Pith Number

pith:6NLSL7EB

pith:2026:6NLSL7EBDR2JFQADERXZSPSCMF

not attested not anchored not stored refs pending

An irreducible real projective plane in the 4-sphere

Gheehyun Nahm, Maggie Miller, Mark Hughes, Seungwon Kim

An irreducible embedded projective plane is constructed in S^4, countering the Kinoshita conjecture via a peripheral map with kernel of order 2.

arxiv:2605.12921 v1 · 2026-05-13 · math.GT

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\usepackage{pith}
\pithnumber{6NLSL7EBDR2JFQADERXZSPSCMF}

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Record completeness

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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

We construct an irreducible embedded projective plane in S^4. This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list.

C2weakest assumption

The construction assumes that a specific handlebody or embedding in 4D can be arranged so the peripheral map from the boundary of the tubular neighborhood to the complement has kernel precisely of order 2, which is used to establish irreducibility.

C3one line summary

An irreducible embedded projective plane is constructed in S^4, countering the Kinoshita conjecture via a peripheral map with kernel of order 2.

Receipt and verification

First computed	2026-05-18T03:09:10.218945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f35725fc811c7492c003246f993e4261770db741b88e4d2f5f6ad761195c1433

Aliases

arxiv: 2605.12921 · arxiv_version: 2605.12921v1 · doi: 10.48550/arxiv.2605.12921 · pith_short_12: 6NLSL7EBDR2J · pith_short_16: 6NLSL7EBDR2JFQAD · pith_short_8: 6NLSL7EB

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/6NLSL7EBDR2JFQADERXZSPSCMF \
  | 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: f35725fc811c7492c003246f993e4261770db741b88e4d2f5f6ad761195c1433

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "653586dc2732e9fa58bc6e66150c57ed4266660d7463dfb57cd74d0f0fa61a79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T02:56:46Z",
    "title_canon_sha256": "c3c0c44589cebd87931959a60da9a3a88e45d9307ac2028b67e31c840d80b3ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12921",
    "kind": "arxiv",
    "version": 1
  }
}