Pith Number

pith:Z5S43ROZ

pith:2002:Z5S43ROZYXZANBOO42Q7HWWCJO

not attested not anchored not stored refs pending

Lower bounds for Kazhdan-Lusztig polynomials from patterns

Sara Billey, Tom Braden

arxiv:math/0202252 v5 · 2002-02-24 · math.RT · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5S43ROZYXZANBOO42Q7HWWCJO}

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	2026-07-04T14:35:56.406569Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf65cdc5d9c5f20685cee6a1f3dac24bb931d5e190ee2d048036ff1ac6f495bf

Aliases

arxiv: math/0202252 · arxiv_version: math/0202252v5 · doi: 10.48550/arxiv.math/0202252 · pith_short_12: Z5S43ROZYXZA · pith_short_16: Z5S43ROZYXZANBOO · pith_short_8: Z5S43ROZ

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/Z5S43ROZYXZANBOO42Q7HWWCJO \
  | 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: cf65cdc5d9c5f20685cee6a1f3dac24bb931d5e190ee2d048036ff1ac6f495bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53c0f6944d37ea63366618825e435a6378b0450c1a926b31bd7d18ffb385b32a",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2002-02-24T18:49:56Z",
    "title_canon_sha256": "05dfcae2ccc270a6c6a451cd502ca176165fcacf9d32f48ca3090181317b5734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0202252",
    "kind": "arxiv",
    "version": 5
  }
}