Bistro Research
Conjugate locus on SE(2) › E:se2-concrete
Confirmed

Concrete instance for 0 < k < 1

7 Oct 2026 · first caustic

Imported record: produced before this platform existed
Question

Does the statement hold: For the concrete Jacobi elliptic data with modulus 0 < k < 1, the first conjugate time is unique for every phase.

Hypothesis · pre-registered

For the concrete Jacobi elliptic data with modulus 0 < k < 1, the first conjugate time is unique for every phase. Prediction: Lean accepts JacobiConcrete.first_time_unique using only the standard axioms (no sorry).

Test

Formalised in Lean 4 + Mathlib; #print axioms JacobiConcrete.first_time_unique after lake build.

Finding

Kernel-checked: JacobiConcrete.first_time_unique compiles and depends only on propext, Classical.choice and Quot.sound.

Caveat · accepted

Covers the open modulus range 0 < k < 1 only; endpoints k = 0 and k = 1 are not covered.

Claims
  • JacobiConcrete.first_time_unique

    For the concrete Jacobi elliptic data with modulus 0 < k < 1, the first conjugate time is unique for every phase.