Pith Number

pith:K6MDJ447

pith:2025:K6MDJ4476TURBIKT3N4JQMRYKW

not attested not anchored not stored refs pending

Closing the Gap: Efficient Algorithms for Discrete Wasserstein Barycenters

Jiaqi Wang, Weijun Xie

arxiv:2511.04607 v2 · 2025-11-06 · 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{K6MDJ4476TURBIKT3N4JQMRYKW}

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	2026-08-04T01:58:07.196610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

579834f39ff4e910a153db78983238558d6468e7004feb6a9f10c5eff0b4e324

Aliases

arxiv: 2511.04607 · arxiv_version: 2511.04607v2 · doi: 10.48550/arxiv.2511.04607 · pith_short_12: K6MDJ4476TUR · pith_short_16: K6MDJ4476TURBIKT · pith_short_8: K6MDJ447

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/K6MDJ4476TURBIKT3N4JQMRYKW \
  | 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: 579834f39ff4e910a153db78983238558d6468e7004feb6a9f10c5eff0b4e324

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32f438568dd1e6ce88b28e2ee76e292f983762e41b91fcb0b27c0ad312e2d18b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-11-06T17:58:42Z",
    "title_canon_sha256": "6919b1d170b318da617bdb41cb0d466e46269739eb0ef16305140b4e8d6cfcc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.04607",
    "kind": "arxiv",
    "version": 2
  }
}