eight_tick_cycle
The declaration sets the eight-tick correction cycle to the constant natural number 8 inside the Recognition Science error-correction model. Thermodynamic analyses of ledger fault tolerance and periodic return to ground states cite this value when counting discrete correction steps. The definition is a direct constant assignment that encodes the eight-tick octave period.
claimThe eight-tick correction cycle is the natural number $8$.
background
The module develops the error-correction viewpoint of RS thermodynamics, where physical laws remain stable because ledger dynamics implements fault tolerance. Recognition defects are deviations from the J=0 ground state; defect energy is the cost of creating such a deviation; an error syndrome is the detectable signature of a defect; and correction dynamics describe return to equilibrium. The module explicitly identifies the 8-tick cycle as the error-correction period of the stabilizer code realized by the ledger, with the phi-ladder supplying code distance.
proof idea
Direct definition that assigns the constant 8.
why it matters in Recognition Science
The definition supplies the discrete period required by the eight-tick octave (T7) inside the forcing chain. It anchors the correction-protocol completeness statements that appear later in the same module and links the thermodynamic ledger to the stabilizer-code picture of quantum error correction. No downstream uses are recorded yet, leaving open how the period will be invoked in explicit fault-tolerance thresholds.
scope and limits
- Does not define the correction map or its action on states.
- Does not prove that eight applications suffice to reach ground states.
- Does not connect the period to specific values of defect energy or J-cost.
- Does not derive the number 8 from the Recognition Composition Law or phi-ladder.
formal statement (Lean)
80def eight_tick_cycle : ℕ := 8
proof body
Definition body.
81
82/-- A correction protocol is complete if it maps all states to ground states
83 within a finite number of applications. -/