A complete kernel-only Lean proof of the three-copy Werner endpoint for every dimension

For C an operator on (C^d)^⊗3 of rank at most 2, let q(C) = sum over subsets S of {1,2,3} of (-1/2)^|S| times ||Tr_S C||_F^2. The inequality q(C) >= 0 is the three-copy Werner endpoint. I prove nothing new about Werner states in this note: the endpoint was already proved for every d >= 3 by Tomar, whose Lean formalization covers 3 <= d <= 8 only. What I contribute is a complete kernel-only Lean 4 proof of the endpoint for every d, by an independent, self-contained route: one exact rational certificate of the t = 1/d -> 0 limit of a strengthened moment relaxation, carried to every dimension by a lemma chain, with the certificate's exact identity proved in the Lean kernel. The final theorem depends only on the standard axioms propext, Classical.choice, and Quot.sound, with no sorry and no native_decide, and I had its statement independently checked to confirm it says what I claim here.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23895071
Primary Topic
Quantum Mechanics and Applications
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

A complete kernel-only Lean proof of the three-copy Werner endpoint for every dimension

Tyler Duic
1 links
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

A complete kernel-only Lean proof of the three-copy Werner endpoint for every dimension

Tyler Duic
preprint en

Abstract

For C an operator on (C^d)^⊗3 of rank at most 2, let q(C) = sum over subsets S of {1,2,3} of (-1/2)^|S| times ||Tr_S C||_F^2. The inequality q(C) >= 0 is the three-copy Werner endpoint. I prove nothing new about Werner states in this note: the endpoint was already proved for every d >= 3 by Tomar, whose Lean formalization covers 3 <= d <= 8 only. What I contribute is a complete kernel-only Lean 4 proof of the endpoint for every d, by an independent, self-contained route: one exact rational certificate of the t = 1/d -> 0 limit of a strengthened moment relaxation, carried to every dimension by a lemma chain, with the certificate's exact identity proved in the Lean kernel. The final theorem depends only on the standard axioms propext, Classical.choice, and Quot.sound, with no sorry and no native_decide, and I had its statement independently checked to confirm it says what I claim here.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon