Pith Number

pith:WQ3OUZR5

pith:2026:WQ3OUZR5Y5YDUVUCIPRJ5H4R3U

not attested not anchored not stored refs pending

An isoperimetric inequality for Neumann eigenvalues with radial log-concave measures

Anqiang Zhu, Kui Wang, Xiaomei Sun

arxiv:2608.08748 v1 · 2026-08-09 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WQ3OUZR5Y5YDUVUCIPRJ5H4R3U}

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	2026-08-11T01:25:13.126321Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b436ea663dc7703a568243e29e9f91dd1742bf7ece85e2b68f95da342cb88af8

Aliases

arxiv: 2608.08748 · arxiv_version: 2608.08748v1 · doi: 10.48550/arxiv.2608.08748 · pith_short_12: WQ3OUZR5Y5YD · pith_short_16: WQ3OUZR5Y5YDUVUC · pith_short_8: WQ3OUZR5

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/WQ3OUZR5Y5YDUVUCIPRJ5H4R3U \
  | 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: b436ea663dc7703a568243e29e9f91dd1742bf7ece85e2b68f95da342cb88af8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0f1535a721b4cd9f8be14707148ce3bc0afa24566e527fea14365adb2092135",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-08-09T14:53:04Z",
    "title_canon_sha256": "668d395f01322fd84de040bd25931181bd37518f078b3af88ba107fe1068efc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08748",
    "kind": "arxiv",
    "version": 1
  }
}