Pith Number

pith:MGN3QJPP

pith:2017:MGN3QJPP5CMDLULU7BKRFWJ5IA

not attested not anchored not stored refs pending

An upper bound for the smallest area of a minimal surface in manifolds of dimension four

Nan Wu, Zhifei Zhu

arxiv:1702.07034 v2 · 2017-02-22 · 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{MGN3QJPP5CMDLULU7BKRFWJ5IA}

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.

Receipt and verification

First computed	2026-05-18T00:30:05.527796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

619bb825efe89835d174f85512d93d402a1f74d5ad074e8605345e086cba1edd

Aliases

arxiv: 1702.07034 · arxiv_version: 1702.07034v2 · doi: 10.48550/arxiv.1702.07034 · pith_short_12: MGN3QJPP5CMD · pith_short_16: MGN3QJPP5CMDLULU · pith_short_8: MGN3QJPP

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/MGN3QJPP5CMDLULU7BKRFWJ5IA \
  | 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: 619bb825efe89835d174f85512d93d402a1f74d5ad074e8605345e086cba1edd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba5b52993d57f3c9c72716f7945f517c8e7cd86cedc10144581e9ca9c64b2c90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-02-22T22:53:33Z",
    "title_canon_sha256": "3c18ffcd9d180bb7152869cb55a3d890244c278cb5550ee70474926e4f948971"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.07034",
    "kind": "arxiv",
    "version": 2
  }
}