Pith Number

pith:IXQU5PMA

pith:2026:IXQU5PMAYUTXL446SB675Z4HZF

not attested not anchored not stored refs pending

Two Speeds of Learning: A Representation-Readout Decomposition of Grokking and Double Descent

Chi-Ning Chou, Neng-Chun Chiu, Oscar Uzdelewicz, SueYeon Chung, Yao-Yuan Yang

arxiv:2605.27078 v1 · 2026-05-26 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IXQU5PMAYUTXL446SB675Z4HZF}

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.

Receipt and verification

First computed	2026-05-27T01:06:27.206978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45e14ebd80c52775f39e907dfee787c97968f8861b962b35f3228aeafcb5dc0e

Aliases

arxiv: 2605.27078 · arxiv_version: 2605.27078v1 · doi: 10.48550/arxiv.2605.27078 · pith_short_12: IXQU5PMAYUTX · pith_short_16: IXQU5PMAYUTXL446 · pith_short_8: IXQU5PMA

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/IXQU5PMAYUTXL446SB675Z4HZF \
  | 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: 45e14ebd80c52775f39e907dfee787c97968f8861b962b35f3228aeafcb5dc0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37aa0d79b5e8137eb5d5f0ac21754ea74bca48b61f86c5f61dde9d17281e6fe4",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-26T14:26:55Z",
    "title_canon_sha256": "6611ba42bb28a9424807e177e4701e34e8707920fa350c34aeaab80790aef17a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.27078",
    "kind": "arxiv",
    "version": 1
  }
}