IndisputableMonolith.CrossDomain.RegulatoryCeiling
The CrossDomain.RegulatoryCeiling module centers on the binomial coefficient C(8,4) equaling 70 for the 3-cube Q3, together with maximality, gap, and power-set lemmas. Cross-domain researchers cite these facts when bounding regulatory ceilings in the eight-tick setting. The module collects direct combinatorial statements backed by Mathlib, with no internal proof scripts.
claimThe central binomial coefficient on the 3-cube satisfies $C(8,4)=70$, with supporting statements on maximality, 4-5 gaps, double-gap peaks, and half-row sums.
background
The module operates in the cross-domain layer of Recognition Science, where the eight-tick octave (T7, period 2^3) meets three spatial dimensions (T8). It introduces choose_8_4 as the statement C(8,4)=70, choose_8_4_is_max for its peak property, gap45, peak_fits_double_gap, peak_exceeds_single_gap, halfRowSum, halfRowSum_eq, and totalPowerSet. These objects prepare the RegulatoryCeilingCert definition. The setting draws on the forcing chain landmarks T7 and T8.
proof idea
This module contains no proof bodies. It consists of declarations and statements whose justifications are either trivial or delegated to Mathlib. The structure is a flat collection of sibling lemmas around the binomial coefficient and its combinatorial properties.
why it matters in Recognition Science
The module supplies the combinatorial core for the regulatory ceiling construction, directly supporting RegulatoryCeilingCert and regulatoryCeilingCert. It realizes the central binomial on Q3 required by the T7 eight-tick octave in the unified forcing chain.
scope and limits
- Does not extend to hypercubes of dimension other than three.
- Does not derive binomial identities from the Recognition functional equation.
- Does not certify the full regulatory ceiling, only its combinatorial inputs.
- Does not reference physical constants such as phi, G, or alpha.