Pith Number

pith:WPP4ACFT

pith:2018:WPP4ACFTD7HPPLNZS7VIJ54FMZ

not attested not anchored not stored refs pending

Critical domains for the first nonzero Neumann eigenvalue in Riemannian manifolds

Mouhamed Moustapha Fall, Tobias Weth

arxiv:1803.07592 v1 · 2018-03-20 · math.AP · 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{WPP4ACFTD7HPPLNZS7VIJ54FMZ}

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	2026-05-18T00:20:29.484042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3dfc008b31fcef7adb997ea84f785664be381748928e9c6f02d305f7ed64375

Aliases

arxiv: 1803.07592 · arxiv_version: 1803.07592v1 · doi: 10.48550/arxiv.1803.07592 · pith_short_12: WPP4ACFTD7HP · pith_short_16: WPP4ACFTD7HPPLNZ · pith_short_8: WPP4ACFT

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/WPP4ACFTD7HPPLNZS7VIJ54FMZ \
  | 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: b3dfc008b31fcef7adb997ea84f785664be381748928e9c6f02d305f7ed64375

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9bdac412fbf5f2f0a568c57a107735c77e035db8476ccc525e36b219adc6a5f",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-03-20T18:27:40Z",
    "title_canon_sha256": "7ebc1bbf1326aa9a5b32a8250c76519effab7b770e014c18f2f91d0da4091f99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.07592",
    "kind": "arxiv",
    "version": 1
  }
}