Pith Number

pith:LPKAVAR5

pith:2011:LPKAVAR5FRFJCB6PJXNWMCSS3T

not attested not anchored not stored refs pending

Kac's Theorem for equipped graphs and for maximal rank representations

William Crawley-Boevey

arxiv:1107.5726 v2 · 2011-07-28 · 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{LPKAVAR5FRFJCB6PJXNWMCSS3T}

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	2026-05-18T04:13:46.750998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd40a823d2c4a9107cf4ddb660a52dce5522750b03807dc10f9a8ba64fd2e52

Aliases

arxiv: 1107.5726 · arxiv_version: 1107.5726v2 · doi: 10.48550/arxiv.1107.5726 · pith_short_12: LPKAVAR5FRFJ · pith_short_16: LPKAVAR5FRFJCB6P · pith_short_8: LPKAVAR5

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/LPKAVAR5FRFJCB6PJXNWMCSS3T \
  | 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: 5bd40a823d2c4a9107cf4ddb660a52dce5522750b03807dc10f9a8ba64fd2e52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "968575932c46b2fdb4d85dd18367798c0143ade4c7b1d5e01495323c89d0bea9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-07-28T14:36:48Z",
    "title_canon_sha256": "bcc3bf23ab6f3a1e8fac328caf57312c7b0599eab5f320cb9bbd8183d82a748e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5726",
    "kind": "arxiv",
    "version": 2
  }
}