Pith Number

pith:YS6LBB4Z

pith:2010:YS6LBB4ZV7TGAU7H2KIRSYXQFG

not attested not anchored not stored refs pending

An explicit example of Frobenius periodicity

Almar Kaid, Holger Brenner

arxiv:1011.4186 v2 · 2010-11-18 · math.AG · 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{YS6LBB4ZV7TGAU7H2KIRSYXQFG}

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	2026-05-18T03:41:02.592683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4bcb08799afe66053e7d2911962f02980c93cea8fa71cb1b28e4b7a2282b550

Aliases

arxiv: 1011.4186 · arxiv_version: 1011.4186v2 · doi: 10.48550/arxiv.1011.4186 · pith_short_12: YS6LBB4ZV7TG · pith_short_16: YS6LBB4ZV7TGAU7H · pith_short_8: YS6LBB4Z

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/YS6LBB4ZV7TGAU7H2KIRSYXQFG \
  | 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: c4bcb08799afe66053e7d2911962f02980c93cea8fa71cb1b28e4b7a2282b550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f2fe968b92ae5e0c1e43efd9d6af0033b908b413689d6989e9e0cf2f675e497",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-11-18T13:13:31Z",
    "title_canon_sha256": "d229201b1309c1afdc2400a7edef314d68e2676c2a2fcbd133e2a1530607f50c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4186",
    "kind": "arxiv",
    "version": 2
  }
}