Pith Number

pith:U2G2VQYN

pith:2015:U2G2VQYNM2J3YJ5DFEKBUQJGSC

not attested not anchored not stored refs pending

Sharp Gaussian estimates for Schr\"odinger heat kernels: $L^p$ integrability conditions

Jacek Dziuba\'nski, Karol Szczypkowski, Krzysztof Bogdan

arxiv:1511.07167 v3 · 2015-11-23 · 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{U2G2VQYNM2J3YJ5DFEKBUQJGSC}

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	2026-05-18T01:04:57.752574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68daac30d6693bc27a329141a412690bfbcdbf28513d08d4ebd39bb5a613242

Aliases

arxiv: 1511.07167 · arxiv_version: 1511.07167v3 · doi: 10.48550/arxiv.1511.07167 · pith_short_12: U2G2VQYNM2J3 · pith_short_16: U2G2VQYNM2J3YJ5D · pith_short_8: U2G2VQYN

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/U2G2VQYNM2J3YJ5DFEKBUQJGSC \
  | 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: a68daac30d6693bc27a329141a412690bfbcdbf28513d08d4ebd39bb5a613242

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "196214edf1c05b52d90449895cd3f2949e5d7de644d9effdcf4dce588b51b634",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-11-23T10:36:35Z",
    "title_canon_sha256": "d42a502e57c9be5e5b377f265abbbc761160f7acadf32e82d93fd2c9ed4167eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07167",
    "kind": "arxiv",
    "version": 3
  }
}