Pith Number

pith:5ZO2545P

pith:2012:5ZO2545PMBVNFLC6TFSEHOZNWD

not attested not anchored not stored refs pending

The abelian sandpile model on a random binary tree

Ellen Saada, Frank Redig, Wioletta Ruszel

arxiv:1202.5131 v2 · 2012-02-23 · math.PR · cond-mat.dis-nn · 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{5ZO2545PMBVNFLC6TFSEHOZNWD}

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	2026-05-18T01:58:20.450483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee5daef3af606ad2ac5e996443bb2db0c1e4d7f7cb27a28fed497cda028918f3

Aliases

arxiv: 1202.5131 · arxiv_version: 1202.5131v2 · doi: 10.48550/arxiv.1202.5131 · pith_short_12: 5ZO2545PMBVN · pith_short_16: 5ZO2545PMBVNFLC6 · pith_short_8: 5ZO2545P

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/5ZO2545PMBVNFLC6TFSEHOZNWD \
  | 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: ee5daef3af606ad2ac5e996443bb2db0c1e4d7f7cb27a28fed497cda028918f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "074f5c9f02688292527bfac2b5a6637f9877fb6e44c4f2ef69092be3273df667",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-02-23T09:36:40Z",
    "title_canon_sha256": "d2ff008ab72729dd6fa97884b91ae371d74794e439c5ea50036b45f822e46701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5131",
    "kind": "arxiv",
    "version": 2
  }
}