Pith Number

pith:LXVZLDUL

pith:2022:LXVZLDULYHLVE5HO7CLNI3HYZR

not attested not anchored not stored refs pending

Macaulay duality and its geometry

Jan O. Kleppe, Steven L. Kleiman

arxiv:2210.10934 v3 · 2022-10-20 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LXVZLDULYHLVE5HO7CLNI3HYZR}

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.

Cited by

1 paper in Pith

Log-concavity of polynomials arising from equivariant cohomology

Receipt and verification

First computed	2026-07-05T06:35:24.449949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5deb958e8bc1d75274eef896d46cf8cc71753eb70d84f34a6ec17ab3c256c801

Aliases

arxiv: 2210.10934 · arxiv_version: 2210.10934v3 · doi: 10.48550/arxiv.2210.10934 · pith_short_12: LXVZLDULYHLV · pith_short_16: LXVZLDULYHLVE5HO · pith_short_8: LXVZLDUL

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/LXVZLDULYHLVE5HO7CLNI3HYZR \
  | 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: 5deb958e8bc1d75274eef896d46cf8cc71753eb70d84f34a6ec17ab3c256c801

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58063ee6acd46c951141f942ec571d4c31e013068b93d6ba71d2d2ad8bd02e2c",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2022-10-20T00:05:07Z",
    "title_canon_sha256": "18e8eda7a874d86627f1ac6b202605e02bad30a188e494bc904a964a5f6fd7bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.10934",
    "kind": "arxiv",
    "version": 3
  }
}