Pith Number

pith:AGW62PWN

pith:2026:AGW62PWN7WJWR7RHYFU6YCTQEA

not attested not anchored not stored refs pending

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers

Tim Tsz-Kit Lau, Weijie Su

arxiv:2605.18106 v1 · 2026-05-18 · math.OC · cs.AI · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AGW62PWN7WJWR7RHYFU6YCTQEA}

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	2026-05-20T00:05:16.256873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01aded3ecdfd9368fe27c169ec0a70201549e666d84b46179b94754cc0701943

Aliases

arxiv: 2605.18106 · arxiv_version: 2605.18106v1 · doi: 10.48550/arxiv.2605.18106 · pith_short_12: AGW62PWN7WJW · pith_short_16: AGW62PWN7WJWR7RH · pith_short_8: AGW62PWN

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/AGW62PWN7WJWR7RHYFU6YCTQEA \
  | 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: 01aded3ecdfd9368fe27c169ec0a70201549e666d84b46179b94754cc0701943

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d1e837dc255c73e9aabdd747dd4186a6c3a8e9419359216da526552cb1b3a46",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-18T09:17:26Z",
    "title_canon_sha256": "b73a3b7f9c2a5fe09a2df9d25b75825b77f0d9ff376cc6bcd44b38ccb1086189"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18106",
    "kind": "arxiv",
    "version": 1
  }
}