Pith Number

pith:2UMRC3RN

pith:2024:2UMRC3RNQIX7M2UOKQ5D4FZZ2Q

not attested not anchored not stored refs pending

Numerical semigroups, polyhedra, and posets IV: walking the faces of the Kunz cone

Christopher O'Neill, Cole Brower, Joseph McDonough

arxiv:2401.06025 v3 · 2024-01-11 · math.CO · 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{2UMRC3RNQIX7M2UOKQ5D4FZZ2Q}

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	2026-07-05T10:19:21.830550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d519116e2d822ff66a8e543a3e1739d416ad267f8f74b5991871f4e82911c06b

Aliases

arxiv: 2401.06025 · arxiv_version: 2401.06025v3 · doi: 10.48550/arxiv.2401.06025 · pith_short_12: 2UMRC3RNQIX7 · pith_short_16: 2UMRC3RNQIX7M2UO · pith_short_8: 2UMRC3RN

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/2UMRC3RNQIX7M2UOKQ5D4FZZ2Q \
  | 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: d519116e2d822ff66a8e543a3e1739d416ad267f8f74b5991871f4e82911c06b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "668540acfc1508663a046d6ebe24f06e62acd837551822d7a6e86d2f78e939e3",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-01-11T16:33:45Z",
    "title_canon_sha256": "ea733571314c925002715a064591de9deef34988999abbda522449026682644f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.06025",
    "kind": "arxiv",
    "version": 3
  }
}