gamma_def
The gamma_def declaration supplies a parameter-free alias for the PPN γ coefficient in the ILG framework, fixed at 1 to recover the general relativity limit. Researchers citing post-Newtonian expansions or comparing modified gravity to GR would reference this name directly in papers. It is realized as a direct noncomputable alias to the constant-1 definition of gamma already present in the same module.
claimDefine $γ_{def} := γ$, where $γ(C_{lag}, α) = 1$ is the leading-order parametrized post-Newtonian γ parameter in the general relativity limit.
background
The module supplies potential-based PPN definitions as a scaffold that expresses the metric potentials Φ and Ψ in terms of the underlying action parameters ψ. The local gamma is introduced as the constant function returning 1 for arbitrary lag and alpha inputs, enforcing the GR limit at leading order. Upstream results include the Euler-Mascheroni constant γ ≈ 0.577 used in other modules, the network-science gamma fixed at 3 for degree distributions, and the for structure recording meta-realization axioms; none of these alter the constant-1 assignment here.
proof idea
The definition is a one-line alias that directly references the gamma definition from the same PPN module, which itself is the constant function returning 1.
why it matters in Recognition Science
This supplies a clean name for paper references inside the PPN scaffold of the ILG relativity module. It supports direct comparison of ILG predictions against the GR limit where γ = 1 is required, consistent with the overall Recognition Science program of deriving classical limits from the forcing chain. No downstream theorems yet cite it, and it touches no open questions beyond completing the basic parameter list.
scope and limits
- Does not incorporate higher-order post-Newtonian corrections.
- Does not depend on specific numerical values of C_lag or alpha.
- Does not compute deviations from the GR limit.
- Does not reference the Euler-Mascheroni constant or network gamma.
formal statement (Lean)
18noncomputable def gamma_def := gamma
proof body
Definition body.
19
20/-- PPN β definition (for paper reference). -/