Pith Number

pith:V7FXYBI7

pith:2011:V7FXYBI732S4PJHSUJS26FAU25

not attested not anchored not stored refs pending

Characterizing rings in terms of the extent of injectivity and projectivity of their modules

Jos\'e E. Simental, Sergio R. L\'opez-Permouth

arxiv:1111.2090 v2 · 2011-11-09 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7FXYBI732S4PJHSUJS26FAU25}

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	2026-05-18T03:17:36.054165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afcb7c051fdea5c7a4f2a265af1414d76cb63d3b825caf8687ce15a0773ead9c

Aliases

arxiv: 1111.2090 · arxiv_version: 1111.2090v2 · doi: 10.48550/arxiv.1111.2090 · pith_short_12: V7FXYBI732S4 · pith_short_16: V7FXYBI732S4PJHS · pith_short_8: V7FXYBI7

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/V7FXYBI732S4PJHSUJS26FAU25 \
  | 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: afcb7c051fdea5c7a4f2a265af1414d76cb63d3b825caf8687ce15a0773ead9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bc4735b4aa7b9e9c177f73d7b59673357e2fdd77df47436e711bb0d64ce93c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-11-09T02:28:25Z",
    "title_canon_sha256": "5384b7aad7d2353118985d8759f84f948c874308109b9f63451d21c6bcb53759"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2090",
    "kind": "arxiv",
    "version": 2
  }
}