Pith Number

pith:2CMPZYAL

pith:2026:2CMPZYAL5GI652OFBDTWOJ22SR

not attested not anchored not stored refs pending

Continuum-marginal optimal transport: a mesh-free kernel method

Yumiharu Nakano

A reproducing kernel Hilbert space embedding of the weak continuity equation yields a sample-only objective for recovering minimum-energy velocity fields that match a continuum of probability marginals.

arxiv:2604.24226 v2 · 2026-04-27 · math.OC · cs.NA · math.NA · stat.ML

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\usepackage{pith}
\pithnumber{2CMPZYAL5GI652OFBDTWOJ22SR}

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Record completeness

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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.

Claims

C1strongest claim

The weak continuity equation is embedded in a reproducing kernel Hilbert space, yielding a sample-only objective that requires no spatial discretization. The velocity is parametrized by any linear-in-parameters dictionary or neural network, and is optimized by mini-batch stochastic methods. Synthetic experiments confirm that the method achieves accurate drift recovery and marginal consistency.

C2weakest assumption

That embedding the weak continuity equation in an RKHS produces an objective whose minimizer recovers the true velocity field from finite samples without additional regularization or post-hoc corrections.

C3one line summary

A reproducing kernel Hilbert space embedding yields a sample-only objective for solving continuum-marginal optimal transport without spatial discretization.

Receipt and verification

First computed	2026-06-03T01:05:14.040404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d098fce00be991eee9c508e767275a944613f532112459d0d6a324a23270a213

Aliases

arxiv: 2604.24226 · arxiv_version: 2604.24226v2 · doi: 10.48550/arxiv.2604.24226 · pith_short_12: 2CMPZYAL5GI6 · pith_short_16: 2CMPZYAL5GI652OF · pith_short_8: 2CMPZYAL

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/2CMPZYAL5GI652OFBDTWOJ22SR \
  | 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: d098fce00be991eee9c508e767275a944613f532112459d0d6a324a23270a213

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c98b952905cd45dd57b2459e06b31141d6343958f8153e3f27cc5f52bff80e7c",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-27T09:33:52Z",
    "title_canon_sha256": "b9ba38886e8889554d2873d35066f686e51ff0418e689d3e959dd55108cdaa1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24226",
    "kind": "arxiv",
    "version": 2
  }
}