Pith Number

pith:V2DV6AWX

pith:2019:V2DV6AWXWHHFODSJICW5CGGU4U

not attested not anchored not stored refs pending

Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics

Minh Ha Quang

arxiv:1908.09275 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{V2DV6AWXWHHFODSJICW5CGGU4U}

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	2026-07-04T23:59:38.781702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae875f02d7b1ce570e4940add118d4e526f21c3aea41d35e242313d3a772763c

Aliases

arxiv: 1908.09275 · arxiv_version: 1908.09275v1 · doi: 10.48550/arxiv.1908.09275 · pith_short_12: V2DV6AWXWHHF · pith_short_16: V2DV6AWXWHHFODSJ · pith_short_8: V2DV6AWX

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/V2DV6AWXWHHFODSJICW5CGGU4U \
  | 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: ae875f02d7b1ce570e4940add118d4e526f21c3aea41d35e242313d3a772763c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03c14db0fd4462d07694339139bc61dbd97b69b4f93af494575d7361271c07fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-25T08:26:15Z",
    "title_canon_sha256": "8f5b1630aedd2b3088afcb94c4a545803449632f26a2ce2b1179e2242587fa9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09275",
    "kind": "arxiv",
    "version": 1
  }
}