Module adelic 

The adelic carrier — a value living at both kinds of place at once.

𝔸_ℚ  =  ℝ  ×  ∏′_p ℚ_p
        ▲            ▲
   infinite place    finite places

An Adelic pairs a finite component (pure RNS over a Basis — the carry-free, embarrassingly parallel arithmetic) with an infinite component (a rigorous Ball — the real interval that answers every Archimedean question: sign, comparison, magnitude, decimal output).

• Exactness comes from the finite part (reconstructed at the boundary).
• Sign / order / output come from the infinite part — never from the residues, which are constitutionally blind to size.

Overflow is a detected event: when the finite reconstruction cannot be validated against the infinite ball, RangeError::ReconstructionFailed is returned and the caller extends the basis (see the headline test in the refactor plan §11).

Structs

Adelic

A value carried at the finite places (F) and the infinite place (Ball).

RnsFrac

A rational carried as one field element p·q⁻¹ (mod pᵢ) per channel.

Traits

Finite

The finite (∏ ℚ_p) component of an adelic value: RNS arithmetic plus a reconstruction routine that may detect range overflow.

Type Aliases

AdelicInt

Integer instantiation.

AdelicRat

Rational instantiation.