Pith Number

pith:F6ERCMKG

pith:2013:F6ERCMKGQE7STU76G25HPHZ5TA

not attested not anchored not stored refs pending

Non ultracontractive heat kernel bounds by Lyapunov conditions

Arnaud Guillin, Fran\c{c}ois Bolley (CEREMADE), Xinyu Wang

arxiv:1311.2221 v2 · 2013-11-09 · math.FA · 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{F6ERCMKGQE7STU76G25HPHZ5TA}

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	2026-05-18T02:46:32.804556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f89113146813f29d3fe36ba779f3d98352b94e1b1814c03f0044893ff661a24

Aliases

arxiv: 1311.2221 · arxiv_version: 1311.2221v2 · doi: 10.48550/arxiv.1311.2221 · pith_short_12: F6ERCMKGQE7S · pith_short_16: F6ERCMKGQE7STU76 · pith_short_8: F6ERCMKG

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/F6ERCMKGQE7STU76G25HPHZ5TA \
  | 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: 2f89113146813f29d3fe36ba779f3d98352b94e1b1814c03f0044893ff661a24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0138c5b7423c9cb70338f8bd937d76a64b879d8acd0839d29ca012d331e453ad",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-09T21:34:52Z",
    "title_canon_sha256": "7009263aad5fc3a6cf9031c4d7f5358e46ad6f842db3e71155f047fb88ca5942"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2221",
    "kind": "arxiv",
    "version": 2
  }
}