Pith Number

pith:6ZXVA4T5

pith:2024:6ZXVA4T5GSLU54KIVRZ2LQ4SYA

not attested not anchored not stored refs pending

Attention is a smoothed cubic spline

Lek-Heng Lim, Yucong Liu, Zehua Lai

arxiv:2408.09624 v1 · 2024-08-19 · cs.AI · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ZXVA4T5GSLU54KIVRZ2LQ4SYA}

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

Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights

Copositive Matrices with Ordered Off-Diagonal Entries

A Mathematical Explanation of Transformers

Algebraic Invariants of Lightning Self-Attention

Receipt and verification

First computed	2026-07-05T08:56:34.777802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f66f50727d34974ef148ac73a5c392c02115fbc98ee1445843a02c5728beebde

Aliases

arxiv: 2408.09624 · arxiv_version: 2408.09624v1 · doi: 10.48550/arxiv.2408.09624 · pith_short_12: 6ZXVA4T5GSLU · pith_short_16: 6ZXVA4T5GSLU54KI · pith_short_8: 6ZXVA4T5

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/6ZXVA4T5GSLU54KIVRZ2LQ4SYA \
  | 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: f66f50727d34974ef148ac73a5c392c02115fbc98ee1445843a02c5728beebde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4295901b02d95f529566f4a713ed8c86468e7578a19c08366c092241fa1408f",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2024-08-19T00:56:44Z",
    "title_canon_sha256": "f48c6486bf13bb933b5c514d939aabc89653b9a741aae9b988e942d5b23bb7c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.09624",
    "kind": "arxiv",
    "version": 1
  }
}