Pith Number

pith:F3FKR2Y2

pith:2014:F3FKR2Y2LBSVP3WNIZBR3QUS2P

not attested not anchored not stored refs pending

Liouville heat kernel: regularity and bounds

Ofer Zeitouni, Pascal Maillard, R\'emi Rhodes, Vincent Vargas

arxiv:1406.0491 v4 · 2014-06-02 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F3FKR2Y2LBSVP3WNIZBR3QUS2P}

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	2026-05-18T00:12:57.318338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ecaa8eb1a586557eecd46431dc292d3d473ea7d18a4c9a53c8bd8471e39e83d

Aliases

arxiv: 1406.0491 · arxiv_version: 1406.0491v4 · doi: 10.48550/arxiv.1406.0491 · pith_short_12: F3FKR2Y2LBSV · pith_short_16: F3FKR2Y2LBSVP3WN · pith_short_8: F3FKR2Y2

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/F3FKR2Y2LBSVP3WNIZBR3QUS2P \
  | 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: 2ecaa8eb1a586557eecd46431dc292d3d473ea7d18a4c9a53c8bd8471e39e83d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c7c654d2dcfc97ff314f2930da81b59b8e9f646309df5da6d61a1f97854738c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-06-02T19:42:50Z",
    "title_canon_sha256": "c410c20a642c4d108425fa9711bb95ac43ac31a43f7bd67060a737e9c009c7e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.0491",
    "kind": "arxiv",
    "version": 4
  }
}