Pith Number

pith:XAZ3N4GZ

pith:2026:XAZ3N4GZD46SCQ67M7TDWD7JY5

not attested not anchored not stored refs pending

Exponential Capacity in Multilayer Hetero-Associative Neural Networks

Adriano Barra, Andrea Ladiana, Andrea Lepre, Elena Agliari

arxiv:2607.29554 v1 · 2026-07-31 · cond-mat.dis-nn · 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{XAZ3N4GZD46SCQ67M7TDWD7JY5}

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	2026-08-03T01:38:23.736480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b833b6f0d91f3d2143df67e63b0fe9c74fade2b4b925d62da8799903e8398293

Aliases

arxiv: 2607.29554 · arxiv_version: 2607.29554v1 · doi: 10.48550/arxiv.2607.29554 · pith_short_12: XAZ3N4GZD46S · pith_short_16: XAZ3N4GZD46SCQ67 · pith_short_8: XAZ3N4GZ

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/XAZ3N4GZD46SCQ67M7TDWD7JY5 \
  | 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: b833b6f0d91f3d2143df67e63b0fe9c74fade2b4b925d62da8799903e8398293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08570562f6989a8589c6b79bc06b5e92c1b653c2278d3a2f914a133c73c695cd",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-07-31T15:46:21Z",
    "title_canon_sha256": "4d1c394c63c2a1b0c09f2ded79b12211c99f5d24389c80a9335f0aa4c2c1bbff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29554",
    "kind": "arxiv",
    "version": 1
  }
}