Pith Number

pith:VSF5E2PM

pith:2021:VSF5E2PMYTQPFWRRRG7YDTF5US

not attested not anchored not stored refs pending

Randomized Stochastic Gradient Descent Ascent

Gabriel Peyr\'e, Marco Cuturi, Othmane Sebbouh

arxiv:2111.13162 v1 · 2021-11-25 · cs.LG · math.OC · 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{VSF5E2PMYTQPFWRRRG7YDTF5US}

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	2026-07-05T03:35:18.082574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac8bd269ecc4e0f2da3189bf81ccbda496af2af510625fa4aa1a38e414ff0da2

Aliases

arxiv: 2111.13162 · arxiv_version: 2111.13162v1 · doi: 10.48550/arxiv.2111.13162 · pith_short_12: VSF5E2PMYTQP · pith_short_16: VSF5E2PMYTQPFWRR · pith_short_8: VSF5E2PM

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/VSF5E2PMYTQPFWRRRG7YDTF5US \
  | 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: ac8bd269ecc4e0f2da3189bf81ccbda496af2af510625fa4aa1a38e414ff0da2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc527307db157f98c2465a9240a9c48f34ea2ab587d179befda4959543e053aa",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-11-25T16:44:19Z",
    "title_canon_sha256": "f4da98507defba10dc1d019cc38debfdddda9e1926ea765925811e1ff2815529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.13162",
    "kind": "arxiv",
    "version": 1
  }
}