Pith Number

pith:CJFCA5T5

pith:2009:CJFCA5T5WLRH75FGLEJAHVKRQO

not attested not anchored not stored refs pending

A new approach to the Koszul property in representation theory using graded subalgebras

Brian Parshall, Leonard Scott

arxiv:0910.0633 v4 · 2009-10-04 · math.GR · 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{CJFCA5T5WLRH75FGLEJAHVKRQO}

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	2026-05-18T03:56:45.360498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

124a20767db2e27ff4a6591203d551838e50690c9f815f7ea8a9c89622bc8d28

Aliases

arxiv: 0910.0633 · arxiv_version: 0910.0633v4 · doi: 10.48550/arxiv.0910.0633 · pith_short_12: CJFCA5T5WLRH · pith_short_16: CJFCA5T5WLRH75FG · pith_short_8: CJFCA5T5

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/CJFCA5T5WLRH75FGLEJAHVKRQO \
  | 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: 124a20767db2e27ff4a6591203d551838e50690c9f815f7ea8a9c89622bc8d28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87f691228e0a55d83393f8268faad7eeb55b6300cc4c39c346a4709ad13c1543",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-10-04T19:25:52Z",
    "title_canon_sha256": "395dad7a5cf32165fe48883476daea89f2ad3e645d56bdd24fcd030b596f3a8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.0633",
    "kind": "arxiv",
    "version": 4
  }
}