Pith Number

pith:ZMBHD5ID

pith:1999:ZMBHD5IDWHJ2DA2G7SBGGJUACA

not attested not anchored not stored refs pending

Convergence to the maximal invariant measure for a zero-range process with random rates

Claudio Landim, Enrique D. Andjel, Herve Guiol, Pablo A. Ferrari

arxiv:math/9911205 v2 · 1999-11-25 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZMBHD5IDWHJ2DA2G7SBGGJUACA}

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	2026-05-18T04:36:42.369241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb0271f503b1d3a18346fc82632680102a4400cf7aaeef120befc34f5bff89f3

Aliases

arxiv: math/9911205 · arxiv_version: math/9911205v2 · doi: 10.48550/arxiv.math/9911205 · pith_short_12: ZMBHD5IDWHJ2 · pith_short_16: ZMBHD5IDWHJ2DA2G · pith_short_8: ZMBHD5ID

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/ZMBHD5IDWHJ2DA2G7SBGGJUACA \
  | 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: cb0271f503b1d3a18346fc82632680102a4400cf7aaeef120befc34f5bff89f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90251632464ae9f9e1d53f520d8c789abe16a5b221e4120f2b1839522497b2a9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-11-25T18:02:06Z",
    "title_canon_sha256": "80e7506b88f47d4e690ae372c218f46c0cbb2dd28b12fe48713a49b76b7d48f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911205",
    "kind": "arxiv",
    "version": 2
  }
}