Pith Number

pith:PVXJC3IA

pith:2024:PVXJC3IAXMLLBWSAGYTSYQAZU4

not attested not anchored not stored refs pending

On the geometry of Wasserstein barycenter I

Bang-Xian Han, Deng-Yu Liu, Zhuo-Nan Zhu

arxiv:2412.01190 v2 · 2024-12-02 · 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{PVXJC3IAXMLLBWSAGYTSYQAZU4}

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

Wasserstein Barycenter Convexity Detects Hilbertian Geometry

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

Receipt and verification

First computed	2026-07-05T11:23:20.282945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d6e916d00bb16b0da4036272c4019a70261378ab09125e13bf19c42846bd7cd

Aliases

arxiv: 2412.01190 · arxiv_version: 2412.01190v2 · doi: 10.48550/arxiv.2412.01190 · pith_short_12: PVXJC3IAXMLL · pith_short_16: PVXJC3IAXMLLBWSA · pith_short_8: PVXJC3IA

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/PVXJC3IAXMLLBWSAGYTSYQAZU4 \
  | 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: 7d6e916d00bb16b0da4036272c4019a70261378ab09125e13bf19c42846bd7cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5f7162612ff060c8fc4193cfa8ad59ab2bc9d18a5dc969f0808ebc4b575dc86",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-12-02T06:48:42Z",
    "title_canon_sha256": "730750be5fa6bc36d6f3c1fccaa19f90882857c01911f2a8a37fb4e67a6cd198"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.01190",
    "kind": "arxiv",
    "version": 2
  }
}