breath_cycle
plain-language theorem explainer
The breath cycle supplies the fixed period length 1024 used to normalize decay rates inside the memory ledger. Modelers of thermodynamic memory retention cite it when scaling base decay by memory cost to obtain per-cycle forgetting rates. The declaration is a direct constant assignment.
Claim. The memory breath cycle length is the natural number $1024$.
background
The Memory Ledger module treats memory as a thermodynamic system in which retention competes with free-energy decay. Supporting definitions include LedgerMemoryTrace for encoding memory states and base_decay_rate for the underlying decay parameter. The breath cycle appears in the denominator of the forgetting rate, which is formed as base decay times memory cost divided by this period.
proof idea
The declaration is a one-line definition that directly assigns the constant 1024.
why it matters
This constant feeds the parent results breath_cycle_pos, forgetting_rate, emotional_forgets_slower, forgetting_decreases, and low_temp_bistable. It discretizes time for rate calculations inside the Recognition Science thermodynamic treatment of memory. The power-of-two choice is consistent with the eight-tick octave structure.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.