Pith Number

pith:U5SHKQL6

pith:2025:U5SHKQL6XZWQ2F62BDRKWYWWFG

not attested not anchored not stored refs pending

Hierarchical Refinement: Optimal Transport to Infinity and Beyond

Benjamin J. Raphael, Julian Gold, Peter Halmos, Xinhao Liu

arxiv:2503.03025 v3 · 2025-03-04 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U5SHKQL6XZWQ2F62BDRKWYWWFG}

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

A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution

Receipt and verification

First computed	2026-07-05T11:54:44.815174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a76475417ebe6d0d17da08e2ab62d6299db7e5de9d5c8c30b240a4d75a089bd1

Aliases

arxiv: 2503.03025 · arxiv_version: 2503.03025v3 · doi: 10.48550/arxiv.2503.03025 · pith_short_12: U5SHKQL6XZWQ · pith_short_16: U5SHKQL6XZWQ2F62 · pith_short_8: U5SHKQL6

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/U5SHKQL6XZWQ2F62BDRKWYWWFG \
  | 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: a76475417ebe6d0d17da08e2ab62d6299db7e5de9d5c8c30b240a4d75a089bd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98dcec8340aa125ec94ff33e7856f4959397d37b553ebc0c3d1e8e17fb0e0077",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-03-04T22:00:12Z",
    "title_canon_sha256": "eb149f67010c23003d773c42f19c36ad0d75c9f6effbb5c85dc8cd759a5361fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.03025",
    "kind": "arxiv",
    "version": 3
  }
}