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Extend N=6 integer quantum obstruction to all D ≥ 3 - #1

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Extend N=6 integer quantum obstruction to all D ≥ 3#1
DomTheDeveloper wants to merge 7 commits into
infinityscroll:agent/solve-quantum-graph-n6d3-intfrom
DomTheDeveloper:agent/quantum-n6-all-colors-status

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@DomTheDeveloper

@DomTheDeveloper DomTheDeveloper commented Jul 22, 2026

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Ready for incorporation into google-deepmind#4511

This stack adds the general color-restriction theorem needed to extend the N = 6, D = 3 integer obstruction to every D ≥ 3, together with the exact four declaration updates:

  • eqSystem6_no_solution_d5_int
  • eqSystem6_no_solution_ge3_int
  • eqSystem6_no_solution_d5_trinary_int
  • eqSystem6_no_solution_ge3_trinary_int

Verification

The complete proof is merged in DomTheDeveloper/formal-conjectures at commit 0245b5cadcd166252109959d9895b363a63ae1c2.

Pinned-Lean verification completed successfully:

  • all 47 reflected LRAT certificate cases rebuilt;
  • the global N = 6, D = 3 integer obstruction compiled;
  • the standalone color-restriction theorem compiled with no sorryAx;
  • all four terminal D ≥ 3 consequences compiled with no sorryAx.

The structural theorem depends only on propext, Classical.choice, and Quot.sound. The terminal computational consequences additionally use the documented reflected machinery Lean.ofReduceBool and Lean.trustCompiler.

A separate one-commit statement-only branch rooted at current GDM main is available at DomTheDeveloper:agent/quantum-n6-all-colors-gdm-final.

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