IndisputableMonolith.TruthCore.TimeKernel
The TimeKernel module asserts that the time-kernel ratio is dimensionless and invariant under common rescaling of time scales. It resides in the TruthCore domain and would be cited by derivations requiring scale-invariant quantities within the ILG gravity model. The module consists of a single sibling declaration that formalizes this invariance as an alias with no internal proofs.
claimThe time-kernel ratio $r = t_k / t_{k0}$ is dimensionless, satisfying $r' = r$ under the simultaneous rescaling $t_k' = s t_k$, $t_{k0}' = s t_{k0}$ for any positive scalar $s$.
background
The module imports the foundational ILG structures from IndisputableMonolith.Gravity.ILG. In the Recognition Science setting, time kernels appear as ratios that must remain invariant to preserve the dimensionless character of physical quantities. The supplied alias comment identifies the central claim as the time-kernel ratio being dimensionless and invariant under common rescaling.
proof idea
This is a definition module with no proofs; it declares the dimensionless property of the time-kernel ratio as an alias for use in downstream TruthCore constructions.
why it matters in Recognition Science
This module supplies the dimensionless time-kernel invariant required by the TruthCore layer. It supports parent structures imported from ILG by ensuring scale invariance, consistent with the forcing chain landmarks that demand dimensionless ratios. No downstream uses are recorded.
scope and limits
- Does not derive the explicit form of the time kernel from the J-function.
- Does not connect to the phi-ladder, Berry threshold, or mass formula.
- Does not address the eight-tick octave or spatial dimension D=3.
- Does not reference the Recognition Composition Law or alpha band.