Pith Number

pith:NQNMDS42

pith:2013:NQNMDS422KGDB4NFBNY3NZFEDB

not attested not anchored not stored refs pending

Strong Krull primes and flat modules

Jay Shapiro, Neil Epstein

arxiv:1303.7458 v3 · 2013-03-29 · 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{NQNMDS422KGDB4NFBNY3NZFEDB}

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	2026-05-18T01:24:38.802896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c1ac1cb9ad28c30f1a50b71b6e4a418408bd2df8a8dd031f8c5ea6bc2d710e1

Aliases

arxiv: 1303.7458 · arxiv_version: 1303.7458v3 · doi: 10.48550/arxiv.1303.7458 · pith_short_12: NQNMDS422KGD · pith_short_16: NQNMDS422KGDB4NF · pith_short_8: NQNMDS42

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/NQNMDS422KGDB4NFBNY3NZFEDB \
  | 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: 6c1ac1cb9ad28c30f1a50b71b6e4a418408bd2df8a8dd031f8c5ea6bc2d710e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af8094314c27fcbf856329138e1b7f6c961e350b69f84087deeccfa783bdf714",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-03-29T19:00:11Z",
    "title_canon_sha256": "147512b72b98ed609f7d8d6e7508563dcfc320972907bf0ad49cbb199eb54000"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.7458",
    "kind": "arxiv",
    "version": 3
  }
}