Pith Number

pith:BWCFNFAJ

pith:2026:BWCFNFAJMWNNQ5AYEINB43CJ5G

not attested not anchored not stored refs pending

Tight Worst-Case Bounds for the Smallest Eigenvalue of ReLU NTK Gram Matrices

Zhao Song

arxiv:2608.03368 v1 · 2026-08-04 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BWCFNFAJMWNNQ5AYEINB43CJ5G}

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

Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks

Receipt and verification

First computed	2026-08-05T01:35:37.705953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d84569409659ad87418221a1e6c49e99d88e4c22a14151303829dcdad685928

Aliases

arxiv: 2608.03368 · arxiv_version: 2608.03368v1 · doi: 10.48550/arxiv.2608.03368 · pith_short_12: BWCFNFAJMWNN · pith_short_16: BWCFNFAJMWNNQ5AY · pith_short_8: BWCFNFAJ

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/BWCFNFAJMWNNQ5AYEINB43CJ5G \
  | 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: 0d84569409659ad87418221a1e6c49e99d88e4c22a14151303829dcdad685928

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2f3e8ba26aabca16ebab8b25816ea163a9e37ec95d403f72c65bacd9c81633f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-08-04T09:19:53Z",
    "title_canon_sha256": "fb0a79e229f9f2f070d61db8cc51dfa2ac435a23728d415e3e83a3f0fb40f0e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03368",
    "kind": "arxiv",
    "version": 1
  }
}