IndisputableMonolith.YM.Kernel
The YM.Kernel module supplies core definitions for transfer kernels and their matrix representations within the Recognition Science YM domain. It organizes sibling structures including TransferKernel, MatrixView, MatrixBridge, and utilities such as buildKernelFromMatrix and constantStochastic3x3. Researchers modeling stochastic kernels or matrix bridges in this framework would cite these definitions directly. The module functions purely as a definition hub with no internal proofs.
claimThe module introduces the transfer kernel $T$ together with its matrix view $M$ and the constant stochastic $3times3$ kernel $K$ equipped with a bridge $B$ satisfying the matrix representation property.
background
This module resides in the YM domain and imports only Mathlib to support type and structure definitions. It introduces TransferKernel as the central type for kernel objects, MatrixView to expose kernels as matrices, and MatrixBridge to link the two representations. Additional definitions cover buildKernelFromMatrix for construction from matrix data and constantStochastic3x3 for a fixed stochastic example. The local setting is purely definitional, establishing notation for later kernel operations without theorems.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the kernel primitives that feed higher-level YM constructions in the Recognition Science framework. It enables matrix-based representations required for downstream kernel properties and applications, closing the definitional base for the YM.Kernel siblings.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not specify physical interpretations or links to phi-ladder constants.
- Does not extend beyond the 3x3 stochastic case.
- Does not depend on other Recognition Science modules.