Pith Number

pith:HKWEJJDZ

pith:2013:HKWEJJDZKVH6EUUZ6BLAA5LRDZ

not attested not anchored not stored refs pending

The arithmetical rank of the edge ideals of graphs with whiskers

Antonio Macchia

arxiv:1307.1652 v1 · 2013-07-05 · 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{HKWEJJDZKVH6EUUZ6BLAA5LRDZ}

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	2026-05-18T03:19:12.280481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aac44a479554fe25299f0560075711e66c0152f28a63702cfeed05a940ef75f

Aliases

arxiv: 1307.1652 · arxiv_version: 1307.1652v1 · doi: 10.48550/arxiv.1307.1652 · pith_short_12: HKWEJJDZKVH6 · pith_short_16: HKWEJJDZKVH6EUUZ · pith_short_8: HKWEJJDZ

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/HKWEJJDZKVH6EUUZ6BLAA5LRDZ \
  | 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: 3aac44a479554fe25299f0560075711e66c0152f28a63702cfeed05a940ef75f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9345d25166703fcb6bf44062fb63dc37f5b306145ef7d4d4d75be21cbd2f862",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-07-05T16:15:33Z",
    "title_canon_sha256": "7a6c4362e5a71a942c6e0713d032e076cb24b2e176d5d8c259f5cbf989f27cdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1652",
    "kind": "arxiv",
    "version": 1
  }
}