Pith Number

pith:5RTJOOWV

pith:2026:5RTJOOWVKJFHU2QNX66M7ZX722

not attested not anchored not stored refs pending

Hidden Boundary Motion in Transformer Optimization: Function-Space Orthogonalization of Affine Weight and Bias Updates

Liu Donghan, Liu Honghai, Ren Weihong, Sheng Yixuan, Wang Zhiyong, Zhang Gongyue

arxiv:2607.22927 v1 · 2026-07-24 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5RTJOOWVKJFHU2QNX66M7ZX722}

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	2026-07-28T00:22:02.492592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec66973ad5524a7a6a0dbfbccfe6ffd692049e665dd8f02744ab36ee3fe64324

Aliases

arxiv: 2607.22927 · arxiv_version: 2607.22927v1 · doi: 10.48550/arxiv.2607.22927 · pith_short_12: 5RTJOOWVKJFH · pith_short_16: 5RTJOOWVKJFHU2QN · pith_short_8: 5RTJOOWV

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/5RTJOOWVKJFHU2QNX66M7ZX722 \
  | 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: ec66973ad5524a7a6a0dbfbccfe6ffd692049e665dd8f02744ab36ee3fe64324

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "147622cf20b6b60ee04f0d0d4b2d50280c82684807da3dff5cc0c691c65b0d2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-24T21:51:43Z",
    "title_canon_sha256": "a14d10e22c55c355c01ef96fe9290511af1186efe1b7199e30fec65cf3ef522f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22927",
    "kind": "arxiv",
    "version": 1
  }
}