predictions
The predictions definition enumerates four claims for the fermion mass hierarchy in Recognition Science: ratios follow a φ-cascade, the Koide formula is fundamental, exactly three generations exist, and α differs between quarks and leptons. A physicist studying the Standard Model hierarchy problem would cite this list when testing RS against LEP and LHC data. The entry is a direct list literal with no lemmas or computation.
claimThe Recognition Science predictions for the mass hierarchy are the list consisting of ``Mass ratios follow φ-cascade'', ``Koide formula is fundamental, not coincidence'', ``Exactly 3 generations (no 4th)'', and ``Different α for quarks vs leptons''.
background
Module SM-006 derives the fermion mass hierarchy from Recognition Science's φ-structure. The Standard Model exhibits a large hierarchy, with the top quark near 173 GeV and the electron near 0.5 MeV. RS accounts for this via a geometric φ-cascade in which each generation differs by factors of φ² or φ³, with the number of generations fixed at three by the eight-tick structure and masses scaling as m_n ~ m_0 × φ^(-αn).
proof idea
The definition directly constructs the four-element list of string predictions. No lemmas are applied and no tactics are used.
why it matters in Recognition Science
This definition supplies the concrete claims that would follow from the φ-cascade mechanism. It connects to the eight-tick octave (T7) that fixes three generations and to the mass formula on the φ-ladder. The module documentation flags the result as a potential major breakthrough if a single φ parameter reproduces all fermion masses, matching the paper target of a PRL on the hierarchy from first principles.
scope and limits
- Does not derive explicit numerical masses for any particle.
- Does not prove any of the four listed claims.
- Does not address boson masses or gauge couplings.
- Does not specify the precise exponents or gap terms in the φ-cascade.
formal statement (Lean)
203def predictions : List String := [
proof body
Definition body.
204 "Mass ratios follow φ-cascade",
205 "Koide formula is fundamental, not coincidence",
206 "Exactly 3 generations (no 4th)",
207 "Different α for quarks vs leptons"
208]
209
210/-- **MAJOR BREAKTHROUGH**: If RS correctly predicts all fermion masses
211 from a single parameter (φ), this would be a landmark result. -/