Pith Number

pith:BPC6XACR

pith:2019:BPC6XACRDMB5YUDLMZHXLIWQZ6

not attested not anchored not stored refs pending

Tensor product and Hadamard product for the Wasserstein means

Jinmi Hwang, Sejong Kim

arxiv:1908.09261 v1 · 2019-08-25 · 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{BPC6XACRDMB5YUDLMZHXLIWQZ6}

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	2026-07-04T23:59:38.585114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bc5eb80511b03dc506b664f75a2d0cf8a215b307ff1b78f9af85503542d367b

Aliases

arxiv: 1908.09261 · arxiv_version: 1908.09261v1 · doi: 10.48550/arxiv.1908.09261 · pith_short_12: BPC6XACRDMB5 · pith_short_16: BPC6XACRDMB5YUDL · pith_short_8: BPC6XACR

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/BPC6XACRDMB5YUDLMZHXLIWQZ6 \
  | 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: 0bc5eb80511b03dc506b664f75a2d0cf8a215b307ff1b78f9af85503542d367b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c85772f4e902bf6f23aa700af070a9ed13f0d4ace7afcd594df7bf7b69119f7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-25T07:03:10Z",
    "title_canon_sha256": "e73fd48e3a5820583afe4048008b971ec187f5f10f4140bdada7ffc857d9e640"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09261",
    "kind": "arxiv",
    "version": 1
  }
}