IndisputableMonolith.Foundation.ConstantDerivations
The ConstantDerivations module supplies explicit RS-native expressions for the bit cost and derived constants. Researchers tracing the forcing chain from self-similarity to measurable quantities would cite it when converting J-cost into c, G, and the alpha band. The module consists of targeted definitions together with short positivity and equality proofs that rest directly on the imported PhiForcing, DimensionForcing, and LawOfExistence results.
claim$J_{ m bit}=\ln\phi$, $E_{ m coh}$ the coherent energy scale, period 8 the eight-tick octave, $c=1$, $\hbar=\phi^{-5}$, $G=\phi^5/\pi$, and $\alpha^{-1}\in(137.030,137.039)$.
background
The module follows the three upstream modules whose doc-comments define the setting. PhiForcing shows that self-similarity on a discrete ledger with J-cost forces the golden ratio. DimensionForcing establishes that spatial dimension D=3 is forced. LawOfExistence equates existence to zero defect. ConstantDerivations then converts these structures into concrete constants by setting the fundamental bit cost J_bit = ln(φ) and building the remaining quantities from it.
proof idea
This is a definition module whose content is a sequence of abbrevs and short theorems. Each constant (J_bit, E_coh, c_rs, G_rs, period_8) receives an explicit algebraic definition in terms of φ; the accompanying _pos and _eq lemmas are one-line wrappers that apply the positivity and equality results already proved in PhiForcing and DimensionForcing.
why it matters in Recognition Science
The derivations supply the concrete constants required by the master forcing-chain theorem in RealityFromDistinction, which starts from a single distinction and reaches spacetime together with the physical constants. The module therefore closes the step that converts the abstract J-cost and phi-ladder into the RS-native values c=1, G=φ^5/π, and the alpha interval cited in the framework landmarks.
scope and limits
- Does not derive numerical values for constants outside the stated algebraic expressions.
- Does not address renormalization or running of the constants.
- Does not connect the derived constants to laboratory units beyond the native RS scaling.
- Does not prove uniqueness of the constant set beyond the forcing chain already established upstream.
used by (1)
depends on (3)
declarations in this module (20)
-
def
J_bit -
theorem
J_bit_pos -
def
E_coh -
theorem
E_coh_pos -
def
period_8 -
def
c_rs -
theorem
c_rs_eq_one -
theorem
c_pos -
def
G_rs -
theorem
G_rs_eq -
theorem
G_pos -
theorem
G_algebraic_in_ -
theorem
G_ -
def
gap_correction -
def
planck_length_rs -
theorem
planck_length_eq_one -
def
planck_mass_rs -
theorem
planck_mass_eq -
theorem
all_constants_from_phi -
def
derivation_narrative