base_decay_rate_pos
plain-language theorem explainer
The base decay rate is shown to be strictly positive. Researchers modeling memory retention as a thermodynamic process cite it to ensure forgetting proceeds at a nonzero rate in the ledger. The proof is a direct one-line application of division positivity to the constants 1 and phi.
Claim. $0 < 1/φ$ where $φ$ is the self-similar fixed point of the Recognition Science forcing chain.
background
The Memory Ledger module treats memory traces as a thermodynamic system in which retention competes with free-energy decay governed by Recognition Science. The definition base_decay_rate := 1/φ supplies the constant decay factor, with φ the fixed point forced at T6 of the Unified Forcing Chain. This positivity result is invoked by the downstream theorems emotional_forgets_slower and forgetting_decreases to control the sign of apply_forgetting.
proof idea
One-line wrapper that applies div_pos to zero_lt_one and phi_pos.
why it matters
The result feeds emotional_forgets_slower and forgetting_decreases, which establish slower decay for emotional traces and monotonic decrease of forgetting with time. It supplies the sign needed for the thermodynamic memory model to evolve toward lower free energy, consistent with the phi-ladder and eight-tick octave structure.
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