Pith Number

pith:WV5JWCN6

pith:2024:WV5JWCN67KVCXYNHRC4242BRSI

not attested not anchored not stored refs pending

A phase transition between positional and semantic learning in a solvable model of dot-product attention

Florent Krzakala, Freya Behrens, Hugo Cui, Lenka Zdeborov\'a

arxiv:2402.03902 v2 · 2024-02-06 · 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{WV5JWCN67KVCXYNHRC4242BRSI}

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

1 paper in Pith

Physics of Skill Learning

Receipt and verification

First computed	2026-07-05T10:10:39.564725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b57a9b09befaaa2be1a788b9ae6831922b33116ffffa86afe26469c4fde69d12

Aliases

arxiv: 2402.03902 · arxiv_version: 2402.03902v2 · doi: 10.48550/arxiv.2402.03902 · pith_short_12: WV5JWCN67KVC · pith_short_16: WV5JWCN67KVCXYNH · pith_short_8: WV5JWCN6

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/WV5JWCN67KVCXYNHRC4242BRSI \
  | 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: b57a9b09befaaa2be1a788b9ae6831922b33116ffffa86afe26469c4fde69d12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27f5ab9e5f9979f2aeaea643aac346da5163a9898f7affc896fdbc4096003685",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-02-06T11:13:54Z",
    "title_canon_sha256": "dd4e0c1a599a339388732ba11304b3a6f55142b23630c7d58a5b71e2a137928b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.03902",
    "kind": "arxiv",
    "version": 2
  }
}