Pith Number

pith:ZMJPTQ2W

pith:2010:ZMJPTQ2WJSXLTU6QG42VH6RVQL

not attested not anchored not stored refs pending

Some properties and applications of $F$-finite $F$-modules

Mordechai Katzman

arxiv:1009.2668 v2 · 2010-09-14 · 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{ZMJPTQ2WJSXLTU6QG42VH6RVQL}

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	2026-05-18T04:30:04.550244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb12f9c3564caeb9d3d0373553fa3582fbe0456f7b18a8cb43fe4ffc0fa9372f

Aliases

arxiv: 1009.2668 · arxiv_version: 1009.2668v2 · doi: 10.48550/arxiv.1009.2668 · pith_short_12: ZMJPTQ2WJSXL · pith_short_16: ZMJPTQ2WJSXLTU6Q · pith_short_8: ZMJPTQ2W

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/ZMJPTQ2WJSXLTU6QG42VH6RVQL \
  | 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: cb12f9c3564caeb9d3d0373553fa3582fbe0456f7b18a8cb43fe4ffc0fa9372f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79ba592224aede1905d9d29da54c0de5ecde697677329df5799f5aa504bfb20e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-09-14T13:54:57Z",
    "title_canon_sha256": "0edf959f44fba9dba59c70a0a5046a0c87e63bc6dd5b2efe34f1e0d7142bccd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2668",
    "kind": "arxiv",
    "version": 2
  }
}