Pith Number

pith:BV4TZZWS

pith:2007:BV4TZZWSB44PHN22XZXKDT4UFB

not attested not anchored not stored refs pending

On decomposition numbers and Alvis-Curtis duality

Bernd Ackermann, Sibylle Schroll

arxiv:0709.3223 v2 · 2007-09-20 · 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{BV4TZZWSB44PHN22XZXKDT4UFB}

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	2026-05-17T23:47:32.071169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d793ce6d20f38f3b75abe6ea1cf94284296c85b74bd37df0327a243370619e6

Aliases

arxiv: 0709.3223 · arxiv_version: 0709.3223v2 · doi: 10.48550/arxiv.0709.3223 · pith_short_12: BV4TZZWSB44P · pith_short_16: BV4TZZWSB44PHN22 · pith_short_8: BV4TZZWS

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/BV4TZZWSB44PHN22XZXKDT4UFB \
  | 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: 0d793ce6d20f38f3b75abe6ea1cf94284296c85b74bd37df0327a243370619e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "668167995a1b7709cc255513880e67c4f8469a2d460a77e21fb8a4952b53d755",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2007-09-20T13:12:05Z",
    "title_canon_sha256": "6f6eabccfb6b18a514839a5cee06859b45003f7217edbe358211e1d3c9c5945b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.3223",
    "kind": "arxiv",
    "version": 2
  }
}