Pith Number

pith:JHKZH72T

pith:2024:JHKZH72TSDUALKOSEUNCVDQCSA

not attested not anchored not stored refs pending

How Transformers Get Rich: Approximation and Dynamics Analysis

Lei Wu, Mingze Wang, Ruoxi Yu, Weinan E

arxiv:2410.11474 v3 · 2024-10-15 · cs.LG · math.OC · 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{JHKZH72TSDUALKOSEUNCVDQCSA}

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

5 papers in Pith

Structure Before Collapse: Transient semantic geometry in next-token prediction

Learning Dynamics of Chain-of-Thought State Tracking in a Solvable Transformer Model

Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence

Why Muon Outperforms Adam: A Curvature Perspective

How Do Transformers Learn to Associate Tokens: Gradient Leading Terms Bring Mechanistic Interpretability

Receipt and verification

First computed	2026-07-05T10:06:44.680179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49d593ff5390e805a9d2251a2a8e029026526bdd0c4a41a6e35bee38a5cd0baf

Aliases

arxiv: 2410.11474 · arxiv_version: 2410.11474v3 · doi: 10.48550/arxiv.2410.11474 · pith_short_12: JHKZH72TSDUA · pith_short_16: JHKZH72TSDUALKOS · pith_short_8: JHKZH72T

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/JHKZH72TSDUALKOSEUNCVDQCSA \
  | 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: 49d593ff5390e805a9d2251a2a8e029026526bdd0c4a41a6e35bee38a5cd0baf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "516ba863057d351869b532b6bd25f60c1a0c5d171e08c40673c07334516a29f5",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-10-15T10:22:27Z",
    "title_canon_sha256": "bffb931c9ce77eaa8cf25cb105ad120b42fcd2587f33ca50b3b268bf69c6cf4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.11474",
    "kind": "arxiv",
    "version": 3
  }
}