Pith Number

pith:YJAXVR5O

pith:2011:YJAXVR5ONCXOSB57RVVGRQI2HZ

not attested not anchored not stored refs pending

A module-theoretic interpretation of Schiffler's expansion formula

Jie Zhang, Thomas Br\"ustle

arxiv:1105.5673 v1 · 2011-05-28 · 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{YJAXVR5ONCXOSB57RVVGRQI2HZ}

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	2026-05-18T04:21:01.831706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2417ac7ae68aee907bf8d6a68c11a3e6c2fded5b7d7dae4d4af77155da9fdad

Aliases

arxiv: 1105.5673 · arxiv_version: 1105.5673v1 · doi: 10.48550/arxiv.1105.5673 · pith_short_12: YJAXVR5ONCXO · pith_short_16: YJAXVR5ONCXOSB57 · pith_short_8: YJAXVR5O

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/YJAXVR5ONCXOSB57RVVGRQI2HZ \
  | 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: c2417ac7ae68aee907bf8d6a68c11a3e6c2fded5b7d7dae4d4af77155da9fdad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ce83b042a6e3d2cfa590c4504c5ebc6e28bbab0fd38f0b7abf5be2115e6fd4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-05-28T00:35:31Z",
    "title_canon_sha256": "f3b5c9794cecd42637488249aa77e4a2d707551b1892eb0220affdffb78c2a27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5673",
    "kind": "arxiv",
    "version": 1
  }
}