Pith Number

pith:AF3EX65U

pith:2013:AF3EX65UIEOMYYR2RN7VE7W5LI

not attested not anchored not stored refs pending

Hilbert-Kunz functions over rings regular in codimension one

C.-Y. Jean Chan, Kazuhiko Kurano

arxiv:1301.5278 v2 · 2013-01-22 · 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{AF3EX65UIEOMYYR2RN7VE7W5LI}

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	2026-05-18T03:11:21.797210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01764bfbb4411ccc623a8b7f527edd5a34343aae87a8d9b7fa65457c85b91314

Aliases

arxiv: 1301.5278 · arxiv_version: 1301.5278v2 · doi: 10.48550/arxiv.1301.5278 · pith_short_12: AF3EX65UIEOM · pith_short_16: AF3EX65UIEOMYYR2 · pith_short_8: AF3EX65U

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/AF3EX65UIEOMYYR2RN7VE7W5LI \
  | 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: 01764bfbb4411ccc623a8b7f527edd5a34343aae87a8d9b7fa65457c85b91314

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "607bb8cfeb9b2f664caafe44d8a505ddcf2f8867d79e0de3e4234cb6c3f04646",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-01-22T19:07:33Z",
    "title_canon_sha256": "80aea55b7835ffc1b109c707ac73ae4eaba2d91993928cc7496905132c249948"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5278",
    "kind": "arxiv",
    "version": 2
  }
}