Pith Number

pith:HPFUVNIG

pith:2013:HPFUVNIGWMBGIW33LJHGM5DO4S

not attested not anchored not stored refs pending

Gradings of positive rank on simple Lie algebras

Benedict H. Gross, Jiu-Kang Yu, Mark Reeder, Paul Levy

arxiv:1307.5765 v1 · 2013-07-22 · math.RT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPFUVNIGWMBGIW33LJHGM5DO4S}

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	2026-05-18T03:17:54.645775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bcb4ab506b302645b7b5a4e66746ee4ab5f3f3b42e7d9b40f85a9b3bb9ec60e

Aliases

arxiv: 1307.5765 · arxiv_version: 1307.5765v1 · doi: 10.48550/arxiv.1307.5765 · pith_short_12: HPFUVNIGWMBG · pith_short_16: HPFUVNIGWMBGIW33 · pith_short_8: HPFUVNIG

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/HPFUVNIGWMBGIW33LJHGM5DO4S \
  | 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: 3bcb4ab506b302645b7b5a4e66746ee4ab5f3f3b42e7d9b40f85a9b3bb9ec60e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "062073248074446afc4dfe740c13c543a6ae9f3165e1ff4c10240c19acac6863",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2013-07-22T16:30:18Z",
    "title_canon_sha256": "22b4ff45f61dca1a1070093630f072d51a3c65834d88aed1ce1473d44cba3e18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5765",
    "kind": "arxiv",
    "version": 1
  }
}