Pith Number

pith:ZWKT3N5U

pith:2026:ZWKT3N5UCCLSFLRWLOCIUIYWSO

not attested not anchored not stored refs pending

Wasserstein Barycenter Convexity Detects Hilbertian Geometry

Bang-Xian Han, Deng-Yu Liu

arxiv:2606.28213 v1 · 2026-06-26 · math.MG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWKT3N5UCCLSFLRWLOCIUIYWSO}

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	2026-06-29T01:15:09.479522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd953db7b4109722ae365b848a23169388a6977b106a1b8bba3d9745e2501f1a

Aliases

arxiv: 2606.28213 · arxiv_version: 2606.28213v1 · doi: 10.48550/arxiv.2606.28213 · pith_short_12: ZWKT3N5UCCLS · pith_short_16: ZWKT3N5UCCLSFLRW · pith_short_8: ZWKT3N5U

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/ZWKT3N5UCCLSFLRWLOCIUIYWSO \
  | 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: cd953db7b4109722ae365b848a23169388a6977b106a1b8bba3d9745e2501f1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b19ed2d6ab115af331465e5fb3447d4ccf7f410e00d39fda4de59df1e4c2cd4",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-06-26T16:05:37Z",
    "title_canon_sha256": "45484e1d02852691a330a9d7e1742330a9ca333c3740557c18b2b01e40c06450"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28213",
    "kind": "arxiv",
    "version": 1
  }
}