Pith Number

pith:WCFZWUR3

pith:2026:WCFZWUR3LTVIOUPWDD4VP3MTXX

not attested not anchored not stored refs pending

Cotorsion pairs, thick subcategories, and finitely generated Gorenstein projective modules

Jian Liu, Souvik Dey, Xue-Song Lu

arxiv:2603.01424 v2 · 2026-03-02 · math.RA · math.AC · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCFZWUR3LTVIOUPWDD4VP3MTXX}

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	2026-06-11T01:09:31.911570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b08b9b523b5cea8751f618f957ed93bdf32c6d1276c13de7c0d56ec1038419b0

Aliases

arxiv: 2603.01424 · arxiv_version: 2603.01424v2 · doi: 10.48550/arxiv.2603.01424 · pith_short_12: WCFZWUR3LTVI · pith_short_16: WCFZWUR3LTVIOUPW · pith_short_8: WCFZWUR3

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/WCFZWUR3LTVIOUPWDD4VP3MTXX \
  | 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: b08b9b523b5cea8751f618f957ed93bdf32c6d1276c13de7c0d56ec1038419b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b54e65e1afaed4fe931a72c8a735ebbcb726de25c895a45d00c7b657e4be6dff",
    "cross_cats_sorted": [
      "math.AC",
      "math.RT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-03-02T04:04:11Z",
    "title_canon_sha256": "67926992c41c7eb0d78c745a078e8a886add8851a3eaadd2417ad531ab1c6a0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.01424",
    "kind": "arxiv",
    "version": 2
  }
}