Pith Number

pith:6HUYVZF2

pith:2022:6HUYVZF25IO2FIWXTGVLAZKWSW

not attested not anchored not stored refs pending

Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

Qiuyu Ren, Zhongkai Tao

arxiv:2212.05394 v3 · 2022-12-11 · math.SP · math.AP · 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{6HUYVZF25IO2FIWXTGVLAZKWSW}

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	2026-07-05T05:38:10.449895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1e98ae4baea1da2a2d799aab06556959249abaf61095997f7f5cb42f74f2e77

Aliases

arxiv: 2212.05394 · arxiv_version: 2212.05394v3 · doi: 10.48550/arxiv.2212.05394 · pith_short_12: 6HUYVZF25IO2 · pith_short_16: 6HUYVZF25IO2FIWX · pith_short_8: 6HUYVZF2

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/6HUYVZF25IO2FIWXTGVLAZKWSW \
  | 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: f1e98ae4baea1da2a2d799aab06556959249abaf61095997f7f5cb42f74f2e77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62e29ee53876037a65e6c80172cdfd54fe247eb4cfcd99e8e13f47185cb57795",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2022-12-11T03:23:35Z",
    "title_canon_sha256": "76985dffbab2771630342896e2951290817482258a5ad3f14d04df1aa4af8287"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.05394",
    "kind": "arxiv",
    "version": 3
  }
}