Pith Number

pith:PENZFFWA

pith:2015:PENZFFWAOTFECYIHADHW7J4A3G

not attested not anchored not stored refs pending

A remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator

Laurent Kayser (IECL), Mourad Choulli (IECL)

arxiv:1503.04529 v2 · 2015-03-16 · 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{PENZFFWAOTFECYIHADHW7J4A3G}

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	2026-05-18T01:32:18.743161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

791b9296c074ca41610700cf6fa780d98087b53d1bfbff546a8834ef9459b8f8

Aliases

arxiv: 1503.04529 · arxiv_version: 1503.04529v2 · doi: 10.48550/arxiv.1503.04529 · pith_short_12: PENZFFWAOTFE · pith_short_16: PENZFFWAOTFECYIH · pith_short_8: PENZFFWA

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/PENZFFWAOTFECYIHADHW7J4A3G \
  | 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: 791b9296c074ca41610700cf6fa780d98087b53d1bfbff546a8834ef9459b8f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73dbc6957c9e9a6747aca405c5b5317c8a6b14677d1c334bc237c8d1b92e11e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-16T05:52:16Z",
    "title_canon_sha256": "137349c96d5e05fc6d8989e5e6031e479cef4909d219e6d69a6ba1c8526f0d01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04529",
    "kind": "arxiv",
    "version": 2
  }
}