Pith Number

pith:IDSKE76J

pith:2026:IDSKE76JBT27R7PHDKJON3KN2R

not attested not anchored not stored refs pending

Highly connected non-formal Milnor fibers via polyhedral products

Alexander I. Suciu

Milnor fibers of weighted-homogeneous polynomials can be made arbitrarily highly connected while remaining non-formal.

arxiv:2605.09254 v2 · 2026-05-10 · math.AT · math.AG · math.CO

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Record completeness

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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

the realization theorem of Fernández de Bobadilla, which identifies the Milnor fiber of a weighted-homogeneous polynomial with the complement of a germ of analytic set, can be combined with the systematic Massey product constructions of Grbić-Linton for moment-angle complexes Z_K = Z_K(D^2, S^1) to produce weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.

C2weakest assumption

That the Grbić-Linton Massey product constructions on moment-angle complexes can be transferred via the Fernández de Bobadilla realization theorem without destroying the non-formality or reducing the connectivity of the resulting Milnor fiber.

C3one line summary

Combining a realization theorem for Milnor fibers with arbitrary n-fold Massey product constructions in polyhedral products yields weighted-homogeneous polynomials whose Milnor fibers are arbitrarily highly connected and non-formal.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-19T16:12:20.582047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40e4a27fc90cf5f8fde71a92e6ed4dd468dc982aae37d308186319590ff2c562

Aliases

arxiv: 2605.09254 · arxiv_version: 2605.09254v2 · doi: 10.48550/arxiv.2605.09254 · pith_short_12: IDSKE76JBT27 · pith_short_16: IDSKE76JBT27R7PH · pith_short_8: IDSKE76J

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/IDSKE76JBT27R7PHDKJON3KN2R \
  | 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: 40e4a27fc90cf5f8fde71a92e6ed4dd468dc982aae37d308186319590ff2c562

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a6c849a3415a6c3fef1aa8bae34361a36e169b94f1d837d949d2bf0c07ee314",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-05-10T01:48:37Z",
    "title_canon_sha256": "163d205660fb82b62f1308fac7d5c38ef8f3a1c6df045fbede2ebe8d16ea8d75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09254",
    "kind": "arxiv",
    "version": 2
  }
}