Pith Number

pith:AY2LSM7R

pith:2018:AY2LSM7RPRLSMK76IZWW3BGKDQ

not attested not anchored not stored refs pending

Gorenstein-projective and semi-Gorenstein-projective modules

Claus Michael Ringel, Pu Zhang

arxiv:1808.01809 v4 · 2018-08-06 · 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{AY2LSM7RPRLSMK76IZWW3BGKDQ}

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.

Cited by

1 paper in Pith

On weakly Gorenstein algebras

Receipt and verification

First computed	2026-07-05T00:48:36.146689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b

Aliases

arxiv: 1808.01809 · arxiv_version: 1808.01809v4 · doi: 10.48550/arxiv.1808.01809 · pith_short_12: AY2LSM7RPRLS · pith_short_16: AY2LSM7RPRLSMK76 · pith_short_8: AY2LSM7R

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/AY2LSM7RPRLSMK76IZWW3BGKDQ \
  | 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: 0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0165de3dc4020b47a22656e343c50d5c77970015ae14bf124a5d91623d7e21b",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2018-08-06T10:13:55Z",
    "title_canon_sha256": "0914f6aa4ed07e5c88dc62b114f15bb43689e08621baff74657edda9a8acc597"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01809",
    "kind": "arxiv",
    "version": 4
  }
}