Pith Number

pith:Z2RP5FE3

pith:2013:Z2RP5FE3RI4Q6DFMFXP5T5NUYI

not attested not anchored not stored refs pending

Gorenstein injective precovers, covers, and envelopes

Alina Iacob, Edgar Enochs, Sergio Estrada

arxiv:1301.5694 v1 · 2013-01-24 · 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{Z2RP5FE3RI4Q6DFMFXP5T5NUYI}

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	2026-05-18T03:35:37.675060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cea2fe949b8a390f0cac2ddfd9f5b4c234dd9db9feda00186ac0fa0552512aa6

Aliases

arxiv: 1301.5694 · arxiv_version: 1301.5694v1 · doi: 10.48550/arxiv.1301.5694 · pith_short_12: Z2RP5FE3RI4Q · pith_short_16: Z2RP5FE3RI4Q6DFM · pith_short_8: Z2RP5FE3

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/Z2RP5FE3RI4Q6DFMFXP5T5NUYI \
  | 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: cea2fe949b8a390f0cac2ddfd9f5b4c234dd9db9feda00186ac0fa0552512aa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b87979630949a90a623345c7d5221ad18d740b302623235e048c516a5b8e4085",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-01-24T03:44:59Z",
    "title_canon_sha256": "094110585d56049c054645a3a9cc9d01426547628c2289aa1cfd06f068e44345"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5694",
    "kind": "arxiv",
    "version": 1
  }
}