Validation
Empirical validation scaffold recording test sizes, sub-linear computation time lists, and recognition error lists with a threshold predicate. Researchers examining hypothetical ledger dual-complexity models would cite this structure when bundling checks against theoretical predictions for computation versus recognition scaling. The declaration is a plain structure definition imposing no proof obligations.
claimA record type consisting of a natural number $n$ for test size, a list $T_c$ of pairs in $ℕ × ℕ$ for measured computation times, a list $T_r$ of pairs in $ℕ × ℚ$ for measured recognition errors, and a predicate requiring that the length of $T_c$ equals $n$ while every second component of $T_r$ is at least $1/2$.
background
The Computation Bridge module explores ledger-style dual complexity separating computation from recognition as an explicit scaffold outside the verified certificate chain. It examines hypothetical implications including Turing incompleteness and SAT separation under ledger assumptions, where the double-entry structure creates information-theoretic barriers between computation and observation. Upstream results supply the complete predicate for backpropagation states in SAT solving and model constructions from two-dimensional fluid dynamics.
proof idea
Structure definition. It directly assembles the four fields with the validates predicate enforcing the length and error threshold conditions. No lemmas or tactics are applied.
why it matters in Recognition Science
This structure feeds the CompleteModel which extends LedgerComputation by adding recognition completeness and a Turing special case. It supplies the empirical validation component for the hypothetical P versus NP framework in the ledger model. The module states that such results remain exploratory and outside the verified RS certificate chain, touching the open question of scale-dependent complexity separation.
scope and limits
- Does not prove any separation between P and NP classes.
- Does not supply unconditional theorems for complexity bounds.
- Does not integrate into the verified certificate infrastructure.
- Does not claim empirical data from actual experiments.
formal statement (Lean)
305structure Validation where
306 /-- Test instances up to size n -/
307 test_size : ℕ
308 /-- Measured computation time scales sub-linearly -/
309 Tc_measured : List (ℕ × ℕ)
310 /-- Recognition error = 50% when k < n/2 -/
311 Tr_measured : List (ℕ × ℚ)
312 /-- Confirms theoretical predictions -/
313 validates : Tc_measured.length = test_size ∧
314 Tr_measured.all (fun p => p.2 ≥ 1/2)
315
316/-- The complete computational model -/