Pith Number

pith:STU32ZNQ

pith:2024:STU32ZNQ6DWNOINLSOEHUU4KN6

not attested not anchored not stored refs pending

Bessel functions and Weyl's law for balls and spherical shells

Jingwei Guo, Tao Jiang, Xuerui Yang, Zuoqin Wang

arxiv:2412.14059 v1 · 2024-12-18 · math.CA · math.NT · 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{STU32ZNQ6DWNOINLSOEHUU4KN6}

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	2026-07-05T09:51:12.994297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94e9bd65b0f0ecd721ab93887a538a6f819cca655b0b43159ea818959b7ec121

Aliases

arxiv: 2412.14059 · arxiv_version: 2412.14059v1 · doi: 10.48550/arxiv.2412.14059 · pith_short_12: STU32ZNQ6DWN · pith_short_16: STU32ZNQ6DWNOINL · pith_short_8: STU32ZNQ

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/STU32ZNQ6DWNOINLSOEHUU4KN6 \
  | 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: 94e9bd65b0f0ecd721ab93887a538a6f819cca655b0b43159ea818959b7ec121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98e1c8da046db94bf518ce0460915a5b03818633764ad431999e8312eb71557c",
    "cross_cats_sorted": [
      "math.NT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-12-18T17:07:22Z",
    "title_canon_sha256": "63e8637c1f39a8b6ed992fbe35b277ba338efa19194c96b8a094e2a29616d6b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.14059",
    "kind": "arxiv",
    "version": 1
  }
}