Pith Number

pith:SHIQRYHE

pith:2013:SHIQRYHEOOWVQ6P4YFWHHZBAYE

not attested not anchored not stored refs pending

The Hilbert-Kunz functions of two-dimensional rings of type ADE

Daniel Brinkmann

arxiv:1308.5085 v1 · 2013-08-23 · math.AC · math.AG · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SHIQRYHEOOWVQ6P4YFWHHZBAYE}

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	2026-05-18T03:15:17.347869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91d108e0e473ad5879fcc16c73e420c1049f283e39338149c254b6e593d51328

Aliases

arxiv: 1308.5085 · arxiv_version: 1308.5085v1 · doi: 10.48550/arxiv.1308.5085 · pith_short_12: SHIQRYHEOOWV · pith_short_16: SHIQRYHEOOWVQ6P4 · pith_short_8: SHIQRYHE

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/SHIQRYHEOOWVQ6P4YFWHHZBAYE \
  | 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: 91d108e0e473ad5879fcc16c73e420c1049f283e39338149c254b6e593d51328

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65937d25fd01b82ef5b9bc5f0f44af701bf087793c511a31795fa6989b7762da",
    "cross_cats_sorted": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-08-23T09:53:35Z",
    "title_canon_sha256": "1eafe906a828fd8d4a7faa1ed96d37806f569a645abbd4b3bb774ac71b1f9ebc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5085",
    "kind": "arxiv",
    "version": 1
  }
}