Pith Number

pith:ILVLL55F

pith:2008:ILVLL55FOPHEQMLTGQMCH74MJQ

not attested not anchored not stored refs pending

On the restricted Verma modules at the critical level

Peter Fiebig, Tomoyuki Arakawa

arxiv:0812.3334 v3 · 2008-12-17 · 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{ILVLL55FOPHEQMLTGQMCH74MJQ}

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	2026-05-18T01:34:46.030207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42eab5f7a573ce483173341823ff8c4c377f4c6adf153f0dad308fb822758278

Aliases

arxiv: 0812.3334 · arxiv_version: 0812.3334v3 · doi: 10.48550/arxiv.0812.3334 · pith_short_12: ILVLL55FOPHE · pith_short_16: ILVLL55FOPHEQMLT · pith_short_8: ILVLL55F

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/ILVLL55FOPHEQMLTGQMCH74MJQ \
  | 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: 42eab5f7a573ce483173341823ff8c4c377f4c6adf153f0dad308fb822758278

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a449c597e97f4752d9a7513506b03d4bfc890e42ad43048512e71ceb17c000e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2008-12-17T17:54:21Z",
    "title_canon_sha256": "bff37d8db2e5cdd37293d1d237cde85b4a05f14b87702ed09dec52e39e338664"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3334",
    "kind": "arxiv",
    "version": 3
  }
}