Pith Number

pith:7MFPV7ZZ

pith:2023:7MFPV7ZZOBHICCDQDGRM3OKBJ6

not attested not anchored not stored refs pending

Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds

Mihailo Stojnic

arxiv:2312.08244 v1 · 2023-12-13 · cond-mat.dis-nn · cs.IT · math-ph · math.IT · math.MP · math.PR · 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{7MFPV7ZZOBHICCDQDGRM3OKBJ6}

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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.

Cited by

1 paper in Pith

Deep ReLU networks -- injectivity capacity upper bounds

Receipt and verification

First computed	2026-07-05T07:23:43.359632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb0afaff39704e81087019a2cdb9414fbff3fb21bef9108c9305a641d420d852

Aliases

arxiv: 2312.08244 · arxiv_version: 2312.08244v1 · doi: 10.48550/arxiv.2312.08244 · pith_short_12: 7MFPV7ZZOBHI · pith_short_16: 7MFPV7ZZOBHICCDQ · pith_short_8: 7MFPV7ZZ

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/7MFPV7ZZOBHICCDQDGRM3OKBJ6 \
  | 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: fb0afaff39704e81087019a2cdb9414fbff3fb21bef9108c9305a641d420d852

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "717cd00fc6086d43449ae8234da6143540dd7c9798290aa66a8974374ed05a99",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP",
      "math.PR",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2023-12-13T16:06:18Z",
    "title_canon_sha256": "4cb7b5adbe69867e62d1135951c3f970c3e11770d84c034dfa2acd98345199c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.08244",
    "kind": "arxiv",
    "version": 1
  }
}