Pith Number

pith:ILDBWL2U

pith:2012:ILDBWL2UKQZ7JYLMUEP5Y4C4HX

not attested not anchored not stored refs pending

Apollonian structure in the Abelian sandpile

Charles K. Smart, Lionel Levine, Wesley Pegden

arxiv:1208.4839 v2 · 2012-08-23 · math.AP · cond-mat.stat-mech · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILDBWL2UKQZ7JYLMUEP5Y4C4HX}

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	2026-05-18T02:51:23.570606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c61b2f545433f4e16ca11fdc705c3dcf9f14d73811f158c6cd8b9f6b7da745

Aliases

arxiv: 1208.4839 · arxiv_version: 1208.4839v2 · doi: 10.48550/arxiv.1208.4839 · pith_short_12: ILDBWL2UKQZ7 · pith_short_16: ILDBWL2UKQZ7JYLM · pith_short_8: ILDBWL2U

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/ILDBWL2UKQZ7JYLMUEP5Y4C4HX \
  | 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: 42c61b2f545433f4e16ca11fdc705c3dcf9f14d73811f158c6cd8b9f6b7da745

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f82f6cb894d2b485338ac3526aa513d1a4122ef8d55dc0fd432b65f85e36edd",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-23T19:52:26Z",
    "title_canon_sha256": "05f95799fa8fbdf166b140cc922e85ee08201c88581b68e2fc10ed4937424165"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4839",
    "kind": "arxiv",
    "version": 2
  }
}