Pith Number

pith:ZOOCFGOS

pith:2025:ZOOCFGOS4ZJO3RIJYT7G7USIKB

not attested not anchored not stored refs pending

Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property

Lisa Nicklasson, Thiago Holleben

arxiv:2502.00155 v2 · 2025-01-31 · 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{ZOOCFGOS4ZJO3RIJYT7G7USIKB}

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	2026-07-05T10:15:25.287586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb9c2299d2e652edc509c4fe6fd248505971d32429022a5c25919d27e968bb90

Aliases

arxiv: 2502.00155 · arxiv_version: 2502.00155v2 · doi: 10.48550/arxiv.2502.00155 · pith_short_12: ZOOCFGOS4ZJO · pith_short_16: ZOOCFGOS4ZJO3RIJ · pith_short_8: ZOOCFGOS

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/ZOOCFGOS4ZJO3RIJYT7G7USIKB \
  | 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: cb9c2299d2e652edc509c4fe6fd248505971d32429022a5c25919d27e968bb90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cb085052de417e51cae68b111f3db6e2109b7989b280179f7ec5eca3fe46d4f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2025-01-31T20:45:39Z",
    "title_canon_sha256": "480bf75fe538311cb97df37e9c6e321e284446ba21f492648c14ad12f0a3854b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.00155",
    "kind": "arxiv",
    "version": 2
  }
}