Pith Number

pith:HULU6AXZ

pith:2011:HULU6AXZ6MLKUUP6ORKRUKPZMT

not attested not anchored not stored refs pending

Stochastic gradient descent on Riemannian manifolds

Silvere Bonnabel

arxiv:1111.5280 v4 · 2011-11-22 · math.OC · cs.LG · 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{HULU6AXZ6MLKUUP6ORKRUKPZMT}

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	2026-05-18T00:58:43.274436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d174f02f9f316aa51fe74551a29f964c8ac2ab7bac493b3783f69f9b765dc4c

Aliases

arxiv: 1111.5280 · arxiv_version: 1111.5280v4 · doi: 10.48550/arxiv.1111.5280 · pith_short_12: HULU6AXZ6MLK · pith_short_16: HULU6AXZ6MLKUUP6 · pith_short_8: HULU6AXZ

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/HULU6AXZ6MLKUUP6ORKRUKPZMT \
  | 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: 3d174f02f9f316aa51fe74551a29f964c8ac2ab7bac493b3783f69f9b765dc4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e89ae52c98675fd0eec665537835386a34a886bd82d033b07d32d4a1e61e3286",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-11-22T18:41:12Z",
    "title_canon_sha256": "19888cf26cd1fd92aabdcc8c5b61f68ad210a732983c795f9d6ac76693b30bc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5280",
    "kind": "arxiv",
    "version": 4
  }
}