Pith Number

pith:UTAUUML3

pith:2026:UTAUUML32JJBVZZCWIECEE6EXG

not attested not anchored not stored refs pending

Multigrade Neural Network Approximation

Shijun Zhang, Yuesheng Xu, Zuowei Shen

arxiv:2601.16884 v3 · 2026-01-23 · cs.LG · cs.NA · math.NA · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UTAUUML32JJBVZZCWIECEE6EXG}

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.

Cited by

1 paper in Pith

Geometric Layer-wise Approximation Rates for Deep Networks

Receipt and verification

First computed	2026-06-02T03:04:37.183894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4c14a317bd2521ae722b2082213c4b986435fad9d5dcb5d897a11281aa75e35

Aliases

arxiv: 2601.16884 · arxiv_version: 2601.16884v3 · doi: 10.48550/arxiv.2601.16884 · pith_short_12: UTAUUML32JJB · pith_short_16: UTAUUML32JJBVZZC · pith_short_8: UTAUUML3

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/UTAUUML32JJBVZZCWIECEE6EXG \
  | 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: a4c14a317bd2521ae722b2082213c4b986435fad9d5dcb5d897a11281aa75e35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f954b4577cf0acba283f9240aa02681c77671b5caf82ee522dae6c84eef0a0f6",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-23T16:46:25Z",
    "title_canon_sha256": "dacaaa80beacf5448b0c294f435fc01e1c5e4766d180c46b128ea44647f27c75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.16884",
    "kind": "arxiv",
    "version": 3
  }
}