IndisputableMonolith.Physics.EightTickPeriodicityFromD
Links spatial dimension D = 3 to the eight-tick ledger period via Fibonacci numbers: F(4) = 3 and F(6) = 8. Anyone citing the T7–T8 forcing chain (octave period from dimension) uses this module. The argument is definitional equalities plus the Fibonacci recurrence evaluated at D = 3.
claimWith spatial dimension $D = 3$ and ledger period $P = 8$, the Fibonacci numbers satisfy $F_4 = 3 = D$ and $F_6 = 8 = P$, and both identities arise from the same recurrence at dimension three.
background
Recognition Science forces spatial dimension $D = 3$ (T8) and an eight-tick octave period $2^3 = 8$ (T7) from the same self-similar cost structure. This module packages those two integers as named constants spatialDim and ledgerPeriod, then identifies them with consecutive Fibonacci values.
The Fibonacci sequence is the usual recurrence $F_n = F_{n-1} + F_{n-2}$ with the standard initial data that yields $F_4 = 3$ and $F_6 = 8$. The module therefore supplies a single arithmetic bridge: the same recurrence that produces dimension three also produces the ledger period eight, so the two forcing steps sit on one combinatorial spine.
proof idea
Definition module with short equality lemmas. spatialDim and ledgerPeriod are introduced as the naturals 3 and 8. F4, F5, F6 are the corresponding Fibonacci values; f4_eq_3, f6_eq_8 are direct computations, and f4_eq_spatialDim, f6_eq_ledgerPeriod are rewrites. fibonacci_recurrence records the recurrence step; both_fibonacci_at_D3 packages the pair of identities at $D = 3$. No deep proof search: pure definitional unfolding and arithmetic.
why it matters in Recognition Science
Closes the arithmetic link between T8 ($D = 3$) and T7 (eight-tick octave) inside the Unified Forcing Chain. Downstream physics that needs a single integer source for both spatial dimension and ledger cadence can cite the paired Fibonacci identities rather than two unrelated constants. The module is the natural place to hang any later argument that the octave period is forced once dimension is fixed, or conversely.
scope and limits
- Does not derive D = 3 or period 8 from the J-cost; only equates them to Fibonacci numbers.
- Does not prove uniqueness of the Fibonacci indexing; F4 and F6 are chosen by hand.
- Does not address continuous spacetime or Lorentz structure.
- Does not connect to the mass ladder, alpha band, or Berry threshold.
declarations in this module (15)
-
def
spatialDim -
def
ledgerPeriod -
theorem
ledgerPeriod_eq_8 -
def
F4 -
theorem
f4_eq_3 -
theorem
f4_eq_spatialDim -
def
F6 -
theorem
f6_eq_8 -
theorem
f6_eq_ledgerPeriod -
def
F5 -
theorem
fibonacci_recurrence -
theorem
both_fibonacci_at_D3 -
theorem
eight_tick_fibonacci_connection -
structure
EightTickCert -
def
eightTickCert