Pith Number

pith:PWWEKOUP

pith:2013:PWWEKOUPUAPMOHHA5WWGXV3L7Y

not attested not anchored not stored refs pending

Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators

Gerd Grubb, Heiko Gimperlein

arxiv:1302.6529 v4 · 2013-02-26 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PWWEKOUPUAPMOHHA5WWGXV3L7Y}

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	2026-05-18T02:38:46.328227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dac453a8fa01ec71ce0edac6bd76bfe02820f1ee73f84c4d90831b6f64465df

Aliases

arxiv: 1302.6529 · arxiv_version: 1302.6529v4 · doi: 10.48550/arxiv.1302.6529 · pith_short_12: PWWEKOUPUAPM · pith_short_16: PWWEKOUPUAPMOHHA · pith_short_8: PWWEKOUP

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/PWWEKOUPUAPMOHHA5WWGXV3L7Y \
  | 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: 7dac453a8fa01ec71ce0edac6bd76bfe02820f1ee73f84c4d90831b6f64465df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f969eae99a2959ead20a237cd10f911c6a5e68bf4cf318f50e13bde948ab99e2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-02-26T18:40:28Z",
    "title_canon_sha256": "b8573d12a76a009d7e850b483b35691e4534d367345cb3dc5fd7a4a7b99937ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.6529",
    "kind": "arxiv",
    "version": 4
  }
}