Pith Number

pith:SNBONQAS

pith:2026:SNBONQASJJG67LIGUUIZJ6HOGD

not attested not anchored not stored refs pending

Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks

Hirotaka Takahashi, Kazuki Sakai, Makoto Sasaki, Yohei Kakimoto, Yusuke Sakai, Yuto Omae

arxiv:2606.28662 v1 · 2026-06-27 · cs.LG · cs.AI · cs.NE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SNBONQASJJG67LIGUUIZJ6HOGD}

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	2026-06-30T01:16:46.418554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9342e6c0124a4defad06a51194f8ee30e2ce387f151000844692bd9ebec2af26

Aliases

arxiv: 2606.28662 · arxiv_version: 2606.28662v1 · doi: 10.48550/arxiv.2606.28662 · pith_short_12: SNBONQASJJG6 · pith_short_16: SNBONQASJJG67LIG · pith_short_8: SNBONQAS

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/SNBONQASJJG67LIGUUIZJ6HOGD \
  | 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: 9342e6c0124a4defad06a51194f8ee30e2ce387f151000844692bd9ebec2af26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9376bbcb10f8bd410fb3dd17c25bd9a17adbac14bce24643a4eca76b6aed836",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.NE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-27T00:47:03Z",
    "title_canon_sha256": "4e9b4528858c812110de0b184a54aa9f5c836753be75403307ed1872cec0f3d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28662",
    "kind": "arxiv",
    "version": 1
  }
}