Pith Number

pith:DPWGWDOL

pith:2026:DPWGWDOLTKCUBPUEWT73QZXWKV

not attested not anchored not stored refs pending

Kazhdan--Lusztig polynomials of matroids need not be unimodal

Ronnie Cheng, Shurui Liu

arxiv:2607.24186 v1 · 2026-07-27 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPWGWDOLTKCUBPUEWT73QZXWKV}

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	2026-07-28T02:23:49.857207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bec6b0dcb9a8540be84b4ffb866f65576a0a9b392515ac4fb52f1e7f9c3bc25

Aliases

arxiv: 2607.24186 · arxiv_version: 2607.24186v1 · doi: 10.48550/arxiv.2607.24186 · pith_short_12: DPWGWDOLTKCU · pith_short_16: DPWGWDOLTKCUBPUE · pith_short_8: DPWGWDOL

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/DPWGWDOLTKCUBPUEWT73QZXWKV \
  | 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: 1bec6b0dcb9a8540be84b4ffb866f65576a0a9b392515ac4fb52f1e7f9c3bc25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "877e1006650243fdf98e55d3a294b33d11207e14b10a0997327be14a5c45f4be",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-27T09:07:02Z",
    "title_canon_sha256": "f0d8b6adb1b2b21c64114f21109aed199e593824868b24cbd6ffa59e0d7fb7d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24186",
    "kind": "arxiv",
    "version": 1
  }
}