Pith Number

pith:MPWVKNFW

pith:2011:MPWVKNFWCMORG66UK3T2N3WGOV

not attested not anchored not stored refs pending

On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking Ricci solitons

Akito Futaki, Haizhong Li, Xiang-Dong Li

arxiv:1111.6364 v4 · 2011-11-28 · 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{MPWVKNFWCMORG66UK3T2N3WGOV}

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	2026-05-18T04:01:25.808085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63ed5534b6131d137bd456e7a6eec6756186f0ef771b64ce0824e7b932b7f00d

Aliases

arxiv: 1111.6364 · arxiv_version: 1111.6364v4 · doi: 10.48550/arxiv.1111.6364 · pith_short_12: MPWVKNFWCMOR · pith_short_16: MPWVKNFWCMORG66U · pith_short_8: MPWVKNFW

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/MPWVKNFWCMORG66UK3T2N3WGOV \
  | 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: 63ed5534b6131d137bd456e7a6eec6756186f0ef771b64ce0824e7b932b7f00d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81c7ef7f6d2dfe3bf741e59a9bbf719f4ee5d694be0398c63129096fce7fc17a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-28T08:19:58Z",
    "title_canon_sha256": "03bd427c1c0445795f8149e1c3c286cf3059fa98d55d22ec714e82d97a2d6383"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6364",
    "kind": "arxiv",
    "version": 4
  }
}