Pith Number

pith:LW72ATUL

pith:2016:LW72ATULGAWLDITZQCQBWY3KC5

not attested not anchored not stored refs pending

On the abelianity of the stochastic sandpile model

Fran\c{c}ois Nunzi

arxiv:1607.05561 v1 · 2016-07-19 · 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{LW72ATULGAWLDITZQCQBWY3KC5}

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	2026-05-18T01:10:46.545387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dbfa04e8b302cb1a27980a01b636a176e0b532d18ba791828a19c68e3f79cc5

Aliases

arxiv: 1607.05561 · arxiv_version: 1607.05561v1 · doi: 10.48550/arxiv.1607.05561 · pith_short_12: LW72ATULGAWL · pith_short_16: LW72ATULGAWLDITZ · pith_short_8: LW72ATUL

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/LW72ATULGAWLDITZQCQBWY3KC5 \
  | 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: 5dbfa04e8b302cb1a27980a01b636a176e0b532d18ba791828a19c68e3f79cc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e387bc0b452a483ef8715b2cd8a8cfd1965b018e28177044c6d44bdfdb07f5ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-19T13:03:28Z",
    "title_canon_sha256": "599e90ed805e9475b99bb8f7603584f8c6c7fe72ae9a561ae58bb18c71dd7b8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05561",
    "kind": "arxiv",
    "version": 1
  }
}