Pith Number

pith:MPFETBY2

pith:2026:MPFETBY2TEKVUIR3SPG7WHMWQW

not attested not anchored not stored refs pending

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations

Chon-Fai Kam, Frederic Cadet, Miloud Bessafi, Xavier Cadet

arxiv:2607.13749 v1 · 2026-07-15 · cs.LG · 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{MPFETBY2TEKVUIR3SPG7WHMWQW}

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	2026-07-16T01:23:04.123361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63ca49871a99155a223b93cdfb1d9685ac4c080a988b0a3aeb997acae9249e94

Aliases

arxiv: 2607.13749 · arxiv_version: 2607.13749v1 · doi: 10.48550/arxiv.2607.13749 · pith_short_12: MPFETBY2TEKV · pith_short_16: MPFETBY2TEKVUIR3 · pith_short_8: MPFETBY2

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/MPFETBY2TEKVUIR3SPG7WHMWQW \
  | 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: 63ca49871a99155a223b93cdfb1d9685ac4c080a988b0a3aeb997acae9249e94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1423108f53a56bf46aa53fba0bfe54d2f19c57e5bb09fe54bb8a972cefe17720",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-15T12:04:43Z",
    "title_canon_sha256": "027c9e5014a87c7590839569d69b370ee89203aa393b8006ef29945e53c776af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13749",
    "kind": "arxiv",
    "version": 1
  }
}