Pith Number

pith:WCWKP64V

pith:2018:WCWKP64VY3LEXPUFE666XBZTPS

not attested not anchored not stored refs pending

The number of addends in the decomposition of an element of a numerical semigroup into atoms

Hamid Kulosman

arxiv:1807.10907 v1 · 2018-07-28 · 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{WCWKP64VY3LEXPUFE666XBZTPS}

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	2026-05-18T00:09:35.058747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0aca7fb95c6d64bbe8527bdeb87337cab1ae49fd5c5b7473e515f7b2141ea9a

Aliases

arxiv: 1807.10907 · arxiv_version: 1807.10907v1 · doi: 10.48550/arxiv.1807.10907 · pith_short_12: WCWKP64VY3LE · pith_short_16: WCWKP64VY3LEXPUF · pith_short_8: WCWKP64V

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/WCWKP64VY3LEXPUFE666XBZTPS \
  | 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: b0aca7fb95c6d64bbe8527bdeb87337cab1ae49fd5c5b7473e515f7b2141ea9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cf2ab7a4890aa112a96bd83501aa4cd7fa344f37701b643bcc8e72bc26a2def",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-07-28T07:53:38Z",
    "title_canon_sha256": "8082757bf881591e80af4d45ff53e9d0819ed6eb0285acb5798d60d4e4ce8612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.10907",
    "kind": "arxiv",
    "version": 1
  }
}