Pith Number

pith:BYHUNPZP

pith:2012:BYHUNPZP7NXYNKFQHPIJG5UYHH

not attested not anchored not stored refs pending

Ringel modules and homological subcategories

Changchang Xi, Hongxing Chen

arxiv:1206.0522 v1 · 2012-06-04 · math.RT · math.AC · 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{BYHUNPZP7NXYNKFQHPIJG5UYHH}

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	2026-05-18T03:54:17.436947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e0f46bf2ffb6f86a8b03bd093769839e168e102b910f47f3423364b05695479

Aliases

arxiv: 1206.0522 · arxiv_version: 1206.0522v1 · doi: 10.48550/arxiv.1206.0522 · pith_short_12: BYHUNPZP7NXY · pith_short_16: BYHUNPZP7NXYNKFQ · pith_short_8: BYHUNPZP

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/BYHUNPZP7NXYNKFQHPIJG5UYHH \
  | 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: 0e0f46bf2ffb6f86a8b03bd093769839e168e102b910f47f3423364b05695479

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7bef3c56a0da8dec553eda555efded180bdeeb80aef0d8fb9deab1453c9d8b2",
    "cross_cats_sorted": [
      "math.AC",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-06-04T05:34:43Z",
    "title_canon_sha256": "b59a6808fd50683a3e8b2c9882f651d3b61e505c82d6f202fabc242147384f78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0522",
    "kind": "arxiv",
    "version": 1
  }
}