Pith Number

pith:LAVMIUQX

pith:2026:LAVMIUQXXDOP27ZZVIZYRC2A3Q

not attested not anchored not stored refs pending

Different Layers, Different Manifolds: Module-Wise Weight-Space Geometry in Transformer Optimization

Kirato Yoshihara

arxiv:2606.13276 v1 · 2026-06-11 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LAVMIUQXXDOP27ZZVIZYRC2A3Q}

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	2026-06-12T01:09:50.102479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

582ac45217b8dcfd7f39aa33888b40dc38e7a3a8ef3444d96961918b6df4ec45

Aliases

arxiv: 2606.13276 · arxiv_version: 2606.13276v1 · doi: 10.48550/arxiv.2606.13276 · pith_short_12: LAVMIUQXXDOP · pith_short_16: LAVMIUQXXDOP27ZZ · pith_short_8: LAVMIUQX

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/LAVMIUQXXDOP27ZZVIZYRC2A3Q \
  | 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: 582ac45217b8dcfd7f39aa33888b40dc38e7a3a8ef3444d96961918b6df4ec45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae075212a32f657773cffa41cf4aed9c16e0ea70ab1038d335169a059bbfd3d9",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-11T12:30:05Z",
    "title_canon_sha256": "6b58b31cb6c61a3e655961f7d7b6d0a074699b03ac08137df1518adcc7395a56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13276",
    "kind": "arxiv",
    "version": 1
  }
}