Pith Number

pith:2D7YBW4U

pith:2000:2D7YBW4UT44ILNULVGP2M5MFZD

not attested not anchored not stored refs pending

A Sharp Bound for the Ratio of the First Two Dirichlet Eigenvalues of a Domain in a Hemisphere of S^n

Mark S. Ashbaugh, Rafael D. Benguria

arxiv:math/0008088 v1 · 2000-08-11 · math.SP · 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{2D7YBW4UT44ILNULVGP2M5MFZD}

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	2026-05-18T01:05:38.389784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0ff80db949f3885b68ba99fa67585c8d55051fb5b7911dd4c1518149f06f6ae

Aliases

arxiv: math/0008088 · arxiv_version: math/0008088v1 · doi: 10.48550/arxiv.math/0008088 · pith_short_12: 2D7YBW4UT44I · pith_short_16: 2D7YBW4UT44ILNUL · pith_short_8: 2D7YBW4U

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/2D7YBW4UT44ILNULVGP2M5MFZD \
  | 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: d0ff80db949f3885b68ba99fa67585c8d55051fb5b7911dd4c1518149f06f6ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b43af4980643103d1c361feab4364e0ee68ad11e92cf7aeb09f2794bcc16d86",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2000-08-11T20:45:10Z",
    "title_canon_sha256": "2791ba79a13504035f74e4834fa926e3cc47ee93325659f730c2d7590ecad809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008088",
    "kind": "arxiv",
    "version": 1
  }
}