Pith Number

pith:XVM75CQ7

pith:2011:XVM75CQ73AFOHPTILBPMNVKPR5

not attested not anchored not stored refs pending

Avalanche dynamics of the Abelian sandpile model on the expanded cactus graph

Gregory Gauthier

arxiv:1110.6263 v3 · 2011-10-28 · 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{XVM75CQ73AFOHPTILBPMNVKPR5}

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	2026-05-18T03:56:45.037213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd59fe8a1fd80ae3be68585ec6d54f8f66a999cb9c86793cb61c0cc0ff82be35

Aliases

arxiv: 1110.6263 · arxiv_version: 1110.6263v3 · doi: 10.48550/arxiv.1110.6263 · pith_short_12: XVM75CQ73AFO · pith_short_16: XVM75CQ73AFOHPTI · pith_short_8: XVM75CQ7

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/XVM75CQ73AFOHPTILBPMNVKPR5 \
  | 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: bd59fe8a1fd80ae3be68585ec6d54f8f66a999cb9c86793cb61c0cc0ff82be35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb6f16e694a9315962547b149c851f04bbd87f20072554e47c1690c0f7ede3b6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-10-28T06:57:36Z",
    "title_canon_sha256": "1dbf3d2f40dad6ff84e35a0bc9342f1147cbfee2f44276cd14061add201cc3d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6263",
    "kind": "arxiv",
    "version": 3
  }
}