IndisputableMonolith.NumberTheory.EulerCarrierComplex
EulerCarrierComplex defines the open half-plane Re(s) > 1/2 as the domain for complex carriers in the Recognition Science number theory layer. It is imported by AnalyticTrace, ContourWinding, EulerInstantiation, and SampledTrace to support the axiom-free RH bridge and Euler product cost instantiation. The module contains only definitions with no theorems or proofs.
claimThe open half-plane $H = { s ∈ ℂ | Re(s) > 1/2 }$.
background
The module belongs to the NumberTheory domain and imports Constants (setting the RS time quantum τ₀ = 1 tick) together with Cost for the abstract carrier/sensor framework. Its sole documented object is the open half-plane Re(s) > 1/2, which supplies the region for Euler carriers in the zeta-function setting. Recognition Science derives all physics from one functional equation whose J-uniqueness and phi fixed point yield the eight-tick octave and D = 3; the present module supplies the complex-plane domain needed to instantiate that cost structure analytically.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the domain required by AnalyticTrace to assemble the full RH bridge after replacing former axioms with contourWinding, by ContourWinding for zero winding of holomorphic nonvanishing functions, by EulerInstantiation to realize the RS cost structure via the Euler product, and by SampledTrace to bridge continuous contours to discrete annular samples. It therefore closes the complex-domain step between the J-cost foundation and the analytic trace interface.
scope and limits
- Does not prove any analytic continuation or zero-free properties inside the half-plane.
- Does not connect the half-plane to the phi-ladder, mass formula, or Berry threshold.
- Does not contain the contour winding or zero-holonomy theorems.
- Does not define the Euler product or zeta function itself.