Pith Number

pith:2K5XG4XY

pith:2015:2K5XG4XYI7DOLJTYNOUDBUD4RX

not attested not anchored not stored refs pending

Products of $k$ atoms in Krull monoids

Qinghai Zhong, Yushuang Fan

arxiv:1508.03500 v1 · 2015-08-14 · math.AC · math.CO · 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{2K5XG4XYI7DOLJTYNOUDBUD4RX}

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	2026-05-18T01:35:17.594478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2bb7372f847c6e5a6786ba830d07c8dca1a49a30f6bde4000ca9be4ca9d69b9

Aliases

arxiv: 1508.03500 · arxiv_version: 1508.03500v1 · doi: 10.48550/arxiv.1508.03500 · pith_short_12: 2K5XG4XYI7DO · pith_short_16: 2K5XG4XYI7DOLJTY · pith_short_8: 2K5XG4XY

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/2K5XG4XYI7DOLJTYNOUDBUD4RX \
  | 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: d2bb7372f847c6e5a6786ba830d07c8dca1a49a30f6bde4000ca9be4ca9d69b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6820e5e02ab22110f1422660cac73061579df1062216f5cace4293f46abf948c",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-14T13:41:17Z",
    "title_canon_sha256": "85db3d30861bff2416bcbc59eb941807a906a5e3926397c7e406ca3968636b41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03500",
    "kind": "arxiv",
    "version": 1
  }
}