Pith Number

pith:PUC4U5J5

pith:2009:PUC4U5J553QJVATV7L5J2SMAVC

not attested not anchored not stored refs pending

Stanley decompositions and Hilbert depth in the Koszul complex

Christian Krattenthaler (Universit\"at Wien), Jan Uliczka (Universit\"at Osnabr\"uck), Winfried Bruns (Universit\"at Osnabr\"uck)

arxiv:0909.0686 v2 · 2009-09-03 · 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{PUC4U5J553QJVATV7L5J2SMAVC}

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	2026-05-18T04:39:16.855465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d05ca753deee09a8275fafa9d4980a8bbdfcd10574958b028015e0ca67162bc

Aliases

arxiv: 0909.0686 · arxiv_version: 0909.0686v2 · doi: 10.48550/arxiv.0909.0686 · pith_short_12: PUC4U5J553QJ · pith_short_16: PUC4U5J553QJVATV · pith_short_8: PUC4U5J5

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/PUC4U5J553QJVATV7L5J2SMAVC \
  | 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: 7d05ca753deee09a8275fafa9d4980a8bbdfcd10574958b028015e0ca67162bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fec153d4d7193af5b719df2c4520aa6ae1d73dca67da233bbe52837910ea7088",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-09-03T15:29:46Z",
    "title_canon_sha256": "209e07319adbe754661f0bf960310cde7add4d9bb26192601b77d234597b3224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0686",
    "kind": "arxiv",
    "version": 2
  }
}