Pith Number

pith:E33NNX2J

pith:2017:E33NNX2JGNOG65ECP4MHAEBGFZ

not attested not anchored not stored refs pending

Characterizations of numerical semigroup complements via Ap\'ery sets

Caleb McKinley Shor, T. Alden Gassert

arxiv:1705.04256 v2 · 2017-05-11 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E33NNX2JGNOG65ECP4MHAEBGFZ}

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	2026-05-18T00:22:21.002992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26f6d6df49335c6f74827f187010262e4cbb644d048a32d0bc6fca6bd6e43a92

Aliases

arxiv: 1705.04256 · arxiv_version: 1705.04256v2 · doi: 10.48550/arxiv.1705.04256 · pith_short_12: E33NNX2JGNOG · pith_short_16: E33NNX2JGNOG65EC · pith_short_8: E33NNX2J

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/E33NNX2JGNOG65ECP4MHAEBGFZ \
  | 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: 26f6d6df49335c6f74827f187010262e4cbb644d048a32d0bc6fca6bd6e43a92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67f59d966335759e48b52d67f1c1230cf1d4a5448f5c445d2564109062a72c78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-05-11T16:04:45Z",
    "title_canon_sha256": "754a4d3d567d882f1cd3ee60e77f9ef4ee0cb86624dc83f356d715160ba60777"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04256",
    "kind": "arxiv",
    "version": 2
  }
}