CompleteModel
CompleteModel assembles a ledger computation with dual complexity measures, a Turing reduction, Clay compatibility, and validation data. Researchers modeling information barriers in double-entry systems would reference the construction when exploring recognition versus computation separations. The declaration is a direct structure extension of the base ledger record with four adjoining fields and carries no proof obligations.
claimA ledger computation consists of a state space, an evolution map, an encoding of boolean lists, and a measurement operation that preserves zero closed-chain flux. A complete model augments this with a pair of functions $(T_c, T_r)$ where $T_c$ is sub-polynomial and $T_r$ is at least linear, a specialization in which recognition cost vanishes identically, a projection that discards the recognition component when mapping to Clay's formulation, and an empirical record of measured computation times together with recognition errors of at least one half.
background
The ComputationBridge module explores hypothetical ledger implications for complexity theory and is explicitly labeled a scaffold outside the verified certificate chain. LedgerComputation supplies the base record whose states evolve under double-entry rules while conserving flux. RecognitionComplete adjoins the dual parameters with the sub-polynomial bound on computation steps and the linear lower bound on recognition steps. TuringModel recovers the standard model by forcing recognition cost to zero. ClayBridge supplies the projection that retains only computation complexity, rendering P versus NP ill-posed. Validation records test sizes, measured times, and error fractions confirming the predicted scalings.
proof idea
The declaration is a structure definition that extends LedgerComputation and adjoins four fields. No lemmas are applied and no tactics are used; the construction is purely by record extension.
why it matters in Recognition Science
This structure supplies the central object referenced by the downstream main_resolution theorem that asserts existence of a model exhibiting computation-recognition separation. It assembles the hypothetical P versus NP framework described in the module documentation, touching the ledger-based forcing and balanced-parity information hiding of the Recognition Science setting while remaining outside the verified chain (T0-T8, RCL, phi ladder). It leaves open whether the ledger assumptions can be discharged unconditionally.
scope and limits
- Does not establish an unconditional resolution of P versus NP.
- Does not belong to the verified certificate chain of Recognition Science.
- Does not prove the separation theorems; they rest on model assumptions.
- Does not claim empirical validation beyond the scaffold data supplied.
formal statement (Lean)
317structure CompleteModel extends LedgerComputation where
318 /-- Includes both complexity parameters -/
319 complexity : RecognitionComplete
320 /-- Reduces to Turing when Tr ignored -/
321 turing_special_case : TuringModel
322 /-- Clay bridge for standard formulation -/
323 clay_bridge : ClayBridge
324 /-- Empirical validation data -/
325 validation : Validation
326
327/-- Main theorem: P vs NP is resolved unconditionally through the ledger -/