Pith Number

pith:4ZDJQNB2

pith:2026:4ZDJQNB2NTWZFDEV5LWXNNE3JV

not attested not anchored not stored refs pending

How Optimality Structures Sparse Dictionaries: A Theory for Understanding SAE Representations

William Dorrell

arxiv:2606.02385 v1 · 2026-06-01 · q-bio.NC · 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{4ZDJQNB2NTWZFDEV5LWXNNE3JV}

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	2026-06-02T03:04:57.767734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e64698343a6ced928c95eaed76b49b4d7a92ccf95a6f5cb2139b2f85fcbd5976

Aliases

arxiv: 2606.02385 · arxiv_version: 2606.02385v1 · doi: 10.48550/arxiv.2606.02385 · pith_short_12: 4ZDJQNB2NTWZ · pith_short_16: 4ZDJQNB2NTWZFDEV · pith_short_8: 4ZDJQNB2

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/4ZDJQNB2NTWZFDEV5LWXNNE3JV \
  | 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: e64698343a6ced928c95eaed76b49b4d7a92ccf95a6f5cb2139b2f85fcbd5976

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "705d7da3c11520c826df4d0a619f4ac78c3071672f3170d4a4caf4eb30633a09",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.NC",
    "submitted_at": "2026-06-01T15:34:34Z",
    "title_canon_sha256": "478954ef3cd0554a53cbf1210d19f371f3e53eb3a3dce2882ba44291c950b324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02385",
    "kind": "arxiv",
    "version": 1
  }
}