Pith Number

pith:U4BERXR7

pith:2026:U4BERXR7T7FLLRICIFML2JOHBL

not attested not anchored not stored refs pending

Sharp Endpoint Eigenfunction Estimates for the Two-Dimensional Hermite Operator

Cheng Zhang, Guiyu Xie

arxiv:2608.08423 v1 · 2026-08-09 · math.AP · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U4BERXR7T7FLLRICIFML2JOHBL}

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	2026-08-11T01:22:36.069311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a70248de3f9fcab5c5024158bd25c70afe1e6025309b17fe9d9222cbd773a91f

Aliases

arxiv: 2608.08423 · arxiv_version: 2608.08423v1 · doi: 10.48550/arxiv.2608.08423 · pith_short_12: U4BERXR7T7FL · pith_short_16: U4BERXR7T7FLLRIC · pith_short_8: U4BERXR7

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/U4BERXR7T7FLLRICIFML2JOHBL \
  | 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: a70248de3f9fcab5c5024158bd25c70afe1e6025309b17fe9d9222cbd773a91f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66555222b1e5c70456fac8b862bf9da7d1a4a68a1d1b620335d8ba689cb257fe",
    "cross_cats_sorted": [
      "math.CA",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-09T02:43:57Z",
    "title_canon_sha256": "bc474bd95f9cf26227579300f034b35a849da417e7ba6e977c8c15ad047711d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08423",
    "kind": "arxiv",
    "version": 1
  }
}