Pith Number

pith:LXWVALZL

pith:2026:LXWVALZLTQJZVLSV4SFQRZ3AF2

not attested not anchored not stored refs pending

Stability of the Monge Map in Semi-Dual Optimal Transport

Anton Selitskiy, David Millard

The semi-dual optimal transport formulation allows Monge maps to converge under conditions that do not require the dual potential to be optimal.

arxiv:2605.05569 v3 · 2026-05-07 · math.OC · cs.LG

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Record completeness

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4 Citations open

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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

We derive necessary and sufficient conditions for the convergence of Monge maps without requiring optimality of the dual potential.

C2weakest assumption

The derivation relies on standard regularity assumptions for the cost function and marginal measures in optimal transport; the abstract does not specify whether these are relaxed or if additional technical conditions are introduced.

C3one line summary

Semi-dual OT formulation has degenerate saddle-point structure; necessary and sufficient conditions for Monge map convergence are derived without requiring dual potential optimality.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:05:15.401111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ded502f2b9c139aae55e48b08e7602e92de7ec592d6344c8747ebff08de59fa

Aliases

arxiv: 2605.05569 · arxiv_version: 2605.05569v3 · doi: 10.48550/arxiv.2605.05569 · pith_short_12: LXWVALZLTQJZ · pith_short_16: LXWVALZLTQJZVLSV · pith_short_8: LXWVALZL

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LXWVALZLTQJZVLSV4SFQRZ3AF2 \
  | 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: 5ded502f2b9c139aae55e48b08e7602e92de7ec592d6344c8747ebff08de59fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "864d89ccb6419222a83e4b402fe30d4d26fc025ba2266097f3a8884871f4fa7d",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-07T01:22:20Z",
    "title_canon_sha256": "cfef1ede2dcce7e53932a2e4334a824792fb27145605189a785093407d594d40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.05569",
    "kind": "arxiv",
    "version": 3
  }
}