Pith Number

pith:UYNC4NJT

pith:2011:UYNC4NJTBIT5JI3HVMFNGHAMME

not attested not anchored not stored refs pending

Neumann eigenvalue sums on triangles are (mostly) minimal for equilaterals

R. S. Laugesen, S. S. Son, Z. C. Pan

arxiv:1102.0071 v1 · 2011-02-01 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UYNC4NJTBIT5JI3HVMFNGHAMME}

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	2026-05-18T04:30:13.275461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a61a2e35330a27d4a367ab0ad31c0c61348dcf4f02c7deb5a8c06f0e39479674

Aliases

arxiv: 1102.0071 · arxiv_version: 1102.0071v1 · doi: 10.48550/arxiv.1102.0071 · pith_short_12: UYNC4NJTBIT5 · pith_short_16: UYNC4NJTBIT5JI3H · pith_short_8: UYNC4NJT

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/UYNC4NJTBIT5JI3HVMFNGHAMME \
  | 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: a61a2e35330a27d4a367ab0ad31c0c61348dcf4f02c7deb5a8c06f0e39479674

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9c923c181d3dfeb73f07d8a313797d40751fc67ef61b068217914e4673d698f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-02-01T03:35:54Z",
    "title_canon_sha256": "02ffa61eda9e587de61c1f6760951037b435c922b58b24cffc1f7c9251c94d84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0071",
    "kind": "arxiv",
    "version": 1
  }
}