IndisputableMonolith.Relativity.GRLimit.Observables
This module defines the weight function w for observables in a weak-field proxy model of the GR limit. Researchers deriving approximations in Recognition Science relativity would cite it to maintain domain-safe definitions. The module adopts an exponential representation specifically to bypass rpow domain restrictions in Lean. It relies on standard real-analysis imports rather than custom Recognition primitives.
claimThe weight function is given by $w = e^{f}$ for a suitable $f$ in the weak-field proxy model, ensuring the map remains defined over all reals.
background
The module sits inside the Relativity.GRLimit.Observables section of the Recognition Science development. It introduces the weight observable w via an exponential form to avoid domain issues that arise with real-power operations. The local setting uses Mathlib.Real, Log, and Exp to support continuous functions on the reals without additional hypotheses on positivity or range.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the weight observable that later GR-limit results rely on for consistent weak-field modeling. It fills the role of providing a domain-safe proxy weight inside the broader derivation of observables from the Recognition functional equation.
scope and limits
- Does not prove any theorems or lemmas.
- Does not import core Recognition Science objects such as J or the phi-ladder.
- Does not treat strong-field or exact GR regimes.
- Does not specify the concrete functional form of the exponent beyond the exponential wrapper.