IndisputableMonolith.Mathematics.FibonacciSequenceFromRS
The module derives Fibonacci numbers from Recognition Science parameters, with the key identity F(4) = 3 = D linking the sequence to spatial dimension. Researchers tracing the forcing chain to T8 would cite these equalities when matching integer sequences to RS constants. The module consists of direct verifications plus a recurrence at the eight-tick level.
claimTheorems establish $F_4 = D = 3$ and $F_6 = 2D^3$, together with the recurrence $F_{n+2} = F_{n+1} + F_n$ at the eight-tick octave, where $F_n$ denotes the Fibonacci sequence and $D$ is the spatial dimension forced by the RS chain.
background
The module sits in the Mathematics domain and imports Constants, whose sole documented object is the RS time quantum $ au_0 = 1$ tick. It supplies explicit matches between Fibonacci terms and RS landmarks, notably the correction that $F(4) = 3 = D$ rather than an earlier indexing. The setting is the unified forcing chain (T0-T8) in which T7 fixes the eight-tick period and T8 forces $D = 3$.
proof idea
The module is a collection of direct equalities (fib3_eq_2 through fib8_eq_21, fib4_eq_D, fib6_eq_2cubeD) plus the recurrence fib_recurrence_8 and the certificate FibonacciCert. Each equality is a one-line verification against the RS definition of $D$; the recurrence is stated at the eight-tick level without further inductive machinery.
why it matters in Recognition Science
The module supplies the concrete integer identities needed to close the step from the phi-ladder to $D = 3$ (T8). It therefore supports any downstream argument that extracts spatial dimension or octave structure from the J-uniqueness and self-similar fixed point. No used_by edges are recorded yet.
scope and limits
- Does not derive the Fibonacci recurrence from the J-cost function.
- Does not treat non-integer indices or generalized Binet forms.
- Does not connect the sequence to the alpha band or mass ladder.
- Does not address the Berry threshold or $Z_{cf}$.