IndisputableMonolith.Mathematics.NumberTheoryFromRS
NumberTheoryFromRS extracts number theoretic identities from Recognition Science, centered on the property φ² = φ + 1. Researchers constructing the phi-ladder and mass formulas cite these results. The module organizes a sequence of identities and counts built directly on the RS time quantum τ₀ = 1 tick imported from Constants.
claimThe module establishes the identity $φ^2 = φ + 1$ and related Fibonacci relations for powers of $φ$ in RS-native units with $τ_0 = 1$.
background
The module operates in the Recognition Science setting where physics derives from a single functional equation. It imports the fundamental RS time quantum $τ_0 = 1$ tick from Constants. The central definition is the golden ratio $φ$ satisfying $φ^2 = φ + 1$, the self-similar fixed point that anchors the phi-ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the number theoretic layer that supports the Recognition framework's phi-ladder constructions and constant derivations. It connects the defining property of $φ$ to downstream counting functions and mass formulas on the ladder.
scope and limits
- Does not derive the Recognition Composition Law.
- Does not compute numerical values for physical constants.
- Does not address spatial dimensions or the forcing chain.
- Does not treat the Berry creation threshold or J-uniqueness.