Pith Number

pith:TH6UZUYX

pith:2026:TH6UZUYXS6R5JI4I2ICMMMPKPY

not attested not anchored not stored refs pending

Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case

Guillaume Wang

The Sinkhorn algorithm converges at an O(k^{-1} log k) rate in ell_1 marginal error under the asymptotically scalable condition.

arxiv:2604.26265 v3 · 2026-04-29 · math.OC

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\pithnumber{TH6UZUYXS6R5JI4I2ICMMMPKPY}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications 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 prove that the Sinkhorn algorithm converges at a rate of O(k^{-1} log k) in ℓ1-norm marginal error, in the asymptotically scalable case.

C2weakest assumption

The analysis requires the problem to be in the asymptotically scalable case, whose precise definition and verification conditions are not detailed in the abstract.

C3one line summary

Sinkhorn algorithm converges at O(k^{-1} log k) rate in l1-norm marginal error for asymptotically scalable instances, nearly matching the Omega(k^{-1}) lower bound.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-30T01:17:38.782775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99fd4cd31797a3d4a388d204c631ea7e1cf55cc9395ec1db724c55ad653df7f9

Aliases

arxiv: 2604.26265 · arxiv_version: 2604.26265v3 · doi: 10.48550/arxiv.2604.26265 · pith_short_12: TH6UZUYXS6R5 · pith_short_16: TH6UZUYXS6R5JI4I · pith_short_8: TH6UZUYX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TH6UZUYXS6R5JI4I2ICMMMPKPY \
  | 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: 99fd4cd31797a3d4a388d204c631ea7e1cf55cc9395ec1db724c55ad653df7f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c21083ce87169f1c07174107917e1032fbeb439bae7345321bbccf896c231d70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-29T03:48:58Z",
    "title_canon_sha256": "e49e128194bfaeade319541a85f4cdb338aa413fd56792cfab87a8851af9100e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26265",
    "kind": "arxiv",
    "version": 3
  }
}