Pith Number

pith:FC47AFDE

pith:2026:FC47AFDEY5UHWXWWPTWU5Z7Z6T

not attested not anchored not stored refs pending

From Expressivity to Sample Complexity: Narrow Teachers for Transformers via C-RASP

Guillaume Rabusseau, Michael Hahn, Michael Rizvi-Martel, Satwik Bhattamishra

arxiv:2607.11760 v1 · 2026-07-13 · cs.LG · cs.CL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FC47AFDEY5UHWXWWPTWU5Z7Z6T}

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	2026-07-14T02:22:31.258565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28b9f01464c7687b5ed67ced4ee7f9f4e885384ba71d7bc32aec4e1cc1a94959

Aliases

arxiv: 2607.11760 · arxiv_version: 2607.11760v1 · doi: 10.48550/arxiv.2607.11760 · pith_short_12: FC47AFDEY5UH · pith_short_16: FC47AFDEY5UHWXWW · pith_short_8: FC47AFDE

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/FC47AFDEY5UHWXWWPTWU5Z7Z6T \
  | 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: 28b9f01464c7687b5ed67ced4ee7f9f4e885384ba71d7bc32aec4e1cc1a94959

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92111e657a6a25d556f09513b1ac81963e16adf596a8823c70a69da0c4dbd528",
    "cross_cats_sorted": [
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-13T16:22:36Z",
    "title_canon_sha256": "472886b120c4ab959e59b91f4df75c9a8c6d6ffb2c7432bc692f5abeffb1ac9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11760",
    "kind": "arxiv",
    "version": 1
  }
}