Pith Number

pith:Y4KB7ZZP

pith:2004:Y4KB7ZZPHIJ47AKK5BLOQMQ7AG

not attested not anchored not stored refs pending

Noncommutative Double Bruhat cells and their factorizations

Arkady Berenstein, Vladimir Retakh

arxiv:math/0407010 v2 · 2004-07-01 · math.QA · 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{Y4KB7ZZPHIJ47AKK5BLOQMQ7AG}

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	2026-07-04T14:38:52.972014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7141fe72f3a13cf814ae856e8321f0196c823804bc3a97c9ebb764cdf9a877c

Aliases

arxiv: math/0407010 · arxiv_version: math/0407010v2 · doi: 10.48550/arxiv.math/0407010 · pith_short_12: Y4KB7ZZPHIJ4 · pith_short_16: Y4KB7ZZPHIJ47AKK · pith_short_8: Y4KB7ZZP

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/Y4KB7ZZPHIJ47AKK5BLOQMQ7AG \
  | 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: c7141fe72f3a13cf814ae856e8321f0196c823804bc3a97c9ebb764cdf9a877c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88d585de9333245ed913deec278542268cab9782c7e9fd67e8bd2dd6a54aa004",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2004-07-01T04:07:48Z",
    "title_canon_sha256": "edddca050c43f2a0f1cee6fe0b1bbf41ae809baf768b176fc6e022b9e6d0d30e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407010",
    "kind": "arxiv",
    "version": 2
  }
}