Pith Number

pith:AP756RWU

pith:2014:AP756RWUHXULD2DCG2FOLLTS7X

not attested not anchored not stored refs pending

Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions

Naotaka Kajino, Sebastian Andres

arxiv:1407.3240 v4 · 2014-07-11 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AP756RWUHXULD2DCG2FOLLTS7X}

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	2026-05-18T01:31:19.122529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ffdf46d43de8b1e862368ae5ae72fdc27e409251066de1fea902403fa1fdd3

Aliases

arxiv: 1407.3240 · arxiv_version: 1407.3240v4 · doi: 10.48550/arxiv.1407.3240 · pith_short_12: AP756RWUHXUL · pith_short_16: AP756RWUHXULD2DC · pith_short_8: AP756RWU

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/AP756RWUHXULD2DCG2FOLLTS7X \
  | 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: 03ffdf46d43de8b1e862368ae5ae72fdc27e409251066de1fea902403fa1fdd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04f53a13aaef9908695e43b7c228a3e790d46a5e6129bc66c039a93651ab7fc8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-07-11T18:17:58Z",
    "title_canon_sha256": "f7e2dcb9eac6ad5e0b3e761cc4aeec32b3f0fb7e742ce91f2b167adf10908733"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3240",
    "kind": "arxiv",
    "version": 4
  }
}