Pith Number

pith:5ZVZ3LDS

pith:2011:5ZVZ3LDSLPHNFBXJICA7U44F3T

not attested not anchored not stored refs pending

Measure Estimates, Harnack Inequalities and Ricci Lower Bound

Xiangwen Zhang, Yu Wang

arxiv:1102.5567 v2 · 2011-02-28 · math.AP · 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{5ZVZ3LDSLPHNFBXJICA7U44F3T}

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	2026-05-18T04:24:43.564284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee6b9dac725bced286e94081fa7385dcde5537c7b60abe44b10b73282b28675d

Aliases

arxiv: 1102.5567 · arxiv_version: 1102.5567v2 · doi: 10.48550/arxiv.1102.5567 · pith_short_12: 5ZVZ3LDSLPHN · pith_short_16: 5ZVZ3LDSLPHNFBXJ · pith_short_8: 5ZVZ3LDS

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/5ZVZ3LDSLPHNFBXJICA7U44F3T \
  | 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: ee6b9dac725bced286e94081fa7385dcde5537c7b60abe44b10b73282b28675d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "684cb0d250f5df28aa6560f8907132d57907ad41e15720cc638cc89c29ae6256",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-02-28T01:15:30Z",
    "title_canon_sha256": "3263484891d6d18dbbf1f4f85b78390c6be3de1749814136fde4da0a1d7bff69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5567",
    "kind": "arxiv",
    "version": 2
  }
}