Pith Number

pith:O6BSQ6R2

pith:2026:O6BSQ6R225TB45WLI6IYOH2NNE

not attested not anchored not stored refs pending

Ergodicity of stochastic reaction-diffusion equations on unbounded domains driven by space-time white noise

Jianliang Zhai, Shijie Shang, Tusheng Zhang

arxiv:2606.26619 v1 · 2026-06-25 · 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{O6BSQ6R225TB45WLI6IYOH2NNE}

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	2026-06-26T01:15:36.401803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7783287a3ad7661e76cb4791871f4d69079e8b32bee7a4c0c47a0adf13aac6e9

Aliases

arxiv: 2606.26619 · arxiv_version: 2606.26619v1 · doi: 10.48550/arxiv.2606.26619 · pith_short_12: O6BSQ6R225TB · pith_short_16: O6BSQ6R225TB45WL · pith_short_8: O6BSQ6R2

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/O6BSQ6R225TB45WLI6IYOH2NNE \
  | 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: 7783287a3ad7661e76cb4791871f4d69079e8b32bee7a4c0c47a0adf13aac6e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b6f4f81f19713c8d1c1b4559208bc82b6b162d131e3e26d47f9929b6bfb5bf4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-25T05:30:51Z",
    "title_canon_sha256": "f0732703305c2f0cd757d736d340b4936c059d5d0d9457dbb29d98f0e90ecb7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26619",
    "kind": "arxiv",
    "version": 1
  }
}