Pith Number

pith:4MUT6WQD

pith:2010:4MUT6WQDC22FCX2WASOFXHANPO

not attested not anchored not stored refs pending

Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data

A. Grigor'yan, K. Kirsten, M. van den Berg, P. Gilkey

arxiv:1011.1726 v2 · 2010-11-08 · math.SP · 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{4MUT6WQDC22FCX2WASOFXHANPO}

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	2026-05-18T04:20:51.078164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3293f5a0316b4515f56049c5b9c0d7bb62221e5c83dd578fa4d3b914926f010

Aliases

arxiv: 1011.1726 · arxiv_version: 1011.1726v2 · doi: 10.48550/arxiv.1011.1726 · pith_short_12: 4MUT6WQDC22F · pith_short_16: 4MUT6WQDC22FCX2W · pith_short_8: 4MUT6WQD

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/4MUT6WQDC22FCX2WASOFXHANPO \
  | 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: e3293f5a0316b4515f56049c5b9c0d7bb62221e5c83dd578fa4d3b914926f010

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5787b874ce86a9f7601d5d7a54dda40160d990a38f907759ebb4f1d58af75c4e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-11-08T08:26:39Z",
    "title_canon_sha256": "f1282efb60fda767b28d3efa8feb6a4d56b2be9c64a783c7d0d02402555a8139"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1726",
    "kind": "arxiv",
    "version": 2
  }
}