Pith Number

pith:U7KGTTLO

pith:2016:U7KGTTLOKEX5A6VINIPM44YK5A

not attested not anchored not stored refs pending

Minimal relations and catenary degrees in Krull monoids

Alfred Geroldinger, Yushuang Fan

arxiv:1603.06356 v2 · 2016-03-21 · 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{U7KGTTLOKEX5A6VINIPM44YK5A}

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	2026-05-18T01:09:06.556014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7d469cd6e512fd07aa86a1ece730ae82abe4a7724de48f9c0ef7818834a6f7e

Aliases

arxiv: 1603.06356 · arxiv_version: 1603.06356v2 · doi: 10.48550/arxiv.1603.06356 · pith_short_12: U7KGTTLOKEX5 · pith_short_16: U7KGTTLOKEX5A6VI · pith_short_8: U7KGTTLO

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/U7KGTTLOKEX5A6VINIPM44YK5A \
  | 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: a7d469cd6e512fd07aa86a1ece730ae82abe4a7724de48f9c0ef7818834a6f7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5167f60333f0a114aa1be81f2f38ee6c9f44cd659b4e14d1728aa9afbdfff342",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-03-21T09:05:09Z",
    "title_canon_sha256": "60e86052210c73baa53ff0938bf9adb0ee3ee2dd00f1d9301a144e8965589db6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06356",
    "kind": "arxiv",
    "version": 2
  }
}