Pith Number

pith:MHLU6MWI

pith:2026:MHLU6MWIT4D6GZSJV7EH7QZNIL

not attested not anchored not stored refs pending

Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model

Andrea Montanari, Kangjie Zhou

arxiv:2606.28573 v1 · 2026-06-26 · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHLU6MWIT4D6GZSJV7EH7QZNIL}

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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	2026-06-30T00:15:19.553173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61d74f32c89f07e36649afc87fc32d42d8762f9041fab85e0bbd18a0d3265d94

Aliases

arxiv: 2606.28573 · arxiv_version: 2606.28573v1 · doi: 10.48550/arxiv.2606.28573 · pith_short_12: MHLU6MWIT4D6 · pith_short_16: MHLU6MWIT4D6GZSJ · pith_short_8: MHLU6MWI

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/MHLU6MWIT4D6GZSJV7EH7QZNIL \
  | 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: 61d74f32c89f07e36649afc87fc32d42d8762f9041fab85e0bbd18a0d3265d94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "740dadf286db3ed577503dca3f21ee1f609620919e6c9a3e2567e77904170697",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-26T19:57:08Z",
    "title_canon_sha256": "7acbe0346de5ba1d17f676d72f7ab2851975daef70b3b1a7c2269e59aadd9d62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28573",
    "kind": "arxiv",
    "version": 1
  }
}