Pith Number

pith:QFPB6HZM

pith:2023:QFPB6HZM5AGRNRWBUL5Y2VBZEH

not attested not anchored not stored refs pending

Transformers learn through gradual rank increase

Emmanuel Abbe, Enric Boix-Adsera, Etai Littwin, Joshua Susskind, Samy Bengio

arxiv:2306.07042 v2 · 2023-06-12 · 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{QFPB6HZM5AGRNRWBUL5Y2VBZEH}

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

Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale

Receipt and verification

First computed	2026-07-05T07:22:19.401975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

815e1f1f2ce80d16c6c1a2fb8d543921e92925bc796e1d5ec5c3f5c6462c0322

Aliases

arxiv: 2306.07042 · arxiv_version: 2306.07042v2 · doi: 10.48550/arxiv.2306.07042 · pith_short_12: QFPB6HZM5AGR · pith_short_16: QFPB6HZM5AGRNRWB · pith_short_8: QFPB6HZM

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/QFPB6HZM5AGRNRWBUL5Y2VBZEH \
  | 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: 815e1f1f2ce80d16c6c1a2fb8d543921e92925bc796e1d5ec5c3f5c6462c0322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdf281d4bd7a084e92df1ec962202fa5dab823169ad5050954f388bf889b27de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-06-12T11:41:42Z",
    "title_canon_sha256": "23e7edf53ae0d93c013294598388fe59613e962215a3c8be1ac49f8f8f43f344"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.07042",
    "kind": "arxiv",
    "version": 2
  }
}