Pith Number

pith:HL4XFSRC

pith:2009:HL4XFSRCPWPVDXKTXGWZDAJZD6

not attested not anchored not stored refs pending

Examples of quantum cluster algebras associated to partial flag varieties

Jan E. Grabowski

arxiv:0907.4922 v3 · 2009-07-28 · math.QA · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HL4XFSRCPWPVDXKTXGWZDAJZD6}

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	2026-05-18T04:08:33.701468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af972ca227d9f51dd53b9ad9181391fb287e34046b915c0f949c8db305ce52c

Aliases

arxiv: 0907.4922 · arxiv_version: 0907.4922v3 · doi: 10.48550/arxiv.0907.4922 · pith_short_12: HL4XFSRCPWPV · pith_short_16: HL4XFSRCPWPVDXKT · pith_short_8: HL4XFSRC

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/HL4XFSRCPWPVDXKTXGWZDAJZD6 \
  | 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: 3af972ca227d9f51dd53b9ad9181391fb287e34046b915c0f949c8db305ce52c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59e293640affd52e4bfe5196df7a28c06ff058ce15d6f7187be5dc6d8e0c6e96",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-07-28T16:33:27Z",
    "title_canon_sha256": "7affdbba9132d11c961917b119454f84f375fdf57b356b5727bc8fa5b44deaba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4922",
    "kind": "arxiv",
    "version": 3
  }
}