Pith Number

pith:JTJHPQW6

pith:2026:JTJHPQW6TABFD66PHK4WQXHZYT

not attested not anchored not stored refs pending

Manifold constrained steepest descent for smooth and closed-set optimization

Kaiwei Yang, Lexiao Lai

arxiv:2601.21487 v2 · 2026-01-29 · math.OC · 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{JTJHPQW6TABFD66PHK4WQXHZYT}

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.

Cited by

7 papers in Pith

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

Learned Subspace Compression for Communication-Efficient Pipeline Parallelism

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

Convergence of Spectral Descent for Non-smooth Optimization

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

Receipt and verification

First computed	2026-08-14T00:39:34.339313Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cd277c2de980251fbcf3ab9685cf9c4cb526b6058cb4fe404539e9b263dc8b7

Aliases

arxiv: 2601.21487 · arxiv_version: 2601.21487v2 · doi: 10.48550/arxiv.2601.21487 · pith_short_12: JTJHPQW6TABF · pith_short_16: JTJHPQW6TABFD66P · pith_short_8: JTJHPQW6

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/JTJHPQW6TABFD66PHK4WQXHZYT \
  | 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: 4cd277c2de980251fbcf3ab9685cf9c4cb526b6058cb4fe404539e9b263dc8b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22def95cc5c1ffdb953951e3380ece503712299cc7f6127a2e46f5a1723b7dc9",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-01-29T10:08:37Z",
    "title_canon_sha256": "305f64222992818602a7780b7df50cba498a83e9a40dc75e75af2c8078ce6f86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.21487",
    "kind": "arxiv",
    "version": 2
  }
}