gap45
The gap-45 complexity ceiling is introduced as the natural number 45 inside the RS-coupled axes module. Workers on cross-domain combination theorems in Recognition Science cite this bound when limiting the number of axes that can be treated as independent. The declaration is a direct constant assignment with no computation or proof steps.
claimDefine the gap-45 complexity ceiling as the natural number $45$.
background
The RS-Coupled Axes module supplies infrastructure for cross-domain combination theorems. Two finite axes of equal cardinality count as independent only when they carry distinct recognition primitives. The gap-45 complexity ceiling appears in this setting as an explicit numerical bound on such combinations.
proof idea
The definition is a direct constant assignment of 45 with no lemmas or tactics applied.
why it matters in Recognition Science
This supplies the explicit numerical value for the gap-45 complexity ceiling referenced in the module's infrastructure for axis independence. It supports the clean foundation (zero sorry, zero axiom) for later cross-domain results. No downstream theorems are listed in the current graph.
scope and limits
- Does not prove any arithmetic property of 45.
- Does not state independence criteria for axes.
- Does not link to the forcing chain or phi-ladder.
- Does not bound the number of primitives beyond the ceiling value.
formal statement (Lean)
81def gap45 : ℕ := 45
proof body
Definition body.
82