Pith Number

pith:2QW53NYJ

pith:2021:2QW53NYJB5ZK6Q4S4AQ22M7JBS

not attested not anchored not stored refs pending

Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization

Alexander Korotin, Evgeny Burnaev, Justin Solomon, Lingxiao Li

arxiv:2102.01752 v1 · 2021-02-02 · 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{2QW53NYJB5ZK6Q4S4AQ22M7JBS}

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.

Cited by

2 papers in Pith

Implicit Neural Optimal Transport via Fixed-Point Optimization

Receipt and verification

First computed	2026-07-05T03:44:25.080422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d42dddb7090f72af4392e021ad33e90ca2be792c421515cd2c2f94df6ebe2cd8

Aliases

arxiv: 2102.01752 · arxiv_version: 2102.01752v1 · doi: 10.48550/arxiv.2102.01752 · pith_short_12: 2QW53NYJB5ZK · pith_short_16: 2QW53NYJB5ZK6Q4S · pith_short_8: 2QW53NYJ

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/2QW53NYJB5ZK6Q4S4AQ22M7JBS \
  | 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: d42dddb7090f72af4392e021ad33e90ca2be792c421515cd2c2f94df6ebe2cd8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffe9e383566ec204b72dcd7392c8df9cb2730fce514d91209ca0d7f7232c46e6",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-02-02T21:01:13Z",
    "title_canon_sha256": "309db1adacc2c96d4206db5d9b4755844100c47f2ce5f8d7bd24328f5029916f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.01752",
    "kind": "arxiv",
    "version": 1
  }
}