ledgerPeriod
Ledger period is defined as two raised to the spatial dimension. A researcher tracing the Recognition Science forcing chain at T7 would cite this when fixing the fundamental periodicity for three spatial dimensions. The definition directly substitutes the constant three to obtain the value eight.
claimDefine the ledger period by the equation $L = 2^{D}$ where $D=3$ denotes the spatial dimension.
background
The module formalises step T7 of the forcing chain: once the spatial dimension is fixed at three the ledger period becomes eight, called the eight-tick fundamental periodicity. Spatial dimension is introduced as the constant three. The ledger period is then obtained by exponentiation with base two. This step also prepares the link to the Fibonacci sequence via the relation that the sixth Fibonacci number equals eight and the fourth equals three.
proof idea
The declaration is a direct definition that applies the spatial-dimension constant to the exponentiation operation.
why it matters in Recognition Science
The definition supplies the period value required by the EightTickCert structure and the both_fibonacci_at_D3 theorem. It realises the T7 claim that the ledger period equals eight at D equals three, thereby closing the eight-tick octave. The construction also feeds the relation that the period times the five-rung depth yields a quantity near phi to the eighth power.
scope and limits
- Does not derive the spatial dimension from prior axioms.
- Does not establish the Fibonacci connection.
- Does not compute numerical consequences beyond the definition itself.
formal statement (Lean)
25def ledgerPeriod : ℕ := 2 ^ spatialDim
proof body
Definition body.
26