Pith Number

pith:3GGKQZWQ

pith:2010:3GGKQZWQHXPD6GUWF7B5A3A33Q

not attested not anchored not stored refs pending

Chip-Firing and Riemann-Roch Theory for Directed Graphs

Arash Asadi, Spencer Backman

arxiv:1012.0287 v2 · 2010-12-01 · math.CO · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GGKQZWQHXPD6GUWF7B5A3A33Q}

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	2026-05-18T04:12:32.369455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d98ca866d03dde3f1a962fc3d06c1bdc033d1c68134d904bba27bfe941ec5e0b

Aliases

arxiv: 1012.0287 · arxiv_version: 1012.0287v2 · doi: 10.48550/arxiv.1012.0287 · pith_short_12: 3GGKQZWQHXPD · pith_short_16: 3GGKQZWQHXPD6GUW · pith_short_8: 3GGKQZWQ

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/3GGKQZWQHXPD6GUWF7B5A3A33Q \
  | 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: d98ca866d03dde3f1a962fc3d06c1bdc033d1c68134d904bba27bfe941ec5e0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a5b2c18fb0cea98cc574a12a957c4a2ae25bd61e8fe1bf2f1a0bac25f8bba1a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-01T20:26:47Z",
    "title_canon_sha256": "e3fe7c3c451e8f4ea814b51df5b4082288878b59bdfe979e47e26e64c6ac8363"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0287",
    "kind": "arxiv",
    "version": 2
  }
}