Pith Number

pith:FXTDSA5Z

pith:2011:FXTDSA5Z5OPLMKEPIXSECY6RFQ

not attested not anchored not stored refs pending

Monic representations and Gorenstein-projective modules

Pu Zhang, Xiu-Hua Luo

arxiv:1110.6021 v1 · 2011-10-27 · math.RT · 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{FXTDSA5Z5OPLMKEPIXSECY6RFQ}

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	2026-05-18T04:10:09.917556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de63903b9eb9eb6288f45e44163d12c1e0290104c072192cb8bd2de699012aa

Aliases

arxiv: 1110.6021 · arxiv_version: 1110.6021v1 · doi: 10.48550/arxiv.1110.6021 · pith_short_12: FXTDSA5Z5OPL · pith_short_16: FXTDSA5Z5OPLMKEP · pith_short_8: FXTDSA5Z

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/FXTDSA5Z5OPLMKEPIXSECY6RFQ \
  | 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: 2de63903b9eb9eb6288f45e44163d12c1e0290104c072192cb8bd2de699012aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dbde34e3901e63d35dc6ab12d7baa23e3e663761269ee456406bba3454f64c6",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-10-27T09:18:37Z",
    "title_canon_sha256": "42ab47f9049b3bac82b370d34d323a1006e33c0bc37e142cd37b538dc0e9bdd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6021",
    "kind": "arxiv",
    "version": 1
  }
}