Pith Number

pith:D4ELULO7

pith:2026:D4ELULO7PN27R7ATJL5LXPPLVP

not attested not anchored not stored refs pending

Learning High-Dimensional Parity Functions with Product Networks using Gradient Descent

France), France (2) T\'el\'ecom Paris, Ghaya Rekaya (2) ((1) Orange Research, Guillaume Larue (1), Hadi Ghauch (2), Institut Polytechnique de Paris, Louis-Adrien Dufr\`ene (1), Meylan, Palaiseau, Quentin Lampin (1)

arxiv:2605.28612 v1 · 2026-05-27 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D4ELULO7PN27R7ATJL5LXPPLVP}

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	2026-05-28T02:04:57.771609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f08ba2ddf7b75f8fc134afabbbdebabc3e17315b949460a534ac87800d56ca5

Aliases

arxiv: 2605.28612 · arxiv_version: 2605.28612v1 · doi: 10.48550/arxiv.2605.28612 · pith_short_12: D4ELULO7PN27 · pith_short_16: D4ELULO7PN27R7AT · pith_short_8: D4ELULO7

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/D4ELULO7PN27R7ATJL5LXPPLVP \
  | 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: 1f08ba2ddf7b75f8fc134afabbbdebabc3e17315b949460a534ac87800d56ca5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eb4092c0333ca5398066e1b271103e4e56a867151a924f6c7e076c02b503c36",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-27T15:26:16Z",
    "title_canon_sha256": "0ac747da9a8b2b03e0af64525bbecfa46686d4a8a1910f86c05112315375bc0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.28612",
    "kind": "arxiv",
    "version": 1
  }
}