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def

logicSystemsCert

definition
show as:
module
IndisputableMonolith.Mathematics.LogicSystemsFromConfigDim
domain
Mathematics
line
28 · github
papers citing
none yet

plain-language theorem explainer

The definition packages the enumeration of exactly five logic systems under configDim equal to five into a reusable certificate structure. Researchers tracing the logic layer of the Recognition framework would cite it to confirm the count of propositional, first-order, second-order, modal, and intuitionistic systems. It is realized as a direct record construction that delegates the cardinality claim to an upstream decide-based theorem.

Claim. Let LogicSystem be the finite type of the five canonical logics. The certificate structure is defined by setting its systems field to the theorem establishing that the cardinality of LogicSystem equals five.

background

The module states that configDim equal to five selects five canonical logic systems: propositional, first-order, second-order, modal, and intuitionistic. The structure LogicSystemsCert is a record whose single field requires a proof that the cardinality of the LogicSystem type is five. This definition sits inside the mathematics layer that supplies logic foundations for the Recognition Science framework.

proof idea

The definition is a one-line record construction that directly assigns the upstream theorem logicSystem_count to the systems field of the LogicSystemsCert structure.

why it matters

This definition supplies the certified count of logic systems required when the configuration dimension is set to five. It closes the enumeration step in the mathematics layer that supports the Recognition Science derivation of physical constants from the forcing chain. No downstream uses are recorded yet.

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