IndisputableMonolith.Foundation.SpecialRelativityDeep
SpecialRelativityDeep embeds special relativity into Recognition Science by establishing that the Lorentz factor satisfies γ ≥ 1 always. It links γ to the J-cost function imported from Cost. Physicists extending the RS forcing chain to relativistic kinematics would cite these results. The module organizes a collection of theorems on top of the Constants and Cost modules.
claimThe Lorentz factor satisfies $\gamma \geq 1$ in the RS formulation, where $\gamma$ is tied to the J-cost by the relation J-cost = $\gamma - 1$.
background
The module sits in the Foundation domain and imports Constants (defining the RS time quantum τ₀ = 1 tick) together with Cost (supplying the J-cost function). The J-cost is the central object, given by J(x) = (x + x^{-1})/2 - 1, which equals cosh(log x) - 1 and is identified with γ - 1 via the sibling identity jcost_cosh_is_gamma_minus_one.
This places the work in the deep embedding of special relativity inside the Recognition Science framework, preserving the phi-ladder and eight-tick octave while extending the T0-T8 forcing chain.
proof idea
This is a definition module, no proofs. The module aggregates independent declarations (gamma_ge_one, jcost_cosh_is_gamma_minus_one, mass_energy_RS, etc.) without a single central proof body.
why it matters in Recognition Science
The module supplies the Lorentz factor inequality that supports special relativity derivations inside the RS framework. It connects directly to sibling certification objects such as SpecialRelativityDeepCert. It fills the step of embedding SR kinematics into the T5 J-uniqueness and T6 phi fixed-point stages of the forcing chain.
scope and limits
- Does not derive the full Lorentz transformation rules.
- Does not treat general relativity or curved spacetime.
- Does not compute explicit velocity-dependent values beyond the γ inequality.
- Does not address quantum or field-theoretic extensions.