Pith Number

pith:TXJVHKWU

pith:1996:TXJVHKWUER4L2M22HHIXVJZ4UK

not attested not anchored not stored refs pending

Hilbert-Kunz functions of cubic curves and surfaces

Qun Chen, Ragnar-Olaf Buchweitz

arxiv:alg-geom/9610009 v1 · 1996-10-09 · alg-geom · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TXJVHKWUER4L2M22HHIXVJZ4UK}

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	2026-07-04T15:08:07.123398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd353aad42478bd335a39d17aa73ca2a61c247752f3f5dd878f840594af8b19

Aliases

arxiv: alg-geom/9610009 · arxiv_version: alg-geom/9610009v1 · doi: 10.48550/arxiv.alg-geom/9610009 · pith_short_12: TXJVHKWUER4L · pith_short_16: TXJVHKWUER4L2M22 · pith_short_8: TXJVHKWU

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/TXJVHKWUER4L2M22HHIXVJZ4UK \
  | 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: 9dd353aad42478bd335a39d17aa73ca2a61c247752f3f5dd878f840594af8b19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21a093ca4fbbea96c10821bd55365a7811597511e7c5a1dc08a258b63b261b11",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG"
    ],
    "license": "",
    "primary_cat": "alg-geom",
    "submitted_at": "1996-10-09T20:50:48Z",
    "title_canon_sha256": "0f4ee8b0f686856dcb1999f0a5e0a29d5064ac2d138b664d05d541c2db128db3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "alg-geom/9610009",
    "kind": "arxiv",
    "version": 1
  }
}