Pith Number

pith:YMNR77GJ

pith:2000:YMNR77GJ64Q3BLLYXJSL7GLZM5

not attested not anchored not stored refs pending

Connected components of real double Bruhat cells

Andrei Zelevinsky (Northeastern University)

arxiv:math/0003231 v2 · 2000-03-31 · math.AG · 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{YMNR77GJ64Q3BLLYXJSL7GLZM5}

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	2026-07-04T14:34:26.599436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c31b1ffcc9f721b0ad78ba64bf99796779061c70705092d93852a2d793b78f80

Aliases

arxiv: math/0003231 · arxiv_version: math/0003231v2 · doi: 10.48550/arxiv.math/0003231 · pith_short_12: YMNR77GJ64Q3 · pith_short_16: YMNR77GJ64Q3BLLY · pith_short_8: YMNR77GJ

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/YMNR77GJ64Q3BLLYXJSL7GLZM5 \
  | 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: c31b1ffcc9f721b0ad78ba64bf99796779061c70705092d93852a2d793b78f80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9756f111f6663902a2f63089e707f5a5b873a6c4a74874d66be684c883149dab",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-03-31T14:23:37Z",
    "title_canon_sha256": "9ccba35c258d99577253b01d4af2c481814bbda813df869d35a2a520f15dc0ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0003231",
    "kind": "arxiv",
    "version": 2
  }
}