Pith Number

pith:4RXWIVO4

pith:2023:4RXWIVO4Y6LTOJAI7BWE5PO43A

not attested not anchored not stored refs pending

Beyond spectral gap (extended): The role of the topology in decentralized learning

Hadrien Hendrikx, Martin Jaggi, Thijs Vogels

arxiv:2301.02151 v1 · 2023-01-05 · cs.LG · cs.DC · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4RXWIVO4Y6LTOJAI7BWE5PO43A}

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	2026-07-05T05:30:57.247952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e46f6455dcc797372408f86c4ebddcd8046dd3aded817c58dbaf0d8d0870e139

Aliases

arxiv: 2301.02151 · arxiv_version: 2301.02151v1 · doi: 10.48550/arxiv.2301.02151 · pith_short_12: 4RXWIVO4Y6LT · pith_short_16: 4RXWIVO4Y6LTOJAI · pith_short_8: 4RXWIVO4

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/4RXWIVO4Y6LTOJAI7BWE5PO43A \
  | 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: e46f6455dcc797372408f86c4ebddcd8046dd3aded817c58dbaf0d8d0870e139

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "548eac240a22891f1a0c3a741cf60a5dca5e35fc7cf05742606a96d85e325ff2",
    "cross_cats_sorted": [
      "cs.DC",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-01-05T16:53:38Z",
    "title_canon_sha256": "13732c568396126cf26c8db1a917e857f4d573f53ecac21578109c65269d34e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.02151",
    "kind": "arxiv",
    "version": 1
  }
}