Pith Number

pith:JASZAMZ5

pith:2026:JASZAMZ5STEID4SKDHOFSZ6E4E

not attested not anchored not stored refs pending

A Mean-Field Analysis of Multi-Head Self-Attention under Cross-Entropy Training

Cheng Huan, Hongfwei Yuan

arxiv:2606.10469 v1 · 2026-06-09 · 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{JASZAMZ5STEID4SKDHOFSZ6E4E}

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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

A First-Order Mean Field Control Analysis of Transformer Layers under Cross-Entropy Training

Receipt and verification

First computed	2026-06-10T01:10:20.839644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

482590333d94c881f24a19dc5967c4e1012b7932e63fa5b298860d2039090d30

Aliases

arxiv: 2606.10469 · arxiv_version: 2606.10469v1 · doi: 10.48550/arxiv.2606.10469 · pith_short_12: JASZAMZ5STEI · pith_short_16: JASZAMZ5STEID4SK · pith_short_8: JASZAMZ5

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/JASZAMZ5STEID4SKDHOFSZ6E4E \
  | 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: 482590333d94c881f24a19dc5967c4e1012b7932e63fa5b298860d2039090d30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cabc5ef300969f9928b419065c9dc1aa0fc6bc6ad3187d7a5bbafb6de798099a",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-09T06:38:27Z",
    "title_canon_sha256": "fbf901dcf919f4ac3c8a38d2d8bf35876e760ed1e59d8edffba7e82c980591b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10469",
    "kind": "arxiv",
    "version": 1
  }
}