IndisputableMonolith.NumberTheory.EulerCarrierComplex
The module supplies the open half-plane Re(s) > 1/2 as the domain for complex carrier functions in the Recognition Science number theory layer. Researchers assembling the Euler product instantiation or contour-winding arguments cite it when bridging discrete cost to analytic traces. It is a definition module containing no theorems, only supporting objects such as ComplexCarrierCert and zero-winding certificates that are imported by four downstream modules.
claimThe open half-plane $\{s \in \mathbb{C} \mid \frac12 < \operatorname{Re}(s)\}$.
background
Recognition Science fixes the time quantum $\tau_0 = 1$ tick in the Constants module and defines the abstract cost structure in the Cost module. The present module works inside the NumberTheory domain and introduces the right half-plane as the setting for holomorphic carrier functions. Its siblings define stripHalfPlane, ComplexCarrierCert, contourWinding, and ZeroWindingCert, all operating on this half-plane.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module is imported by AnalyticTrace to assemble the axiom-free RH bridge (replacing zeroWindingOfHolNonvanishing), by ContourWinding to define winding numbers on disks, by EulerInstantiation to instantiate the RS carrier via the Euler product, and by SampledTrace to connect to discrete annular sampling. It supplies the domain required for the zero-winding certificates that close the former axiom gap.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not define the Riemann zeta function or Euler product.
- Does not depend on other NumberTheory modules.
- Does not address the left half-plane or critical line.