Pith Number

pith:2EJN65AO

pith:2017:2EJN65AOQ6Z3BLLW5FONHJFLG5

not attested not anchored not stored refs pending

Hilbert-Kunz multiplicity of binoids

Bayarjargal Batsukh, Holger Brenner

arxiv:1710.05761 v1 · 2017-10-13 · math.AC · 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{2EJN65AOQ6Z3BLLW5FONHJFLG5}

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	2026-05-18T00:32:48.252780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d112df740e87b3b0ad76e95cd3a4ab37507b022105c740e135ca101c9f291f80

Aliases

arxiv: 1710.05761 · arxiv_version: 1710.05761v1 · doi: 10.48550/arxiv.1710.05761 · pith_short_12: 2EJN65AOQ6Z3 · pith_short_16: 2EJN65AOQ6Z3BLLW · pith_short_8: 2EJN65AO

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/2EJN65AOQ6Z3BLLW5FONHJFLG5 \
  | 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: d112df740e87b3b0ad76e95cd3a4ab37507b022105c740e135ca101c9f291f80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "012f99bc33d83b8d96c7ca59793a93ecce7ddf2962f9af1ec4035bbb2301331b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-10-13T15:16:58Z",
    "title_canon_sha256": "4fc01425132bf1d6485092612f0ae1d3448379e76949ca42721a6d42de7f5f0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.05761",
    "kind": "arxiv",
    "version": 1
  }
}