Pith Number

pith:HDH7BUX3

pith:2011:HDH7BUX3UTV3HENJFKJQVY3SRT

not attested not anchored not stored refs pending

Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature

Daniele Valtorta

arxiv:1102.0539 v8 · 2011-02-02 · math.DG · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HDH7BUX3UTV3HENJFKJQVY3SRT}

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	2026-05-18T03:03:10.509606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888

Aliases

arxiv: 1102.0539 · arxiv_version: 1102.0539v8 · doi: 10.48550/arxiv.1102.0539 · pith_short_12: HDH7BUX3UTV3 · pith_short_16: HDH7BUX3UTV3HENJ · pith_short_8: HDH7BUX3

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/HDH7BUX3UTV3HENJFKJQVY3SRT \
  | 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: 38cff0d2fba4ebb391a92a930ae3728cc11b878837effa2d7f8a846b5ce1a888

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "711d14032bfac81d5b427ba5353966705112e228a5063cac0e407d08670d2aef",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-02-02T19:58:17Z",
    "title_canon_sha256": "b6b50521f1adcc9f67a389288b26d0bc7d0c3f3b896ba904780cc0bdce858275"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0539",
    "kind": "arxiv",
    "version": 8
  }
}