Pith Number

pith:L2LSN5US

pith:2026:L2LSN5USUMKHSHURMTOSF3D2XB

not attested not anchored not stored refs pending

Sharp hypercontractivity for free group von Neumann algebras

Haonan Zhang, Xinyuan Xie

arxiv:2606.03423 v1 · 2026-06-02 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L2LSN5USUMKHSHURMTOSF3D2XB}

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	2026-06-03T01:05:57.454803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963

Aliases

arxiv: 2606.03423 · arxiv_version: 2606.03423v1 · doi: 10.48550/arxiv.2606.03423 · pith_short_12: L2LSN5USUMKH · pith_short_16: L2LSN5USUMKHSHUR · pith_short_8: L2LSN5US

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/L2LSN5USUMKHSHURMTOSF3D2XB \
  | 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: 5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e6bb251aa17e6ce254499846cdf21bcd40978c8d735142002b1920f3afe6be5",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-06-02T10:09:13Z",
    "title_canon_sha256": "1cfa0104d74943613d35ea2bc425e453325f4f2e63485f2a7158682e683fb9a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03423",
    "kind": "arxiv",
    "version": 1
  }
}