Pith Number

pith:UTQZUZDH

pith:2017:UTQZUZDH3XQ2MNDFGT4K5XTZFC

not attested not anchored not stored refs pending

A Graphical Approach to Finding the Frobenius Number, Genus and Hilbert Series of a Numerical Semigroup

Alexandru Pascadi

arxiv:1712.02522 v3 · 2017-12-07 · 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{UTQZUZDH3XQ2MNDFGT4K5XTZFC}

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	2026-05-18T00:06:41.022729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4e19a6467dde1a6346534f8aede7928bb96cf98f59c22ffeb2421bc3814df3f

Aliases

arxiv: 1712.02522 · arxiv_version: 1712.02522v3 · doi: 10.48550/arxiv.1712.02522 · pith_short_12: UTQZUZDH3XQ2 · pith_short_16: UTQZUZDH3XQ2MNDF · pith_short_8: UTQZUZDH

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/UTQZUZDH3XQ2MNDFGT4K5XTZFC \
  | 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: a4e19a6467dde1a6346534f8aede7928bb96cf98f59c22ffeb2421bc3814df3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d8a28f1797037131ee38b3f89958ac987a8b8fcecf2ea7d65c22f55d95df282",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-12-07T07:48:23Z",
    "title_canon_sha256": "9f0c727f7cf01b5b8f1004866b27b072eb87caa56b7740441669661d150bcd85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.02522",
    "kind": "arxiv",
    "version": 3
  }
}