Pith Number

pith:37I6P3OY

pith:2025:37I6P3OYFCFSMKVYT4QEWIHKXJ

not attested not anchored not stored refs pending

Transformers with RL or SFT Provably Learn Sparse Boolean Functions, But Differently

Bochen Lyu, Xiaohao Cai, Yiyang Jia, Zhanxing Zhu

arxiv:2511.17852 v2 · 2025-11-22 · 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{37I6P3OYFCFSMKVYT4QEWIHKXJ}

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	2026-05-27T01:04:52.701750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfd1e7edd8288b262ab89f204b20eaba60b4be89fbb853c4414a201d6c3e11eb

Aliases

arxiv: 2511.17852 · arxiv_version: 2511.17852v2 · doi: 10.48550/arxiv.2511.17852 · pith_short_12: 37I6P3OYFCFS · pith_short_16: 37I6P3OYFCFSMKVY · pith_short_8: 37I6P3OY

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/37I6P3OYFCFSMKVYT4QEWIHKXJ \
  | 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: dfd1e7edd8288b262ab89f204b20eaba60b4be89fbb853c4414a201d6c3e11eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83571253e79a41fa8046eca2c4a7fd5b7c053d7d0db4c60500a9bbbe54a90c74",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-11-22T00:38:43Z",
    "title_canon_sha256": "2be2e0a131213221a17634eb3b2e2d755bd5ce2630eeaf003946191e42fbacad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.17852",
    "kind": "arxiv",
    "version": 2
  }
}