Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== - Scale mismatch: many weak decays occur at nuclear/hadronic scale (fm), not atomic electron scale (Å). QAT’s sphere concept must be applied at the appropriate scale (hadron boundary rather than atomic electron sphere) for nuclear decays. The same geometry idea can in principle be applied at multiple scales but that must be explicit. ===
* The SM account of CP violation (CKM matrix) is highly constrained by flavor physics; any geometric mechanism must either reproduce the same structure or supplement it — this is a high bar.
* Experimental constraints on environment-induced changes to weak decay rates are tight (decay constants are extremely stable), so any geometry-dependent variation must be small. That’s not a problem — sphere geometry could produce small phases — but you must compute numbers and compare to data.
* Mathematically: producing a complex CP phase that is consistent with SM flavor mixing likely requires a mechanism to differentiate flavors on the boundary (distinct holonomies or mode localizations for each flavor). That is entirely possible mathematically, but needs a model (e.g., different profile functions for up/down/strange on the sphere).