Pith Number

pith:U3QAPQPI

pith:2017:U3QAPQPIX6MIJT5EXGDKILXASE

not attested not anchored not stored refs pending

Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

Longjie Xie, Renming Song, Yingchao Xie

arxiv:1712.07565 v1 · 2017-12-20 · math.PR · 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{U3QAPQPIX6MIJT5EXGDKILXASE}

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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	2026-05-18T00:27:34.204771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6e007c1e8bf9884cfa4b986a42ee0913e1ecf0c507a6f260e7d804f0607dd55

Aliases

arxiv: 1712.07565 · arxiv_version: 1712.07565v1 · doi: 10.48550/arxiv.1712.07565 · pith_short_12: U3QAPQPIX6MI · pith_short_16: U3QAPQPIX6MIJT5E · pith_short_8: U3QAPQPI

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/U3QAPQPIX6MIJT5EXGDKILXASE \
  | 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: a6e007c1e8bf9884cfa4b986a42ee0913e1ecf0c507a6f260e7d804f0607dd55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e89f5c1cd7043dfe7851bf72c55d33dd4bb5d3c0777904be924e02cbc86fd19",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-12-20T16:37:20Z",
    "title_canon_sha256": "d8eb1585cfd95066e14057142c98c9bbbf1883e31d97054bfd357bc62662e871"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07565",
    "kind": "arxiv",
    "version": 1
  }
}