Pith Number

pith:2NY7TI2V

pith:2012:2NY7TI2VUGI76IQBDWTSHRO5HG

not attested not anchored not stored refs pending

Inequalities on Bruhat graphs, R- and Kazhdan-Lusztig polynomials

Masato Kobayashi

arxiv:1211.4305 v1 · 2012-11-19 · 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{2NY7TI2VUGI76IQBDWTSHRO5HG}

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	2026-05-18T03:40:27.328534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d371f9a355a191ff22011da723c5dd398b4fae630223558c0c825906d380c001

Aliases

arxiv: 1211.4305 · arxiv_version: 1211.4305v1 · doi: 10.48550/arxiv.1211.4305 · pith_short_12: 2NY7TI2VUGI7 · pith_short_16: 2NY7TI2VUGI76IQB · pith_short_8: 2NY7TI2V

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/2NY7TI2VUGI76IQBDWTSHRO5HG \
  | 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: d371f9a355a191ff22011da723c5dd398b4fae630223558c0c825906d380c001

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d89629b5fe39eeb1a2c21308d0e3541d24b9ec464db951a5dab6c47cfced27c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-19T05:28:46Z",
    "title_canon_sha256": "b40709a412b4fceeeeb39e33263da6a49b333c92047582242ed20da8381b2cc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4305",
    "kind": "arxiv",
    "version": 1
  }
}