Explain the Lean theorem `rsSpectrum_bounded` in module `IndisputableMonolith.CrossDomain.CardinalitySpectrum`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

1. What the Declaration Says in Plain English

The theorem states that every number in the canonical rsSpectrum—a specific list of 20 integers representing domain sizes across the Recognition Science stack—is less than or equal to 3125.

2. Why it Matters in Recognition Science

In RS, the cardinalities of domain types are not arbitrary parameters. They decompose into small primitive generators, primarily $D_{spatial} = 3$, $D_{config} = 5$, and $2$. The integer 3125 is exactly $5^5$ ($D_{config}^5$). By bounding the compiled spectrum, the framework establishes that this initial wave of canonical sizes forms a bounded set whose maximum is itself a direct power of an RS primitive, reinforcing the structural non-randomness of the cross-domain layers.

3. How to Read the Formal Statement

The formal statement is written as ∀ n ∈ rsSpectrum, n ≤ 3125:

• ∀ n ∈ rsSpectrum means "For every natural number n that is an element of the list rsSpectrum..."
• n ≤ 3125 means "...the value of n is less than or equal to 3125."

4. Visible Dependencies and Certificates

The theorem depends on the MODEL definition of rsSpectrum, which defines the 20-element list: [2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 16, 25, 45, 64, 70, 125, 216, 256, 360, 3125]. The THEOREM rsSpectrum_bounded is proved instantly by Lean's decide tactic, which computationally checks the inequality for each element. This bounding proof is then packaged as a field in the cardinalitySpectrumCert certificate structure, demonstrating that the ordered spectrum meets the expected structural criteria.

5. What this Declaration Does Not Prove

This theorem does not prove that 3125 is an absolute ceiling for all conceivable RS domains; it strictly applies only to the defined 20-element list. Furthermore, it does not prove why these cardinalities emerge in their respective domains (e.g., why $5^5$ represents a specific lattice), only that the compiled list of cardinalities is computationally bounded by $3125$.