predictions
plain-language theorem explainer
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.
Claim. The 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
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.
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