Pith Number

pith:C5O2X7ML

pith:2009:C5O2X7MLPDDBQSNBDDYCFNZUWQ

not attested not anchored not stored refs pending

Chip-Firing Games, $G$-Parking Functions, and an Efficient Bijective Proof of the Matrix-Tree Theorem

Farbod Shokrieh

arxiv:0907.4761 v2 · 2009-07-27 · 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{C5O2X7MLPDDBQSNBDDYCFNZUWQ}

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	2026-05-18T03:50:11.215159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

175dabfd8b78c61849a118f022b734b4024690328efd0f3b6709f93b3fdac5e7

Aliases

arxiv: 0907.4761 · arxiv_version: 0907.4761v2 · doi: 10.48550/arxiv.0907.4761 · pith_short_12: C5O2X7MLPDDB · pith_short_16: C5O2X7MLPDDBQSNB · pith_short_8: C5O2X7ML

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/C5O2X7MLPDDBQSNBDDYCFNZUWQ \
  | 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: 175dabfd8b78c61849a118f022b734b4024690328efd0f3b6709f93b3fdac5e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8d74222c2390cf50a9b5e401e12118eeaead2febd60a727cea1608245a824f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-07-27T20:10:10Z",
    "title_canon_sha256": "0a5c174dc56348ff5fae536ddf156ba4a157843ace1fda47416616a6bf2b028c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4761",
    "kind": "arxiv",
    "version": 2
  }
}