Pith Number

pith:GQRFILTT

pith:2015:GQRFILTTHCUFN67AEECYUVWGY4

not attested not anchored not stored refs pending

Stanley's nonunimodal Gorenstein h-vector is optimal

Fabrizio Zanello, Juan Migliore

arxiv:1512.01433 v1 · 2015-12-04 · 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{GQRFILTTHCUFN67AEECYUVWGY4}

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	2026-05-18T01:01:08.723663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3422542e7338a856fbe021058a56c6c7277046a7947aff84ce009dcab5dd65e1

Aliases

arxiv: 1512.01433 · arxiv_version: 1512.01433v1 · doi: 10.48550/arxiv.1512.01433 · pith_short_12: GQRFILTTHCUF · pith_short_16: GQRFILTTHCUFN67A · pith_short_8: GQRFILTT

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/GQRFILTTHCUFN67AEECYUVWGY4 \
  | 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: 3422542e7338a856fbe021058a56c6c7277046a7947aff84ce009dcab5dd65e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9992ec654b569d149b5b38667707da4eed8e9f3358abda0fc971302f36146914",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-04T14:37:51Z",
    "title_canon_sha256": "d2f8d99fad163f02be3dbc939e17d378f13f0d2932bb76e29ff0d24786631c2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01433",
    "kind": "arxiv",
    "version": 1
  }
}