Pith Number

pith:NOAU3OVG

pith:2018:NOAU3OVGDYT4AQ44XPBXLIKIA4

not attested not anchored not stored refs pending

The distribution of sandpile groups of random regular graphs

Andr\'as M\'esz\'aros

arxiv:1806.03736 v4 · 2018-06-10 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NOAU3OVGDYT4AQ44XPBXLIKIA4}

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.

Cited by

1 paper in Pith

Chip-Firing Games and Critical Groups

Receipt and verification

First computed	2026-07-05T01:50:14.140478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4

Aliases

arxiv: 1806.03736 · arxiv_version: 1806.03736v4 · doi: 10.48550/arxiv.1806.03736 · pith_short_12: NOAU3OVGDYT4 · pith_short_16: NOAU3OVGDYT4AQ44 · pith_short_8: NOAU3OVG

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/NOAU3OVGDYT4AQ44XPBXLIKIA4 \
  | 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: 6b814dbaa61e27c0439cbbc375a148073161ee9c3c9e458d776003ccc6372cb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc3226500b726c80501a1a7847d9b94e3901e6e3d5b117f3c2ee0f6c0c82f1cf",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-10T22:24:16Z",
    "title_canon_sha256": "e593c37874ce8adedc3060720e75259f5b4a37b485818523f2b4ddacf27d2e5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.03736",
    "kind": "arxiv",
    "version": 4
  }
}