memory_ledger_status
This definition assembles a fixed list of eight theorem names paired with their verification status inside the memory ledger thermodynamics module. A researcher modeling memory retention as free-energy decay against recognition cost would reference it to confirm module completeness. The construction is a direct list literal with no computation or external calls.
claimThe memory ledger status is the list of pairs associating each core property with its proof flag: non-negativity of memory cost, cost reduction by emotional weight, monotonic decrease of forgetting, slower forgetting for emotional traces, entropy maximization at high temperature, bistability at low temperature, non-negative learning rate, and compounding of learning.
background
The Memory Ledger module treats memory traces as thermodynamic objects whose retention competes with free-energy decay under Recognition Science rules. A LedgerMemoryTrace carries complexity, strength, encoding tick, ledger balance, and emotional weight; derived quantities include memory_cost (J-cost of the trace at time t), forgetting_rate (base decay scaled by cost over breath cycle), and apply_forgetting (updated trace after decay). Upstream results supply the evaluation maps for counted resources and scalar fields, plus the individual theorems emotional_reduces_cost, forgetting_decreases, emotional_forgets_slower, and high_temp_maximizes_entropy that establish the listed properties.
proof idea
Direct definition as a list literal that enumerates the eight theorem names together with the string PROVEN. No tactics or lemmas are applied; the body simply constructs the constant list.
why it matters in Recognition Science
The definition records that the entire suite of thermodynamic memory results has been discharged, closing the module whose doc-comment states all theorems are now fully proven with no sorries. It sits inside the Recognition Science derivation of memory from J-cost and the phi-ladder, confirming that the eight-tick octave and free-energy monotonicity have been instantiated for retention dynamics. No downstream uses are recorded, so the entry functions purely as a status checkpoint.
scope and limits
- Does not recompute or verify any theorem dynamically.
- Does not embed the actual proof terms or hypotheses.
- Does not cover thermodynamic properties outside the eight listed entries.
- Does not supply a mechanism for extending the list.
formal statement (Lean)
561def memory_ledger_status : List (String × String) :=
proof body
Definition body.
562 [ ("memory_cost_nonneg", "PROVEN")
563 , ("emotional_reduces_cost", "PROVEN")
564 , ("forgetting_decreases", "PROVEN")
565 , ("emotional_forgets_slower", "PROVEN")
566 , ("high_temp_maximizes_entropy", "PROVEN")
567 , ("low_temp_bistable", "PROVEN")
568 , ("learning_rate_nonneg", "PROVEN")
569 , ("learning_compounds", "PROVEN")
570 ]
571
572#eval memory_ledger_status
573
574end MemoryLedger
575end Thermodynamics
576end IndisputableMonolith