Pith Number

pith:3YZWJWIO

pith:2013:3YZWJWIO7Q2YEB5IQU4VI7KHO2

not attested not anchored not stored refs pending

Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a Cyclic Lemma

Jean-Christophe Aval, Mark Dukes, Michele D'Adderio, Yvan Le Borgne

arxiv:1307.7740 v3 · 2013-07-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3YZWJWIO7Q2YEB5IQU4VI7KHO2}

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	2026-05-18T02:26:01.097069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de3364d90efc358207a88539547d47769b53dee2bc34a330e4c540f7e38e1771

Aliases

arxiv: 1307.7740 · arxiv_version: 1307.7740v3 · doi: 10.48550/arxiv.1307.7740 · pith_short_12: 3YZWJWIO7Q2Y · pith_short_16: 3YZWJWIO7Q2YEB5I · pith_short_8: 3YZWJWIO

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/3YZWJWIO7Q2YEB5IQU4VI7KHO2 \
  | 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: de3364d90efc358207a88539547d47769b53dee2bc34a330e4c540f7e38e1771

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bac3147344da5f2219189093dcc57d4c72b8050b0053dfbb157b7ff389ce2855",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-29T21:06:38Z",
    "title_canon_sha256": "2af1e9269b09b761448ab008ac5dbbc95964d8703fe68926fb65bdf7fc5f2336"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7740",
    "kind": "arxiv",
    "version": 3
  }
}