Pith Number

pith:KESNBNN2

pith:2025:KESNBNN27665GDWHE4AIO3X4FJ

not attested not anchored not stored refs pending

Synchronization of mean-field models on the circle

Andrew Yao, Philippe Rigollet, Yury Polyanskiy

arxiv:2507.22857 v1 · 2025-07-30 · math.DS · cs.LG · math.AP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KESNBNN27665GDWHE4AIO3X4FJ}

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

5 papers in Pith

Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models

Kinetic theory for Transformers and the lost-in-the-middle phenomenon

Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention

Receipt and verification

First computed	2026-07-05T11:45:50.468727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08

Aliases

arxiv: 2507.22857 · arxiv_version: 2507.22857v1 · doi: 10.48550/arxiv.2507.22857 · pith_short_12: KESNBNN27665 · pith_short_16: KESNBNN27665GDWH · pith_short_8: KESNBNN2

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/KESNBNN27665GDWHE4AIO3X4FJ \
  | 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: 5124d0b5baffbdd30ec72700876efc2a43acce02f358a9f6c63ab62056b37e08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5019cc533b85e2c09e8eda78483f040dcd8ce21d549e6cc3c3ff21eea321dd5a",
    "cross_cats_sorted": [
      "cs.LG",
      "math.AP",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-07-30T17:31:57Z",
    "title_canon_sha256": "78c551fe90ed1d6121270aa064575e909d66502c8df79e8f65045d4239072cb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.22857",
    "kind": "arxiv",
    "version": 1
  }
}