Pith Number

pith:2IA4DL5A

pith:2026:2IA4DL5A4BNRZG73V3KFHTTHCQ

not attested not anchored not stored refs pending

Depth Lower Bounds for ReLU Networks with Binary Inputs

Elchanan Mossel, Neil Krishnan

arxiv:2606.18540 v1 · 2026-06-16 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2IA4DL5A4BNRZG73V3KFHTTHCQ}

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	2026-06-19T16:11:40.469697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d201c1afa0e05b1c9bfbaed453ce671431a738590b31fdd3c9b91c2b8c34a2e6

Aliases

arxiv: 2606.18540 · arxiv_version: 2606.18540v1 · doi: 10.48550/arxiv.2606.18540 · pith_short_12: 2IA4DL5A4BNR · pith_short_16: 2IA4DL5A4BNRZG73 · pith_short_8: 2IA4DL5A

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/2IA4DL5A4BNRZG73V3KFHTTHCQ \
  | 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: d201c1afa0e05b1c9bfbaed453ce671431a738590b31fdd3c9b91c2b8c34a2e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83e93a8890851f767ccdc4bbf4696643e35d63739e1bf199a2824ca8e97a48a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-06-16T23:32:20Z",
    "title_canon_sha256": "d89a107093da8b843b3546426e1af262fc8ec197ec84481ae5f95b0c957b06f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18540",
    "kind": "arxiv",
    "version": 1
  }
}