Pith Number

pith:DGX5PKJ5

pith:2026:DGX5PKJ5HHWYCNOSW65CVF4U2R

not attested not anchored not stored refs pending

Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds

Bang-Xian Han, Zhuo-Nan Zhu

arxiv:2605.25448 v1 · 2026-05-25 · math.MG · math.FA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DGX5PKJ5HHWYCNOSW65CVF4U2R}

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	2026-05-26T02:04:36.012233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19afd7a93d39ed8135d2b7ba2a9794d457203ee183b8e3a9cc0e273632901d79

Aliases

arxiv: 2605.25448 · arxiv_version: 2605.25448v1 · doi: 10.48550/arxiv.2605.25448 · pith_short_12: DGX5PKJ5HHWY · pith_short_16: DGX5PKJ5HHWYCNOS · pith_short_8: DGX5PKJ5

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/DGX5PKJ5HHWYCNOSW65CVF4U2R \
  | 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: 19afd7a93d39ed8135d2b7ba2a9794d457203ee183b8e3a9cc0e273632901d79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b520b3ddcc9c33e06b82dc12ac0a9ad138e32794f80ec58d0041eab9efad82f8",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-25T05:58:49Z",
    "title_canon_sha256": "fb3c5df885e16d0d2ebb001fa6204f148daf078520e8db0a526def62fcda4356"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25448",
    "kind": "arxiv",
    "version": 1
  }
}