Pith Number

pith:GXAD66CG

pith:2008:GXAD66CGVAFHTTSD27QPSBJYSY

not attested not anchored not stored refs pending

Chip-Firing and Rotor-Routing on Directed Graphs

Alexander E. Holroyd, David B. Wilson, James Propp, Karola Meszaros, Lionel Levine, Yuval Peres

arxiv:0801.3306 v4 · 2008-01-22 · 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{GXAD66CGVAFHTTSD27QPSBJYSY}

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	2026-05-18T02:24:57.642212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35c03f7846a80a79ce43d7e0f9053896072d8c03ebbee1bb76a870b899c0712c

Aliases

arxiv: 0801.3306 · arxiv_version: 0801.3306v4 · doi: 10.48550/arxiv.0801.3306 · pith_short_12: GXAD66CGVAFH · pith_short_16: GXAD66CGVAFHTTSD · pith_short_8: GXAD66CG

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/GXAD66CGVAFHTTSD27QPSBJYSY \
  | 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: 35c03f7846a80a79ce43d7e0f9053896072d8c03ebbee1bb76a870b899c0712c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "026d593564290f0ebafd66ba7e3c10eb0ae1dc7d718347bb33e28369766655bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-01-22T18:08:35Z",
    "title_canon_sha256": "4bfae1c3e3a59ec178cab3b4cafc07f423d8082bffa21d5cba86bd02f668c1ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.3306",
    "kind": "arxiv",
    "version": 4
  }
}