Pith Number

pith:FOLU3SP2

pith:2026:FOLU3SP2IWH3OB4PSAG32TIILM

not attested not anchored not stored refs pending

Real-rootedness of Kazhdan--Lusztig and $Z$-polynomials of thagomizer matroids and graphic matroids of $K_{2,n}$

Philip B. Zhang

arxiv:2608.02303 v1 · 2026-08-03 · 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{FOLU3SP2IWH3OB4PSAG32TIILM}

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	2026-08-04T02:11:46.549341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b974dc9fa458fb7078f900dbd4d085b17a82ed776ff10b75f193e1c23da388f

Aliases

arxiv: 2608.02303 · arxiv_version: 2608.02303v1 · doi: 10.48550/arxiv.2608.02303 · pith_short_12: FOLU3SP2IWH3 · pith_short_16: FOLU3SP2IWH3OB4P · pith_short_8: FOLU3SP2

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/FOLU3SP2IWH3OB4PSAG32TIILM \
  | 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: 2b974dc9fa458fb7078f900dbd4d085b17a82ed776ff10b75f193e1c23da388f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8139cf2c6f8603d47b1dc273e47e5938832ff244b68783c213680dca5198b9f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-03T14:28:37Z",
    "title_canon_sha256": "06e75738e9208b5e531a7a395550b799c3377b46af4abe84830e401818070561"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02303",
    "kind": "arxiv",
    "version": 1
  }
}