Pith Number

pith:PK2OWHSE

pith:2017:PK2OWHSES4TXEPEXDEECLGIVU7

not attested not anchored not stored refs pending

Koszul duality for Kac-Moody groups and characters of tilting modules

Geordie Williamson, Pramod Achar, Shotaro Makisumi, Simon Riche

arxiv:1706.00183 v1 · 2017-06-01 · 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{PK2OWHSES4TXEPEXDEECLGIVU7}

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	2026-05-18T00:43:14.828965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ab4eb1e449727723c971908259915a7e61381dd8831ce7b9a7c40730cad842d

Aliases

arxiv: 1706.00183 · arxiv_version: 1706.00183v1 · doi: 10.48550/arxiv.1706.00183 · pith_short_12: PK2OWHSES4TX · pith_short_16: PK2OWHSES4TXEPEX · pith_short_8: PK2OWHSE

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/PK2OWHSES4TXEPEXDEECLGIVU7 \
  | 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: 7ab4eb1e449727723c971908259915a7e61381dd8831ce7b9a7c40730cad842d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc3a546de97849cdfe83be13217066486160cfa1050e2a472b8d78b9f0216a76",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2017-06-01T07:02:51Z",
    "title_canon_sha256": "5246134645be101a351e657418f67d6ef9eda351fa7f1d6f7268c406b1acdac2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.00183",
    "kind": "arxiv",
    "version": 1
  }
}