IndisputableMonolith.Complexity.TuringBridge
This module defines SAT instances and auxiliary structures to interface computational complexity with Recognition Science via J-cost. Complexity theorists working in RS foundations would cite it when mapping NP problems onto the phi-ladder. The module consists entirely of definitions and declarations with no proofs.
claimAn SAT instance consists of $n$ Boolean variables and $m$ clauses. Related objects include the J-cost landscape over such instances, resolution time, natural properties, and certificates such as $\hat{R}$ and the open gap.
background
The module sits in the Complexity domain and imports Constants (where $\tau_0 = 1$ tick) together with JcostCore. It introduces SATInstance as a structure with $n$ variables and $m$ clauses, then defines JCostLandscape, ResolutionTime, NaturalProperty, RHatCertificate, SeparationClaim, encoding_faithful, landscape_linear, OpenGap, and TuringBridgeCert. These objects translate standard SAT data into RS-native cost and defect measures.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the interface layer that later results use to embed SAT into the Recognition framework. It feeds SeparationClaim, the_open_gap, and TuringBridgeCert, thereby linking complexity questions to the forcing chain (T0-T8) and the Recognition Composition Law.
scope and limits
- Does not prove any NP-completeness or time bounds.
- Does not derive numerical values for resolution time.
- Does not connect SAT clauses to specific physical constants.
- Does not contain the main TuringBridgeCert theorem body.
depends on (2)
declarations in this module (13)
-
structure
SATInstance -
structure
JCostLandscape -
structure
ResolutionTime -
structure
NaturalProperty -
structure
RHatCertificate -
def
rhat_is_non_natural -
structure
SeparationClaim -
theorem
encoding_faithful -
theorem
landscape_linear -
structure
OpenGap -
def
the_open_gap -
structure
TuringBridgeCert -
def
turingBridgeCert