Pith Number

pith:XLG7B7RF

pith:2011:XLG7B7RFBICNM6THI3CPLE45R7

not attested not anchored not stored refs pending

General estimate of the first eigenvalue on manifolds

Mu-Fa chen

arxiv:1111.6663 v1 · 2011-11-29 · math.PR · math.DG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XLG7B7RFBICNM6THI3CPLE45R7}

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	2026-05-18T04:07:28.797170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bacdf0fe250a04d67a6746c4f5939d8fc6adb76bb1388366646b8eccb2329949

Aliases

arxiv: 1111.6663 · arxiv_version: 1111.6663v1 · doi: 10.48550/arxiv.1111.6663 · pith_short_12: XLG7B7RFBICN · pith_short_16: XLG7B7RFBICNM6TH · pith_short_8: XLG7B7RF

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/XLG7B7RFBICNM6THI3CPLE45R7 \
  | 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: bacdf0fe250a04d67a6746c4f5939d8fc6adb76bb1388366646b8eccb2329949

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d9ca48f3b7ab1f02193d6b056daf003ab14013624eee8a9d541bc1ca79cabc",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-29T01:49:08Z",
    "title_canon_sha256": "5a0834480eb34098d995d78e5115a620c998d6f647e7f5cf42ec25d478885714"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6663",
    "kind": "arxiv",
    "version": 1
  }
}