Pith Number

pith:UQ6BZ5U6

pith:2012:UQ6BZ5U6TW44M3AZCH7XWTHAYX

not attested not anchored not stored refs pending

Harnack inequality for nondivergent parabolic operators on Riemannian manifolds

Ki-Ahm Lee, Seick Kim, Soojung Kim

arxiv:1209.4423 v2 · 2012-09-20 · 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{UQ6BZ5U6TW44M3AZCH7XWTHAYX}

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	2026-05-18T02:23:35.753417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a43c1cf69e9db9c66c1911ff7b4ce0c5feddcc975b6f437728e82768242f0d50

Aliases

arxiv: 1209.4423 · arxiv_version: 1209.4423v2 · doi: 10.48550/arxiv.1209.4423 · pith_short_12: UQ6BZ5U6TW44 · pith_short_16: UQ6BZ5U6TW44M3AZ · pith_short_8: UQ6BZ5U6

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/UQ6BZ5U6TW44M3AZCH7XWTHAYX \
  | 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: a43c1cf69e9db9c66c1911ff7b4ce0c5feddcc975b6f437728e82768242f0d50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1317c537a49663aa33a630e4a36f2d85513dd03bb25bd2142ce9249ef25c63c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-20T04:39:40Z",
    "title_canon_sha256": "ea43d76c8e749d1d72a6d50ade2f4f2e41419215a4843803458027cecdf8e149"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4423",
    "kind": "arxiv",
    "version": 2
  }
}