Pith Number

pith:IPKTHNGO

pith:2012:IPKTHNGO36ZDF6RQE67476AEQE

not attested not anchored not stored refs pending

Discrete/Continuous Elliptic Harnack Inequality and Kernel Estimates for Functions of the Laplacian on a Graph

Laurent Saloff-Coste, Mark Cerenzia

arxiv:1212.4332 v1 · 2012-12-18 · math.PR · 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{IPKTHNGO36ZDF6RQE67476AEQE}

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	2026-05-18T01:37:47.708037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43d533b4cedfb232fa3027bfcff8048136b55d9b521dee61d7a28a87b01d3770

Aliases

arxiv: 1212.4332 · arxiv_version: 1212.4332v1 · doi: 10.48550/arxiv.1212.4332 · pith_short_12: IPKTHNGO36ZD · pith_short_16: IPKTHNGO36ZDF6RQ · pith_short_8: IPKTHNGO

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/IPKTHNGO36ZDF6RQE67476AEQE \
  | 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: 43d533b4cedfb232fa3027bfcff8048136b55d9b521dee61d7a28a87b01d3770

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a541e52a95e01a5032ed95cf66a83d92e47f8a6c42c060503dd17b5d6513001",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-18T12:37:48Z",
    "title_canon_sha256": "98861702fedbccf085a6f4f40d23112c779ed9ce277b0687d7dc88916c544ee3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4332",
    "kind": "arxiv",
    "version": 1
  }
}