Pith Number

pith:VYH3PXJI

pith:2025:VYH3PXJIYE3F2FKSKK4D46VBDA

not attested not anchored not stored refs pending

Kahan's Automatic Step-Size Control for Unconstrained Optimization

Chungen Shen, Lei-Hong Zhang, Linuo Xue, Yifeng Meng

arxiv:2508.06002 v1 · 2025-08-08 · math.OC · cs.NA · math.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{VYH3PXJIYE3F2FKSKK4D46VBDA}

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	2026-07-05T11:50:47.180925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae0fb7dd28c1365d155252b83e7aa11804bea07a316f12ef48fe9192a49dd880

Aliases

arxiv: 2508.06002 · arxiv_version: 2508.06002v1 · doi: 10.48550/arxiv.2508.06002 · pith_short_12: VYH3PXJIYE3F · pith_short_16: VYH3PXJIYE3F2FKS · pith_short_8: VYH3PXJI

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/VYH3PXJIYE3F2FKSKK4D46VBDA \
  | 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: ae0fb7dd28c1365d155252b83e7aa11804bea07a316f12ef48fe9192a49dd880

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0b6e799e4cf724d1a7a1074b18d077ccc82a4f1951054db26ca17dec904e8f5",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-08-08T04:09:48Z",
    "title_canon_sha256": "b8ee92add2fa7f7e439736a354c50b981f7f0e6d617efaeac0651ea17d0085a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.06002",
    "kind": "arxiv",
    "version": 1
  }
}