Pith Number

pith:24AYIJTN

pith:2010:24AYIJTNRZ3RK6PGM32GCT4W67

not attested not anchored not stored refs pending

Hilbert-Kunz theory for nodal cubics, via sheaves

Paul Monsky

arxiv:1012.2354 v3 · 2010-12-10 · 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{24AYIJTNRZ3RK6PGM32GCT4W67}

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	2026-05-18T04:31:50.986676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d70184266d8e771579e666f4614f96f7fa9515e0c63e0d0c72c3a8e2f6e9014e

Aliases

arxiv: 1012.2354 · arxiv_version: 1012.2354v3 · doi: 10.48550/arxiv.1012.2354 · pith_short_12: 24AYIJTNRZ3R · pith_short_16: 24AYIJTNRZ3RK6PG · pith_short_8: 24AYIJTN

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/24AYIJTNRZ3RK6PGM32GCT4W67 \
  | 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: d70184266d8e771579e666f4614f96f7fa9515e0c63e0d0c72c3a8e2f6e9014e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "482f7423f3a22caa7891107d3404021bda30b40b2ac27ce93f00248ca85db410",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-10T19:17:22Z",
    "title_canon_sha256": "f48ff94bd1be19c4a36e469dcdcc24e7d70a5e043d915a63ea26278710722780"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2354",
    "kind": "arxiv",
    "version": 3
  }
}