Pith Number

pith:SKK7L7BJ

pith:2026:SKK7L7BJXFFBJ363EKSX2XYSNC

not attested not anchored not stored refs pending

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^p$ Ridge Integral Spaces for ReLU$^k$ Networks

Juncai He, Zitong Tian

arxiv:2606.24795 v1 · 2026-06-23 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SKK7L7BJXFFBJ363EKSX2XYSNC}

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	2026-06-24T01:15:42.546095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9295f5fc29b94a14efdb22a57d5f1268911df3f1a0dc1cf15b84c59ad931a771

Aliases

arxiv: 2606.24795 · arxiv_version: 2606.24795v1 · doi: 10.48550/arxiv.2606.24795 · pith_short_12: SKK7L7BJXFFB · pith_short_16: SKK7L7BJXFFBJ363 · pith_short_8: SKK7L7BJ

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/SKK7L7BJXFFBJ363EKSX2XYSNC \
  | 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: 9295f5fc29b94a14efdb22a57d5f1268911df3f1a0dc1cf15b84c59ad931a771

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2260b9332790540727cb871fd6fa2b4044dc678d01463d0b6d8e2a890195792a",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-23T16:48:30Z",
    "title_canon_sha256": "22543cacb342f3fd5542f25be769fc6cd43200f90db9c6207d51e404a9cf22d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24795",
    "kind": "arxiv",
    "version": 1
  }
}