Pith Number

pith:PE4V6FY3

pith:2019:PE4V6FY3ROZGIZSSJE2L4XBKGN

not attested not anchored not stored refs pending

Chip-Firing Games and Critical Groups

Darren Glass, Nathan Kaplan

arxiv:1908.04395 v1 · 2019-08-12 · 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{PE4V6FY3ROZGIZSSJE2L4XBKGN}

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	2026-07-05T03:50:12.261095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79395f171b8bb26466524934be5c2a337f55af73fcd5d50437c89d40187902da

Aliases

arxiv: 1908.04395 · arxiv_version: 1908.04395v1 · doi: 10.48550/arxiv.1908.04395 · pith_short_12: PE4V6FY3ROZG · pith_short_16: PE4V6FY3ROZGIZSS · pith_short_8: PE4V6FY3

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/PE4V6FY3ROZGIZSSJE2L4XBKGN \
  | 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: 79395f171b8bb26466524934be5c2a337f55af73fcd5d50437c89d40187902da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7facba877dff829a735eb11a2bf9bbbe0ca5679e8dd00bfbef338ded2d8d957b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-12T21:07:32Z",
    "title_canon_sha256": "1d9021c20a1bd04ef59d3f3a945480d3a55a805c3b31594a5dd419c7c76cd382"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.04395",
    "kind": "arxiv",
    "version": 1
  }
}