Pith Number

pith:NF32LAPU

pith:2011:NF32LAPUE2POEBKJB3COB44NAJ

not attested not anchored not stored refs pending

Algebraic and combinatorial aspects of sandpile monoids on directed graphs

Ken W. Smith, Luis David Garc\'ia-Puente, Martin E. Malandro, Rebecca Garcia, Scott Chapman

arxiv:1105.2357 v2 · 2011-05-12 · 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{NF32LAPUE2POEBKJB3COB44NAJ}

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	2026-05-18T03:48:35.649090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6977a581f4269ee205490ec4e0f38d024cdf0a86eb624ae5c3282da9a7eab27b

Aliases

arxiv: 1105.2357 · arxiv_version: 1105.2357v2 · doi: 10.48550/arxiv.1105.2357 · pith_short_12: NF32LAPUE2PO · pith_short_16: NF32LAPUE2POEBKJ · pith_short_8: NF32LAPU

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/NF32LAPUE2POEBKJB3COB44NAJ \
  | 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: 6977a581f4269ee205490ec4e0f38d024cdf0a86eb624ae5c3282da9a7eab27b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28f4df6feb67927f808608607f0619069720e94618ee0a76806674d34460ecca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-12T02:11:38Z",
    "title_canon_sha256": "ae2d5cf7cf8b39010e6f17950d8d0fd1f1335cfc6278291324cf8403425fb822"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2357",
    "kind": "arxiv",
    "version": 2
  }
}