Pith Number

pith:XZDXCK6W

pith:2025:XZDXCK6WABNOITK5ZSVKRRDCN2

not attested not anchored not stored refs pending

Single-Head Attention in High Dimensions: A Theory of Generalization, Weights Spectra, and Scaling Laws

Emanuele Troiani, Fabrizio Boncoraglio, Florent Krzakala, Lenka Zdeborov\'a, Vittorio Erba, Yizhou Xu

arxiv:2509.24914 v2 · 2025-09-29 · stat.ML · cond-mat.dis-nn · cs.IT · cs.LG · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZDXCK6WABNOITK5ZSVKRRDCN2}

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

2 papers in Pith

Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

How Does Attention Help? Insights from Random Matrices on Signal Recovery from Sequence Models

Receipt and verification

First computed	2026-06-08T01:03:48.814133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be47712bd6005ae44d5dccaaa8c4626ea92d61127284748c250bcec1888e7745

Aliases

arxiv: 2509.24914 · arxiv_version: 2509.24914v2 · doi: 10.48550/arxiv.2509.24914 · pith_short_12: XZDXCK6WABNO · pith_short_16: XZDXCK6WABNOITK5 · pith_short_8: XZDXCK6W

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/XZDXCK6WABNOITK5ZSVKRRDCN2 \
  | 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: be47712bd6005ae44d5dccaaa8c4626ea92d61127284748c250bcec1888e7745

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "add30c3142fdceddb7468fcad03299387ef34802b5bf49094a1d3532cef79013",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.IT",
      "cs.LG",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-09-29T15:19:31Z",
    "title_canon_sha256": "efdf7c679a9d430922df9497e75dcc773afd89eb89f58ca955000ffc74975c94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.24914",
    "kind": "arxiv",
    "version": 2
  }
}