Pith Number

pith:W5HTNHFN

pith:2025:W5HTNHFNN3VPJZQSGI7523ALZ7

not attested not anchored not stored refs pending

A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures

Takafumi Saito, Yumiharu Nakano

arxiv:2507.09206 v1 · 2025-07-12 · 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{W5HTNHFNN3VPJZQSGI7523ALZ7}

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	2026-07-05T11:36:05.445998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b74f369cad6eeaf4e612323fdd6c0bcfc4cfceed4fc7103cfd1338633a039701

Aliases

arxiv: 2507.09206 · arxiv_version: 2507.09206v1 · doi: 10.48550/arxiv.2507.09206 · pith_short_12: W5HTNHFNN3VP · pith_short_16: W5HTNHFNN3VPJZQS · pith_short_8: W5HTNHFN

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/W5HTNHFNN3VPJZQSGI7523ALZ7 \
  | 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: b74f369cad6eeaf4e612323fdd6c0bcfc4cfceed4fc7103cfd1338633a039701

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6e5ade3bb7baef49b1d78478ddaa22fd494587e9016b444a47d672508a4084e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-12T08:55:54Z",
    "title_canon_sha256": "378fe91da99ed28a7d0bbedad80118fbc4b614fe4fac08a6b51f979286f26447"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09206",
    "kind": "arxiv",
    "version": 1
  }
}