Pith Number

pith:J7WOKSPA

pith:2023:J7WOKSPANUSS5VHWN6AM5P66Z7

not attested not anchored not stored refs pending

A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Aman Shukla, Nikolaos Tsilivis, William Merrill

arxiv:2303.11873 v1 · 2023-03-21 · 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{J7WOKSPANUSS5VHWN6AM5P66Z7}

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

13 papers in Pith

Grokking and epoch-wise double descent in quantum neural networks

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning

Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking

Select and Improve: Understanding the Mechanics of Post-Training for Reasoning

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning

Receipt and verification

First computed	2026-07-05T05:53:23.198083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fece549e06d252ed4f66f80cebfdecff7f16d67b83945998b5a4ead70c11fc1

Aliases

arxiv: 2303.11873 · arxiv_version: 2303.11873v1 · doi: 10.48550/arxiv.2303.11873 · pith_short_12: J7WOKSPANUSS · pith_short_16: J7WOKSPANUSS5VHW · pith_short_8: J7WOKSPA

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/J7WOKSPANUSS5VHWN6AM5P66Z7 \
  | 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: 4fece549e06d252ed4f66f80cebfdecff7f16d67b83945998b5a4ead70c11fc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f82caaf97da75923fadf8e57bbb56e959671709649435cc0f726344a9924f3b0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-03-21T14:17:29Z",
    "title_canon_sha256": "03dc2f9e61afcb919b45d185bd02c0aa24ff4f19b932543b1e226d2f095c68dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.11873",
    "kind": "arxiv",
    "version": 1
  }
}