Pith Number

pith:2PGHVRLM

pith:2011:2PGHVRLMKU2RMNY36FB7QPHDMC

not attested not anchored not stored refs pending

Chip-firing games, potential theory on graphs, and spanning trees

Farbod Shokrieh, Matthew Baker

arxiv:1107.1313 v2 · 2011-07-07 · 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{2PGHVRLMKU2RMNY36FB7QPHDMC}

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	2026-05-18T03:49:58.497192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3cc7ac56c553516371bf143f83ce360af0a2d3e4ac15da7708890945a5e59cf

Aliases

arxiv: 1107.1313 · arxiv_version: 1107.1313v2 · doi: 10.48550/arxiv.1107.1313 · pith_short_12: 2PGHVRLMKU2R · pith_short_16: 2PGHVRLMKU2RMNY3 · pith_short_8: 2PGHVRLM

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/2PGHVRLMKU2RMNY36FB7QPHDMC \
  | 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: d3cc7ac56c553516371bf143f83ce360af0a2d3e4ac15da7708890945a5e59cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89c7c7570c5e28e490c9889420fe35f52a0a3587feb5266406eca34601294e25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-07T08:12:34Z",
    "title_canon_sha256": "7b537778f8839e4511d46df1ba0d4fc03ee00af136437f4495f028561ba5c897"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1313",
    "kind": "arxiv",
    "version": 2
  }
}