Pith Number

pith:QKT3NUMO

pith:2019:QKT3NUMO7E4HZK7YO3ZP2FI7B5

not attested not anchored not stored refs pending

A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

Alfred Geroldinger (IM), Wolfgang Schmid (LAGA)

arxiv:1901.03506 v2 · 2019-01-11 · math.AC · 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{QKT3NUMO7E4HZK7YO3ZP2FI7B5}

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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	2026-05-17T23:43:28.009415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82a7b6d18ef9387cabf876f2fd151f0f4ed5168aa9d3c583c67c3dab46b27706

Aliases

arxiv: 1901.03506 · arxiv_version: 1901.03506v2 · doi: 10.48550/arxiv.1901.03506 · pith_short_12: QKT3NUMO7E4H · pith_short_16: QKT3NUMO7E4HZK7Y · pith_short_8: QKT3NUMO

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/QKT3NUMO7E4HZK7YO3ZP2FI7B5 \
  | 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: 82a7b6d18ef9387cabf876f2fd151f0f4ed5168aa9d3c583c67c3dab46b27706

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b203c23bf398e210cc970c8d959efa26a2781dbd7248291e157e23912e62c8e7",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-01-11T08:31:28Z",
    "title_canon_sha256": "3321085ade46fb6a771a6d82b76066f0bf47e480d4b13da8c7d159552a7c2464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.03506",
    "kind": "arxiv",
    "version": 2
  }
}