eight_tick_dissipation_limit
plain-language theorem explainer
Recognition operators evolve ledger states while keeping recognition cost non-increasing for admissible inputs. This supplies the one-step bound needed to derive the integrated dissipation over an 8-tick cycle matching the Landauer limit. The short proof applies the cost-minimization axiom built into the operator definition.
Claim. Let $R$ be a recognition operator and $s$ a ledger state. Denote by $s'$ the state obtained by applying the evolution map of $R$ to $s$. Whenever both $s$ and $s'$ are admissible, the recognition cost of $s'$ is at most the recognition cost of $s$.
background
The module Phase 7.5.2 formalizes how recognition cost relates to thermodynamic entropy and anchors the theory at the Landauer limit. Recognition operators are defined as structures carrying an evolution function on ledger states together with the guarantee that evolution minimizes recognition cost on admissible states. Ledger states track finite collections of active bonds with associated positive real multipliers.
proof idea
After naming the next state, the tactic proof introduces the two admissibility hypotheses and then applies the minimization property directly from the recognition operator structure to obtain the desired inequality.
why it matters
The result establishes the non-increase of cost over one evolution step, which is required to equate the total dissipation in an 8-tick cycle with the Landauer limit for pattern closure. It contributes to the information-theoretic thermodynamics developed in this module and connects to the eight-tick structure in the forcing chain. No downstream uses are recorded yet, leaving its role in bounding total dissipation open for further theorems.
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