Pith Number

pith:PWZF7DWQ

pith:2026:PWZF7DWQKCTEL3EGIVVFIXZEV4

not attested not anchored not stored refs resolved

Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal

Shun Maeta

Any biharmonic simple rotational surface in four-dimensional Euclidean space is minimal.

arxiv:2605.09587 v2 · 2026-05-10 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PWZF7DWQKCTEL3EGIVVFIXZEV4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

Any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal.

C2weakest assumption

The surface is assumed to be a simple rotational surface whose profile curve lies in a fixed 2-plane, allowing the biharmonic equation to reduce cleanly to an ODE system without additional curvature or torsion terms.

C3one line summary

Biharmonic simple rotational surfaces in R^4 are minimal.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] K. Akutagawa and S. Maeta,Biharmonic properly immersed submanifolds in Euclidean spaces, Geom. Dedicata164(2013), 351–355 2013

[2] Brendle,Rotational symmetry of self-similar solutions to the Ricci flow, Invent 2013

[3] R. Caddeo, S. Montaldo, C. Oniciuc and P. Piu,Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor, Ann. Mat. Pura Appl. (4)193(2014), no. 2, 529–550. 16 SHUN MAETA 2014

[4] Chen,Some open problems and conjectures on submanifolds of finite type, Michigan State University, (1988 version) 1988

[5] Chen,Chen’s biharmonic conjecture and submanifolds with parallel nor- malized mean curvature vector, Mathematics7(2019), no 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:41.991883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db25f8ed050a645ec86456a545f24af3c899d5a13a8592217d3c26ac8356577

Aliases

arxiv: 2605.09587 · arxiv_version: 2605.09587v2 · doi: 10.48550/arxiv.2605.09587 · pith_short_12: PWZF7DWQKCTE · pith_short_16: PWZF7DWQKCTEL3EG · pith_short_8: PWZF7DWQ

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/PWZF7DWQKCTEL3EGIVVFIXZEV4 \
  | 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: 7db25f8ed050a645ec86456a545f24af3c899d5a13a8592217d3c26ac8356577

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c919e4df64d37aa066c544bdcb43446f9a3af9ddcaf182b71f2bd4340e0867be",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-10T14:58:36Z",
    "title_canon_sha256": "3715cc5a16093d905e548f996545ffa593b86c46cf2c6f865227b9d670972dcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09587",
    "kind": "arxiv",
    "version": 2
  }
}