Clarification to “On the Nonexistence of Odd Perfect Numbers” (Revised Lemmas 4.1–4.4 and Chapter 8

Section 8 (discussion of Robin's Inequality and divisor sums) has been corrected.An earlier incorrect statement claimed that 2N2N grows faster than eγNlog⁡log⁡NeγNloglogN, which is not true for large NN.This section has now been rewritten to clarify that Robin's Inequality was mentioned only for historical context and is not critical to the main proof strategy based on modular forcing and infinite prime escalation.No changes were needed to the core contradiction argument.Readers are encouraged to refer to the updated version for the corrected background discussion.