Pith Number

pith:5OJ6Q5LQ

pith:2004:5OJ6Q5LQRJRC2HBDDMVTGHBI46

not attested not anchored not stored refs pending

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

Antal A. Jarai, Frank Redig

arxiv:math/0408060 v3 · 2004-08-04 · 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{5OJ6Q5LQRJRC2HBDDMVTGHBI46}

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	2026-05-18T04:31:52.720596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb93e875708a622d1c231b2b331c28e788389f2d8fdf1e1a1c66f857e9dc4c8d

Aliases

arxiv: math/0408060 · arxiv_version: math/0408060v3 · doi: 10.48550/arxiv.math/0408060 · pith_short_12: 5OJ6Q5LQRJRC · pith_short_16: 5OJ6Q5LQRJRC2HBD · pith_short_8: 5OJ6Q5LQ

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/5OJ6Q5LQRJRC2HBDDMVTGHBI46 \
  | 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: eb93e875708a622d1c231b2b331c28e788389f2d8fdf1e1a1c66f857e9dc4c8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc440c28976f111e0c913347378a831fa7b1ae7322d53483b34bde41aa46a3c5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-08-04T15:53:27Z",
    "title_canon_sha256": "0f1257a419f3c7e2ca448cd2e3e711d688ddca163e491bdef7fff44cf2d34440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408060",
    "kind": "arxiv",
    "version": 3
  }
}