Pith Number

pith:OBQLQN4U

pith:2019:OBQLQN4UNDY7JWVWKAHJNJWHS4

not attested not anchored not stored refs pending

Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schr\"odinger operators

Kamil Kaleta, Ren\'e L. Schilling

arxiv:1903.12004 v1 · 2019-03-28 · math.PR · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBQLQN4UNDY7JWVWKAHJNJWHS4}

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	2026-05-17T23:49:58.402957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7060b8379468f1f4dab6500e96a6c7973ade0a4228501333ae154f9435eb74a8

Aliases

arxiv: 1903.12004 · arxiv_version: 1903.12004v1 · doi: 10.48550/arxiv.1903.12004 · pith_short_12: OBQLQN4UNDY7 · pith_short_16: OBQLQN4UNDY7JWVW · pith_short_8: OBQLQN4U

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/OBQLQN4UNDY7JWVWKAHJNJWHS4 \
  | 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: 7060b8379468f1f4dab6500e96a6c7973ade0a4228501333ae154f9435eb74a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e275dab32c7aab2540dfceef3372e1cbaa241d746f42e68c80740f8bc355acf",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-28T14:27:25Z",
    "title_canon_sha256": "7443ab65ea4f6915775aab25958d46cdff32f109fe679b5dffa524450f4dd7e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.12004",
    "kind": "arxiv",
    "version": 1
  }
}