Pith Number

pith:KWBHW2OF

pith:2020:KWBHW2OFUYQ6Q4PFKYSDAJKDB2

not attested not anchored not stored refs pending

Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives

Michael I. Jordan, Michael Muehlebach

arxiv:2002.12493 v2 · 2020-02-28 · math.OC · cs.NA · math.NA · 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{KWBHW2OFUYQ6Q4PFKYSDAJKDB2}

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	2026-07-05T02:30:56.852644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55827b69c5a621e871e556243025430e9205a6b142e05b0d17f257fc985793a2

Aliases

arxiv: 2002.12493 · arxiv_version: 2002.12493v2 · doi: 10.48550/arxiv.2002.12493 · pith_short_12: KWBHW2OFUYQ6 · pith_short_16: KWBHW2OFUYQ6Q4PF · pith_short_8: KWBHW2OF

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/KWBHW2OFUYQ6Q4PFKYSDAJKDB2 \
  | 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: 55827b69c5a621e871e556243025430e9205a6b142e05b0d17f257fc985793a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1480669ffef178830bed96561a37dfc35111e93aaefa0773f7b63d0d5daf0a85",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-02-28T00:32:47Z",
    "title_canon_sha256": "ea1411e0e22b58008be6b4baf2e9646c2d633f5efc84d1f42226eba9bdcdfea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.12493",
    "kind": "arxiv",
    "version": 2
  }
}