forgetting_rate
The forgetting_rate definition supplies the instantaneous decay rate for any memory trace at tick t as base decay rate times memory cost divided by breath cycle length. Thermodynamic modelers of retention would cite this when deriving exponential strength loss in Recognition Science. It is a direct algebraic combination of the three upstream quantities with no additional reasoning steps.
claimFor a memory trace with fields complexity, strength, emotional weight, encoding tick and ledger balance, the forgetting rate at discrete time $t$ is $(1/φ) · C(τ,t) / 1024$, where $C(τ,t)$ is the memory cost that sums complexity-weighted J-cost of strength, logarithmic elapsed-time cost, interference J-cost from ledger balance, and emotional discount $1 - w(1 - 1/φ)$.
background
Memory traces are structures recording complexity, strength, emotional weight (bounded in [0,1]), encoding tick, and ledger balance. The memory cost function assembles three positive terms: complexity times J-cost of strength, log(1 + elapsed ticks / breath cycle), and J-cost of normalized ledger balance, then multiplies by the emotional discount factor. Base decay rate is defined as the reciprocal of φ and breath cycle is the constant 1024. The module treats memory as a thermodynamic system in which retention competes with free-energy decay governed by Recognition Science principles.
proof idea
One-line definition that multiplies base_decay_rate by memory_cost trace t and divides the product by breath_cycle.
why it matters in Recognition Science
This rate is the direct input to apply_forgetting, which computes remaining strength after n cycles via exponential decay, and to the theorems emotional_forgets_slower and forgetting_decreases. It operationalizes the Recognition Science phi-ladder decay and J-cost accounting, linking memory encoding to thermodynamic dissipation on the eight-tick octave.
scope and limits
- Does not model continuous-time dynamics or differential equations.
- Does not incorporate temperature or external stimuli.
- Does not handle interactions among multiple traces.
- Does not address retrieval, consolidation, or re-encoding events.
formal statement (Lean)
209noncomputable def forgetting_rate (trace : LedgerMemoryTrace) (t : ℕ) : ℝ :=
proof body
Definition body.
210 base_decay_rate * memory_cost trace t / breath_cycle
211