Pith Number

pith:TIE3ZXO7

pith:2020:TIE3ZXO7WHRTWZR2JE56ANGNZM

not attested not anchored not stored refs pending

Momentum Improves Optimization on Riemannian Manifolds

Antonio Orvieto, Aurelien Lucchi, Foivos Alimisis, Gary B\'ecigneul

arxiv:2002.04144 v2 · 2020-02-11 · 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{TIE3ZXO7WHRTWZR2JE56ANGNZM}

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	2026-07-05T02:14:52.764695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a09bcdddfb1e33b663a493be034cdcb0f99cf12edb94ce75b9ca88c3527c936

Aliases

arxiv: 2002.04144 · arxiv_version: 2002.04144v2 · doi: 10.48550/arxiv.2002.04144 · pith_short_12: TIE3ZXO7WHRT · pith_short_16: TIE3ZXO7WHRTWZR2 · pith_short_8: TIE3ZXO7

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/TIE3ZXO7WHRTWZR2JE56ANGNZM \
  | 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: 9a09bcdddfb1e33b663a493be034cdcb0f99cf12edb94ce75b9ca88c3527c936

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0d1c1aec32270ac542ee5c88f799aced9770b6e494a22d9e49aad4232a6c03b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-02-11T00:15:17Z",
    "title_canon_sha256": "72039906ae9cc7b5debd450ad3a696783a0434097946404814cbdc9a954e142c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.04144",
    "kind": "arxiv",
    "version": 2
  }
}