM6NN

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Tropical resolutions of configuration hypersurfaces

Daniel Bath, Graham Denham, Mathias Schulze, Uli Walther

Any irreducible configuration hypersurface has its singularities resolved by normalizing the Nash blow-up and then taking a tropical compactification.

arxiv:2605.04252 v2 · 2026-05-05 · math.AG · math-ph · math.AC · math.MP

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Claims

C1strongest claim

We provide a two-step recipe for a resolution of singularities of any irreducible configuration hypersurface. We first consider the normalization of the Nash blow-up, which we identify with an incidence variety introduced by Bloch. ... The latter then a smooth, tropical compactification, using work of Tevelev.

C2weakest assumption

The configuration hypersurface is irreducible; the normalization of the Nash blow-up coincides with Bloch's incidence variety; Tevelev's tropical compactification theorem applies directly to the closure of the smooth torus subvariety; the bipermutohedral matroid combinatorics of Ardila-Denham-Huh yields an explicit smooth model.

C3one line summary

A explicit two-step resolution of singularities for configuration hypersurfaces is constructed via normalized Nash blow-ups identified with Bloch incidence varieties followed by smooth tropical compactifications using bipermutohedral matroid combinatorics.

Receipt and verification

First computed	2026-06-01T01:02:41.514452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55e9884fe1c1a1720d6721053c319e6b5b876203a9df199f767a2c34a9df23d0

Aliases

arxiv: 2605.04252 · arxiv_version: 2605.04252v2 · doi: 10.48550/arxiv.2605.04252 · pith_short_12: KXUYQT7BYGQX · pith_short_16: KXUYQT7BYGQXEDLH · pith_short_8: KXUYQT7B

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KXUYQT7BYGQXEDLHEECTYMM6NN \
  | 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: 55e9884fe1c1a1720d6721053c319e6b5b876203a9df199f767a2c34a9df23d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b71410fab23b5cb22cb28acef2df90e736d4d27ecd028637adfbdb9fe783b86",
    "cross_cats_sorted": [
      "math-ph",
      "math.AC",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-05T19:37:09Z",
    "title_canon_sha256": "dababa5a5742f38b5badc2701720d58f2ddfa1af58ec34cc37abab6cd5fd4fc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04252",
    "kind": "arxiv",
    "version": 2
  }
}