Pith Number

pith:SKM6JBSX

pith:2011:SKM6JBSXE7AHLJF7FT4CH7YELY

not attested not anchored not stored refs pending

The Real-Rootedness and Log-concavities of Coordinator Polynomials of Weyl Group Lattices

David G. L. Wang, Tongyuan Zhao

arxiv:1106.3765 v2 · 2011-06-19 · 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{SKM6JBSXE7AHLJF7FT4CH7YELY}

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	2026-05-18T03:42:24.059150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9299e4865727c075a4bf2cf823ff045e3921be54fb7c36ce01aec27048ddf13a

Aliases

arxiv: 1106.3765 · arxiv_version: 1106.3765v2 · doi: 10.48550/arxiv.1106.3765 · pith_short_12: SKM6JBSXE7AH · pith_short_16: SKM6JBSXE7AHLJF7 · pith_short_8: SKM6JBSX

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/SKM6JBSXE7AHLJF7FT4CH7YELY \
  | 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: 9299e4865727c075a4bf2cf823ff045e3921be54fb7c36ce01aec27048ddf13a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "053862a484ed6171050a3be8daa576631d92f50339f12c0027031a3dfe6e3d06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-19T17:35:48Z",
    "title_canon_sha256": "0f638e28bb547526233018c5e320671e5430e8aa213a2651eae354f6a008a9b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3765",
    "kind": "arxiv",
    "version": 2
  }
}