Pith Number

pith:WKDP4BF5

pith:2009:WKDP4BF5DPEJRHQVVDD6G3EEID

not attested not anchored not stored refs pending

The Catenary Degree of Krull Monoids I

Alfred Geroldinger, David J. Grynkiewicz, Wolfgang Schmid

arxiv:0911.4882 v1 · 2009-11-25 · math.NT · 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{WKDP4BF5DPEJRHQVVDD6G3EEID}

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	2026-05-18T02:58:02.604685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b286fe04bd1bc8989e15a8c7e36c8440d0a5dccaaf6ee43da5c1773b12b82e27

Aliases

arxiv: 0911.4882 · arxiv_version: 0911.4882v1 · doi: 10.48550/arxiv.0911.4882 · pith_short_12: WKDP4BF5DPEJ · pith_short_16: WKDP4BF5DPEJRHQV · pith_short_8: WKDP4BF5

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/WKDP4BF5DPEJRHQVVDD6G3EEID \
  | 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: b286fe04bd1bc8989e15a8c7e36c8440d0a5dccaaf6ee43da5c1773b12b82e27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b06458dfe030f7e4a635f32f9beb46e1e22b46e4cf77a4e42232c876e0a6c13",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-11-25T15:28:47Z",
    "title_canon_sha256": "98d8df7a67afbed8acd29df2baf072be998a324a34318190eda23c70b0a3f9a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4882",
    "kind": "arxiv",
    "version": 1
  }
}