IndisputableMonolith.Relativity.ILG.PPNDerive
This module supplies local extraction formulas for the PPN parameters gamma and beta inside the ILG layer. Researchers deriving post-Newtonian observables from Recognition Science potentials would cite these to replace an earlier trivial stub. The module consists of two named formulas plus a certification theorem that keeps all definitions inside the ILG boundary.
claimThe module defines extraction formulas for the PPN parameters $gamma$ and $beta$ from the potentials $Phi$ and $Psi$, together with the proposition that the PPN derivation holds under the potential-based scaffold.
background
The upstream PPN module supplies a scaffold in which the parametrized post-Newtonian parameters are expressed through the gravitational potentials $Phi$ and $Psi$ obtained from a base field $psi$ and a small set of parameters. This module stays strictly inside the ILG layer so that the main Relativity module never acquires a heavy post-Newtonian dependency. The supplied doc-comment states the intent: keep the formulas local to eliminate the previous $Prop := True$ stub with a small, honest certificate.
proof idea
This is a definition module. It introduces the two extraction formulas gamma_extraction_formula and beta_extraction_formula by direct definition, then states the theorem PPNDerivationHolds (and its abbreviation ppn_derivation_holds) that certifies the formulas under the potential scaffold. No tactic steps or external lemmas are required.
why it matters in Recognition Science
The module discharges the earlier trivial stub and thereby supplies the minimal certificate needed for the ILG layer to connect to observable PPN parameters. It feeds the parent Relativity module without importing the full post-Newtonian stack, preserving the lightweight dependency graph required by the Recognition Science architecture.
scope and limits
- Does not import the full PostNewtonian stack.
- Does not derive higher-order PPN parameters beyond gamma and beta.
- Limits all definitions to the ILG potential scaffold.
- Does not address observational constraints or numerical values.