Pith Number

pith:22ZGY44N

pith:2026:22ZGY44NNBRCSXIXDCQ5J4RBMM

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From Schrodinger Bridge to Optimal Transport over Sub-Riemannian Manifolds

Bahman Gharesifard, Daniel Owusu Adu, Karthik Elamvazhuthi

Entropic regularization by control-aligned noise turns sub-Riemannian optimal transport into a tractable Schrödinger bridge problem.

arxiv:2605.11429 v2 · 2026-05-12 · math.OC

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Claims

C1strongest claim

Under bracket-generating hypotheses we obtain smooth, strictly positive transition densities and a forward--backward characterization of the optimal bridge. This leads to a practical Sinkhorn-type algorithm for the Schrödinger potentials and, as the noise level vanishes, a recovery of the deterministic sub-Riemannian optimal transport problem.

C2weakest assumption

The added noise is aligned with the control directions and the manifold satisfies bracket-generating hypotheses, which are invoked to guarantee smooth strictly positive transition densities for the degenerate diffusion.

C3one line summary

Develops Schrödinger bridge formulation for optimal transport and distribution steering on sub-Riemannian manifolds under bracket-generating conditions, with numerical Sinkhorn solver and deterministic limit recovery.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Daniel Owusu Adu,Optimal transport for averaged control, IEEE Control Systems Letters7(2022), 727–732 2022

[2] Daniel Owusu Adu and Yongxin Chen,Schrödinger bridge over averaged systems, (2024) 2024

[3] Andrei Agrachev and Paul Lee,Optimal transportation under nonholonomic constraints, Transactions of the American Mathematical Society361(2009), no. 11, 6019–6047 2009

[4] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré,Gradient flows: in metric spaces and in the space of probability measures, Springer, 2005 2005

[5] G Ben Arous and Rémi Léandre,Décroissance exponentielle du noyau de la chaleur sur la diagonale (ii), Probability Theory and Related Fields90(1991), no. 3, 377–402 1991

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:43.921977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6b26c738d6862295d1718a1d4f2216326f2d6f33bae5b0d5c73fb6be6d7bc18

Aliases

arxiv: 2605.11429 · arxiv_version: 2605.11429v2 · doi: 10.48550/arxiv.2605.11429 · pith_short_12: 22ZGY44NNBRC · pith_short_16: 22ZGY44NNBRCSXIX · pith_short_8: 22ZGY44N

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/22ZGY44NNBRCSXIXDCQ5J4RBMM \
  | 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: d6b26c738d6862295d1718a1d4f2216326f2d6f33bae5b0d5c73fb6be6d7bc18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a27a4ae0d5326f1ef20cdd2f5dda7581ddf9c780e9cb00b50d4fb0d85d6b713",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-12T02:30:08Z",
    "title_canon_sha256": "3a19822fac5f15f28ab6acf653adce1107c3dd2a9f912fea9abc375430567f5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11429",
    "kind": "arxiv",
    "version": 2
  }
}