Pith Number

pith:6PKKESSH

pith:2017:6PKKESSHNQV5XXCA7TFLDQUUW4

not attested not anchored not stored refs pending

Sharp Gaussian estimates for heat kernels of Schr\"odinger operators

Jacek Dziuba\'nski, Karol Szczypkowski, Krzysztof Bogdan

arxiv:1706.06172 v2 · 2017-06-19 · 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{6PKKESSHNQV5XXCA7TFLDQUUW4}

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	2026-05-18T00:08:05.204583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3d4a24a476c2bdbdc40fccab1c294b7265d8a1b296da2158552bd33b600c0e5

Aliases

arxiv: 1706.06172 · arxiv_version: 1706.06172v2 · doi: 10.48550/arxiv.1706.06172 · pith_short_12: 6PKKESSHNQV5 · pith_short_16: 6PKKESSHNQV5XXCA · pith_short_8: 6PKKESSH

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/6PKKESSHNQV5XXCA7TFLDQUUW4 \
  | 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: f3d4a24a476c2bdbdc40fccab1c294b7265d8a1b296da2158552bd33b600c0e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cb5cf0a67c2ac5c633904867f402ecd86068f7ba1cd229cc6f38903580daabb",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-06-19T20:49:43Z",
    "title_canon_sha256": "be4f94fe3f3d2c13a6bb7f2ff55273bea2cb27793310407de2a7e4b530d7dbe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.06172",
    "kind": "arxiv",
    "version": 2
  }
}