Pith Number

pith:Z2RIVFFT

pith:2024:Z2RIVFFTVJWZOT4W6BMW4UO2OW

not attested not anchored not stored refs pending

Sinkhorn Algorithm for Sequentially Composed Optimal Transports

Kazuki Watanabe, Noboru Isobe

arxiv:2412.03120 v4 · 2024-12-04 · cs.DS · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2RIVFFTVJWZOT4W6BMW4UO2OW}

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	2026-07-05T09:59:56.520633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cea28a94b3aa6d974f96f0596e51da75a92da06e51039d3baf5e7222976bc0d2

Aliases

arxiv: 2412.03120 · arxiv_version: 2412.03120v4 · doi: 10.48550/arxiv.2412.03120 · pith_short_12: Z2RIVFFTVJWZ · pith_short_16: Z2RIVFFTVJWZOT4W · pith_short_8: Z2RIVFFT

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/Z2RIVFFTVJWZOT4W6BMW4UO2OW \
  | 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: cea28a94b3aa6d974f96f0596e51da75a92da06e51039d3baf5e7222976bc0d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570ca06b6f89adc42531daadb363dff9becb4fa44e1e21e362a0d08fe89acef6",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2024-12-04T08:39:45Z",
    "title_canon_sha256": "9572f0b823c16018a2e9cff8c5962e3ea9ae50fee650fae7a75f918e05468545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03120",
    "kind": "arxiv",
    "version": 4
  }
}