Pith Number

pith:WX6EWVET

pith:2026:WX6EWVETGVD4XAKUY353UCDD7A

not attested not anchored not stored refs pending

Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers

Achyuthan Sivasankar

arxiv:2606.12966 v1 · 2026-06-11 · cs.LG · cs.NE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WX6EWVETGVD4XAKUY353UCDD7A}

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	2026-06-12T01:09:35.683333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5fc4b54933547cb8154c6fbba0863f8292d878e00319243b35dc6e5bfcb59e6

Aliases

arxiv: 2606.12966 · arxiv_version: 2606.12966v1 · doi: 10.48550/arxiv.2606.12966 · pith_short_12: WX6EWVETGVD4 · pith_short_16: WX6EWVETGVD4XAKU · pith_short_8: WX6EWVET

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/WX6EWVETGVD4XAKUY353UCDD7A \
  | 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: b5fc4b54933547cb8154c6fbba0863f8292d878e00319243b35dc6e5bfcb59e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c59bbefc73eb7a63433f722f08fbcc989854c985afaa438875338dd32137cef1",
    "cross_cats_sorted": [
      "cs.NE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-11T06:52:10Z",
    "title_canon_sha256": "de75652d1a243595e9348be2824bfa5432bb6a535dfdf98e87eb9aa7ec3e2e78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12966",
    "kind": "arxiv",
    "version": 1
  }
}