Pith Number

pith:3PVMVUTL

pith:2017:3PVMVUTLLCJZEAJOAUBI2CQFLF

not attested not anchored not stored refs pending

Matricial Wasserstein-1 Distance

Allen Tannenbaum, Lipeng Ning, Tryphon T. Georgiou, Yongxin Chen

arxiv:1702.07921 v2 · 2017-02-25 · math.FA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PVMVUTLLCJZEAJOAUBI2CQFLF}

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	2026-05-18T00:49:31.326118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbeacad26b589392012e05028d0a055966ae06d68438d9a651b4cff9e19d6b11

Aliases

arxiv: 1702.07921 · arxiv_version: 1702.07921v2 · doi: 10.48550/arxiv.1702.07921 · pith_short_12: 3PVMVUTLLCJZ · pith_short_16: 3PVMVUTLLCJZEAJO · pith_short_8: 3PVMVUTL

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/3PVMVUTLLCJZEAJOAUBI2CQFLF \
  | 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: dbeacad26b589392012e05028d0a055966ae06d68438d9a651b4cff9e19d6b11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e49d991741f839c9c63048072cf8c3f7f220bff6af5fc38dc821747fcdd8fee",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-02-25T16:58:14Z",
    "title_canon_sha256": "1c7869241da2fa3f53632b7c46f9ca8c86dd3a8e72945de20516625c7b2b88f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.07921",
    "kind": "arxiv",
    "version": 2
  }
}