Pith Number

pith:FXRYDSHL

pith:2018:FXRYDSHLTYM4AWUKXZWGG2DA5Q

not attested not anchored not stored refs pending

Gorenstein projective and injective dimensions over Frobenius extensions

Wei Ren

arxiv:1801.07305 v4 · 2018-01-22 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FXRYDSHLTYM4AWUKXZWGG2DA5Q}

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	2026-05-17T23:40:49.779996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de381c8eb9e19c05a8abe6c636860ec1aeafe8563cdb8bd8f6b62e0d3113ac9

Aliases

arxiv: 1801.07305 · arxiv_version: 1801.07305v4 · doi: 10.48550/arxiv.1801.07305 · pith_short_12: FXRYDSHLTYM4 · pith_short_16: FXRYDSHLTYM4AWUK · pith_short_8: FXRYDSHL

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/FXRYDSHLTYM4AWUKXZWGG2DA5Q \
  | 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: 2de381c8eb9e19c05a8abe6c636860ec1aeafe8563cdb8bd8f6b62e0d3113ac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80131568faac5eabdb32529c9ff6ef0043f7dbd846644df075554299382ee07a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2018-01-22T20:23:21Z",
    "title_canon_sha256": "6c4c62255be173ccbab502fd41911f9a4a0fb24bf1a5ecf1464c82cc1c70fd90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.07305",
    "kind": "arxiv",
    "version": 4
  }
}