Explain the Lean theorem `down_generation_spacing` in module `IndisputableMonolith.Masses.QuarkVerification`. 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.

In plain English, down_generation_spacing states that the rung difference between the strange and down quarks is 11 and between the bottom and down quarks is 17.

In Recognition Science this matters because the spacing is fixed by the torsion schedule {0, 11, 17} arising from cube geometry; the same schedule governs lepton generations, so the mass ratios m_s/m_d = phi^11 and m_b/m_d = phi^17 are parameter-free predictions identical across sectors.

The formal statement is a theorem asserting the conjunction r_down "s" - r_down "d" = 11 ∧ r_down "b" - r_down "d" = 17; the proof applies simp to unfold r_down, tau and Anchor constants, then closes with the omega tactic.

Visible dependencies in the supplied source are r_down, tau, Anchor.E_passive, Anchor.W, passive_field_edges, cube_edges, active_edges_per_tick, D and wallpaper_groups; the result is packaged inside QuarkVerificationCert via quark_verification_cert_exists and parallels the sibling up_generation_spacing.

The declaration does not prove numerical mass values, PDG comparisons, or the origin of the r_down definition beyond the Anchor module; those remain in separate verification and empirical sections.