Pith Number

pith:2WKMYF4H

pith:2011:2WKMYF4HDVTGMOZD4RHUSBTTRL

not attested not anchored not stored refs pending

Invertible unital bimodules over rings with local units, and related exact sequences of groups II

J. G\'omez-Torrecillas, L. El Kaoutit

arxiv:1109.5062 v1 · 2011-09-23 · math.RA · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2WKMYF4HDVTGMOZD4RHUSBTTRL}

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	2026-05-18T04:12:21.857021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d594cc17871d66663b23e44f4906738af27e8745d1abed6f5fa5ccc331c3e798

Aliases

arxiv: 1109.5062 · arxiv_version: 1109.5062v1 · doi: 10.48550/arxiv.1109.5062 · pith_short_12: 2WKMYF4HDVTG · pith_short_16: 2WKMYF4HDVTGMOZD · pith_short_8: 2WKMYF4H

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/2WKMYF4HDVTGMOZD4RHUSBTTRL \
  | 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: d594cc17871d66663b23e44f4906738af27e8745d1abed6f5fa5ccc331c3e798

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b06bd088fae7dcea8786e304788cf68feaf03dab89a8d5a03dcfea230ae1ae53",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-09-23T13:01:30Z",
    "title_canon_sha256": "192b4a629a12e0720cee8ca84c4bef0b2de9d2dbeeaf86d712f26583d637c0cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5062",
    "kind": "arxiv",
    "version": 1
  }
}