Pith Number

pith:NAG4TYMD

pith:2011:NAG4TYMD5LO4HTR6VH7LIAQHME

not attested not anchored not stored refs pending

When is there a nontrivial extension-closed subcategory?

Ryo Takahashi

arxiv:1101.0991 v1 · 2011-01-05 · math.AC · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NAG4TYMD5LO4HTR6VH7LIAQHME}

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	2026-05-18T04:32:01.053091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

680dc9e183eaddc3ce3ea9feb40207611d2f0ae4d52ee3629555c5d108c5331d

Aliases

arxiv: 1101.0991 · arxiv_version: 1101.0991v1 · doi: 10.48550/arxiv.1101.0991 · pith_short_12: NAG4TYMD5LO4 · pith_short_16: NAG4TYMD5LO4HTR6 · pith_short_8: NAG4TYMD

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/NAG4TYMD5LO4HTR6VH7LIAQHME \
  | 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: 680dc9e183eaddc3ce3ea9feb40207611d2f0ae4d52ee3629555c5d108c5331d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ad759f5c1bd12f1e0147dacf8e3b405acaa79018269557e91a44e7dbdb58dbb",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-01-05T14:40:41Z",
    "title_canon_sha256": "d20d9bac081db2c04f27d366dafae95042d709565b7595f406d6aa7bede3cf51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0991",
    "kind": "arxiv",
    "version": 1
  }
}