Pith Number

pith:3Q32SYEI

pith:2026:3Q32SYEIY5BQVDF7CJ4KXWDQ57

not attested not anchored not stored refs pending

Exotic Surfaces in 4-manifolds and Surface Corks

Cindy Zhang

A contractible 4-ball acts as a surface cork that changes the smooth structure of certain exotic embedded surfaces while preserving their homeomorphism type.

arxiv:2604.27545 v2 · 2026-04-30 · math.GT

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\usepackage{pith}
\pithnumber{3Q32SYEIY5BQVDF7CJ4KXWDQ57}

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Record completeness

1 Bitcoin timestamp

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 the first example of a surface cork for certain exotic families constructed from Fintushel and Stern's rim surgery. In particular, this surface cork turns out to be diffeomorphic to a 4-ball.

C2weakest assumption

That the specific rim-surgery families produce pairs (X, F) whose diffeomorphism type is altered by the boundary diffeomorphism of the surface cork while the homeomorphism type remains unchanged, and that the intersection of the cork with F is controllable in the required sense.

C3one line summary

The first surface cork, diffeomorphic to the 4-ball, is constructed to detect exotic smooth structures on embedded surfaces in 4-manifolds produced by rim surgery.

Receipt and verification

First computed	2026-05-27T01:04:58.580838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc37a96088c7430a8cbf1278abd870efdef1014a1702a00b5dd093d62fded4c9

Aliases

arxiv: 2604.27545 · arxiv_version: 2604.27545v2 · doi: 10.48550/arxiv.2604.27545 · pith_short_12: 3Q32SYEIY5BQ · pith_short_16: 3Q32SYEIY5BQVDF7 · pith_short_8: 3Q32SYEI

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/3Q32SYEIY5BQVDF7CJ4KXWDQ57 \
  | 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: dc37a96088c7430a8cbf1278abd870efdef1014a1702a00b5dd093d62fded4c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf3f61cd8aabd5fd486f962f00ce676a608723518bee39ad49977aa6ea322f84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-04-30T07:51:49Z",
    "title_canon_sha256": "5f86180d55995c35021be26fcba299c85f6f8c271f74d449c759eb1844395ec1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27545",
    "kind": "arxiv",
    "version": 2
  }
}