Pith Number

pith:AB64KPE6

pith:2023:AB64KPE6CVCTLZYR3OT6KWSWFQ

not attested not anchored not stored refs pending

Lion Secretly Solves Constrained Optimization: As Lyapunov Predicts

Bo Liu, Kaizhao Liang, Lizhang Chen, Qiang Liu

arxiv:2310.05898 v7 · 2023-10-09 · cs.LG · cs.AI · math.OC · stat.AP · 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{AB64KPE6CVCTLZYR3OT6KWSWFQ}

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

4 papers in Pith

Training Deep Learning Models with Norm-Constrained LMOs

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives

Demystifying Manifold Constraints in LLM Pre-training

CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization

Receipt and verification

First computed	2026-07-05T11:29:46.526723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

007dc53c9e154535e711dba7e55a562c14b384d672aa78866a2eb922fc3dcf18

Aliases

arxiv: 2310.05898 · arxiv_version: 2310.05898v7 · doi: 10.48550/arxiv.2310.05898 · pith_short_12: AB64KPE6CVCT · pith_short_16: AB64KPE6CVCTLZYR · pith_short_8: AB64KPE6

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/AB64KPE6CVCTLZYR3OT6KWSWFQ \
  | 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: 007dc53c9e154535e711dba7e55a562c14b384d672aa78866a2eb922fc3dcf18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "daacbe8b25ac05f0adac0394df1d4a048ddbc19f5e94f149d6c541904e3ca886",
    "cross_cats_sorted": [
      "cs.AI",
      "math.OC",
      "stat.AP",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-10-09T17:41:29Z",
    "title_canon_sha256": "8724efcb5dbf812b0e649a2e899f461196dbb2f12d552e2de0caaacc6897f4b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.05898",
    "kind": "arxiv",
    "version": 7
  }
}