Pith Number

pith:J7KO6NZO

pith:2013:J7KO6NZOH4O3PL5RIJ3QQ4E5VJ

not attested not anchored not stored refs pending

Irrational Hilbert-Kunz multiplicities

Holger Brenner

arxiv:1305.5873 v1 · 2013-05-25 · 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{J7KO6NZOH4O3PL5RIJ3QQ4E5VJ}

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	2026-05-18T03:24:53.452386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fd4ef372e3f1db7afb1427708709daa47c94c2bdd9c09f669522427a779fd55

Aliases

arxiv: 1305.5873 · arxiv_version: 1305.5873v1 · doi: 10.48550/arxiv.1305.5873 · pith_short_12: J7KO6NZOH4O3 · pith_short_16: J7KO6NZOH4O3PL5R · pith_short_8: J7KO6NZO

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/J7KO6NZOH4O3PL5RIJ3QQ4E5VJ \
  | 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: 4fd4ef372e3f1db7afb1427708709daa47c94c2bdd9c09f669522427a779fd55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2a6ba7d6e9dd9aed0fcaf6b83af793d5e1ec342dcb027e2545b97d0e8aa208",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-05-25T00:51:04Z",
    "title_canon_sha256": "f6b8ed8d6663bfa70992df1b2d93c6bf1dfba21d164343d9c7b3286807a396aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.5873",
    "kind": "arxiv",
    "version": 1
  }
}