Pith Number

pith:BBZ62OUD

pith:2021:BBZ62OUDPOBLJGZF3MOTGZZ53L

not attested not anchored not stored refs pending

A dual formula for the noncommutative transport distance

Melchior Wirth

arxiv:2104.11923 v2 · 2021-04-24 · math-ph · math.MP · math.OA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BBZ62OUDPOBLJGZF3MOTGZZ53L}

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

1 paper in Pith

Wigner symmetries single out symmetric Wasserstein distances in all finite dimensions

Receipt and verification

First computed	2026-07-05T04:17:58.681376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0873ed3a837b82b49b25db1d33673ddae430d167f84e027b76802ba6ff26d684

Aliases

arxiv: 2104.11923 · arxiv_version: 2104.11923v2 · doi: 10.48550/arxiv.2104.11923 · pith_short_12: BBZ62OUDPOBL · pith_short_16: BBZ62OUDPOBLJGZF · pith_short_8: BBZ62OUD

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/BBZ62OUDPOBLJGZF3MOTGZZ53L \
  | 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: 0873ed3a837b82b49b25db1d33673ddae430d167f84e027b76802ba6ff26d684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d59af236233c1c06be4f587fc61e24560f1e14e739f7b47ed13cbd86bfedd90c",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2021-04-24T10:55:15Z",
    "title_canon_sha256": "2b0064a3df35bd065b314c74dbf670618e15b48da18c89fd671ece8e03f7d912"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.11923",
    "kind": "arxiv",
    "version": 2
  }
}