IndisputableMonolith.Mathematics.BooleanAlgebraFromRS
This module derives a Boolean algebra from Recognition Science primitives. It defines BoolOp operations, counts atoms, and certifies the algebra with exactly eight atoms. The construction aligns with the eight-tick octave and D=3 from the forcing chain. All content consists of definitions and direct certifications with no complex proofs.
claimThe module defines Boolean operations $\text{BoolOp}$ and certifies a Boolean algebra with $\text{atomCount} = 8 = 2^D$ via $\text{atoms_eq_2cubeD}$ and $\text{BooleanAlgebraCert}$.
background
Recognition Science extracts algebraic structures from the J-cost function and the T0-T8 forcing chain. This module operates in the mathematics subdomain and introduces BoolOp for the algebra operations together with atomCount for the number of atoms. It builds directly on the eight-tick period (T7) to produce a structure whose atom count matches the spatial dimension count (T8).
proof idea
This is a definition module, no proofs. It supplies the operation definitions, the atom-count equalities, and the algebra certificate.
why it matters in Recognition Science
Supplies the Boolean algebra foundation required by the main IndisputableMonolith and the unified forcing chain. It directly supports the emergence of D=3 from the eight-tick octave (T7-T8) and the Recognition Composition Law.
scope and limits
- Does not derive the J-function or the forcing chain.
- Does not address continuous or topological extensions.
- Does not connect to physical constants or mass formulas.