LedgerMemoryTrace
LedgerMemoryTrace supplies the data type for an individual memory entry in the Recognition Science thermodynamic ledger, bundling a positive complexity, emotional weight in [0,1], strength in [0,1], encoding tick, consolidation flag, and integer balance. Thermodynamic modelers cite it when proving emotional cost reduction or slower forgetting under the free-energy decay law. The declaration is a direct structure definition that encodes the field constraints without further proof obligations.
claimA memory trace consists of a natural-number identifier, a positive real complexity $c > 0$, an emotional weight $w$ satisfying $0 ≤ w ≤ 1$, an encoding tick, a strength $s$ satisfying $0 ≤ s ≤ 1$, a boolean consolidation flag, and an integer ledger balance.
background
The MemoryLedger module treats memory retention as a thermodynamic competition between stored strength and free-energy decay, using the Recognition Composition Law and J-cost from CostAlgebra. The structure draws on identity morphisms supplied by ArithmeticOf.id and Octave.id to maintain compositional consistency across the phi-forcing chain. MODULE_DOC states that all listed thermodynamic memory theorems are now fully proven with no sorries.
proof idea
The declaration is a plain structure definition. It directly lists the ten fields together with their positivity and boundedness predicates; no tactics or lemmas are applied.
why it matters in Recognition Science
LedgerMemoryTrace is the central carrier type for the twelve downstream results in the same module, including apply_forgetting, emotional_reduces_cost, emotional_forgets_slower, forgetting_decreases, and equilibrium_remember_prob. It supplies the concrete object on which the thermodynamic memory theorems operate, linking the J-uniqueness step (T5) and the eight-tick octave (T7) to concrete retention-versus-decay calculations.
scope and limits
- Does not encode the forgetting-rate formula or its dependence on breath_cycle.
- Does not impose any relation between complexity and the phi-ladder rung.
- Does not contain temperature or RecognitionSystem parameters.
- Does not guarantee ledger-wide consistency or uniqueness of identifiers.
- Does not define operations such as consolidation or balance updates.
formal statement (Lean)
38structure LedgerMemoryTrace where
39 id : ℕ
40 complexity : ℝ
41 complexity_pos : 0 < complexity
42 emotional_weight : ℝ
43 emotional_bounded : 0 ≤ emotional_weight ∧ emotional_weight ≤ 1
44 encoding_tick : ℕ
45 strength : ℝ
46 strength_bounded : 0 ≤ strength ∧ strength ≤ 1
47 consolidated : Bool
48 ledger_balance : ℤ
49