Pith Number

pith:YJYVFO5E

pith:2026:YJYVFO5E6Q6YQIHGZG5YFSCKEH

not attested not anchored not stored refs pending

Structured Spectral Step-Sizes and a Hanoi Ordering Principle for Gradient Methods

Ran Gu, Yijia Zhou

arxiv:2606.25311 v1 · 2026-06-24 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YJYVFO5E6Q6YQIHGZG5YFSCKEH}

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	2026-06-25T01:18:01.687742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c27152bba4f43d8820e6c9bb82c84a21e30ba462b9291975ad7cfb9fcd8ac83f

Aliases

arxiv: 2606.25311 · arxiv_version: 2606.25311v1 · doi: 10.48550/arxiv.2606.25311 · pith_short_12: YJYVFO5E6Q6Y · pith_short_16: YJYVFO5E6Q6YQIHG · pith_short_8: YJYVFO5E

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/YJYVFO5E6Q6YQIHGZG5YFSCKEH \
  | 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: c27152bba4f43d8820e6c9bb82c84a21e30ba462b9291975ad7cfb9fcd8ac83f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19bbb5db886c5209f40b5a75b6b4652dbc6acdfc79e124cb64ba94cbb74711d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-24T02:25:09Z",
    "title_canon_sha256": "c6e828fb54ab186ec6ac157880322db081db6b18c236304a17e72b4666ef3dd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25311",
    "kind": "arxiv",
    "version": 1
  }
}