Pith Number

pith:Q7G44E4F

pith:2012:Q7G44E4F2FJCSGG3JFFXX5WHXO

not attested not anchored not stored refs pending

The index of a numerical semigroup ring

Oana Veliche

arxiv:1208.5625 v2 · 2012-08-28 · 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{Q7G44E4F2FJCSGG3JFFXX5WHXO}

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	2026-05-18T03:32:58.863844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87cdce1385d1522918db494b7bf6c7bbac85d7d136c17b8c29c5a3f7fbc45687

Aliases

arxiv: 1208.5625 · arxiv_version: 1208.5625v2 · doi: 10.48550/arxiv.1208.5625 · pith_short_12: Q7G44E4F2FJC · pith_short_16: Q7G44E4F2FJCSGG3 · pith_short_8: Q7G44E4F

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/Q7G44E4F2FJCSGG3JFFXX5WHXO \
  | 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: 87cdce1385d1522918db494b7bf6c7bbac85d7d136c17b8c29c5a3f7fbc45687

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fbb80db5e90d0ec1184ed6d7f9f089fa8cad814624b9ddc1d4eaace575b871a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-08-28T11:14:05Z",
    "title_canon_sha256": "0d1c91a44f747ce1dee63b02c28d2f023d109e4b190a1d6bef0e605c5583f53a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5625",
    "kind": "arxiv",
    "version": 2
  }
}