Sylvain Gefffroy

Multiplier towers of the quadratic family x² + c: irreducibility, Galois groups, and maximal Kummer towers

This paper isolates and settles one algebraic component of a broader programme on how arithmetic information is retained by finite critical orbits across modular levels. This program called "Remanent tomography of multiplicatives structures" is currently in progress. In the quadr...

Remanent Tomography of Multiplicative Structures by Dynamic Collisions: Universal Reconstruction and Local–Global Separation

We study a collision-based reconstruction problem for the ideal lattice of the residue ring Z modulo n. For the quadratic transport family $F_c(x) = x^2 + c$, we consider critical orbits and the collision ideals generated by differences of orbit terms modulo n. Closing these coll...

Remanent Tomography of Multiplicative Structures by Dynamic Collisions: Universal Reconstruction and Local–Global Separation

We study a collision-based reconstruction problem for the ideal lattice of the residue ring Z modulo n. For the quadratic transport family $F_c(x) = x^2 + c$, we consider critical orbits and the collision ideals generated by differences of orbit terms modulo n. Closing these coll...

Variable arithmetic periods : A Multiscale Generalization of Ren's Image-Size Method to Logarithmic Depth Using Harmonic Fiber Weighting

This work develops a new method for estimating the size of iterated images of the quadratic map sending x to x squared plus one over finite prime fields, with the aim of controlling the smallest prime carrying a prescribed exact critical period. The approach departs from Ren’s me...

Variable arithmetic periods : A Multiscale Generalization of Ren's Image-Size Method to Logarithmic Depth Using Harmonic Fiber Weighting

This work develops a new method for estimating the size of iterated images of the quadratic map sending x to x squared plus one over finite prime fields, with the aim of controlling the smallest prime carrying a prescribed exact critical period. The approach departs from Ren’s me...