Pith Number

pith:3NZIGKZP

pith:2010:3NZIGKZPA44L4OXUW3SVKV5FYQ

not attested not anchored not stored refs pending

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Jia-Yong Wu

arxiv:1010.4175 v5 · 2010-10-20 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NZIGKZPA44L4OXUW3SVKV5FYQ}

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	2026-05-18T03:48:23.595098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db72832b2f0738be3af4b6e55557a5c43b5cedca8e3a1cbdabc627fc76e27a28

Aliases

arxiv: 1010.4175 · arxiv_version: 1010.4175v5 · doi: 10.48550/arxiv.1010.4175 · pith_short_12: 3NZIGKZPA44L · pith_short_16: 3NZIGKZPA44L4OXU · pith_short_8: 3NZIGKZP

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/3NZIGKZPA44L4OXUW3SVKV5FYQ \
  | 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: db72832b2f0738be3af4b6e55557a5c43b5cedca8e3a1cbdabc627fc76e27a28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b2e70182876b3a89c079b56fdd045c6995fcca9b23ddf5c6e7db57e5b718e21",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-10-20T12:14:40Z",
    "title_canon_sha256": "97d69a0371e1ef8136ab1df1dd3d576535abfcd6f757d94bb0bafe8dfa1ef48e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4175",
    "kind": "arxiv",
    "version": 5
  }
}