Pith Number

pith:WREEN4VA

pith:2012:WREEN4VAUARJV6V26IOYSCBZAX

not attested not anchored not stored refs pending

Minimal Free Resolutions of the $G$-parking Function Ideal and the Toppling Ideal

Frank-Olaf Schreyer, John Wilmes, Madhusudan Manjunath

arxiv:1210.7569 v3 · 2012-10-29 · math.AC · 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{WREEN4VAUARJV6V26IOYSCBZAX}

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	2026-05-18T03:37:52.330300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b44846f2a0a0229afabaf21d89083905e91a0db6411c58ba728caf732987fb64

Aliases

arxiv: 1210.7569 · arxiv_version: 1210.7569v3 · doi: 10.48550/arxiv.1210.7569 · pith_short_12: WREEN4VAUARJ · pith_short_16: WREEN4VAUARJV6V2 · pith_short_8: WREEN4VA

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/WREEN4VAUARJV6V26IOYSCBZAX \
  | 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: b44846f2a0a0229afabaf21d89083905e91a0db6411c58ba728caf732987fb64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46f6a3351340c91edbff93272190a9be06151306a1449fe8da01547263134728",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-10-29T05:44:03Z",
    "title_canon_sha256": "88a9df1fa01a8d267b8fc522cc00aacb68da39f39a45ab6bda10efaaf88cbf62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7569",
    "kind": "arxiv",
    "version": 3
  }
}