Pith Number

pith:PJQ672YU

pith:2006:PJQ672YUZEFMUMQISNQLBB3VBI

not attested not anchored not stored refs pending

Hilbert series of algebras associated to directed graphs

Robert Lee Wilson, Shirlei Serconek, Vladimir Retakh

arxiv:math/0601224 v2 · 2006-01-10 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJQ672YUZEFMUMQISNQLBB3VBI}

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	2026-07-04T14:52:47.955761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a61efeb14c90aca32089360b087750a3b40a5fd3c6e13a7e8315a0620acf789

Aliases

arxiv: math/0601224 · arxiv_version: math/0601224v2 · doi: 10.48550/arxiv.math/0601224 · pith_short_12: PJQ672YUZEFM · pith_short_16: PJQ672YUZEFMUMQI · pith_short_8: PJQ672YU

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/PJQ672YUZEFMUMQISNQLBB3VBI \
  | 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: 7a61efeb14c90aca32089360b087750a3b40a5fd3c6e13a7e8315a0620acf789

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "045149c7e0de1131d602834415e070eff44d5df2f90cdee8dab9f486f2c6e043",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-01-10T18:49:03Z",
    "title_canon_sha256": "95846e2a6e922ad622ed68c0ac89ab56f36ef75ce2f1714e5813f73332d74517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601224",
    "kind": "arxiv",
    "version": 2
  }
}