Pith Number

pith:3TXO7I7C

pith:2026:3TXO7I7CDNUUN3SRLAMFAIOHQH

not attested not anchored not stored refs pending

Upper Bounds for Local Learning Coefficients of Three-Layer Neural Networks

Yuki Kurumadani

arxiv:2603.12785 v2 · 2026-03-13 · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3TXO7I7CDNUUN3SRLAMFAIOHQH}

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	2026-06-10T01:09:58.666538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dceeefa3e21b6946ee5158185021c781e215147f40e39f15273e9daeedb1c65c

Aliases

arxiv: 2603.12785 · arxiv_version: 2603.12785v2 · doi: 10.48550/arxiv.2603.12785 · pith_short_12: 3TXO7I7CDNUU · pith_short_16: 3TXO7I7CDNUUN3SR · pith_short_8: 3TXO7I7C

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/3TXO7I7CDNUUN3SRLAMFAIOHQH \
  | 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: dceeefa3e21b6946ee5158185021c781e215147f40e39f15273e9daeedb1c65c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68602d6949b56b801e427ba5946341782935f17cf58691fe171f869f7b08d25d",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-13T08:41:43Z",
    "title_canon_sha256": "176a63ab841e726d7cfd78a3c6a59dbf405f0cd189dac33eda8c8a2ddbce7550"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.12785",
    "kind": "arxiv",
    "version": 2
  }
}