Analysis

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L163_all_sequence_span_ratio/: For every circle sequence, repeated points allowed, the limiting upper ratio of largest to smallest r-spans is at least 1 + log(r)/(200r) for all sufficiently large r.

L164_all_sequence_span_deviations/: Every circle sequence has upper-span excess and lower-span deficit with limsup at least a positive absolute constant times the square root of log r, for all sufficiently large r.

L165_consecutive_gap_growth_conjunction/: The three mean-normalized consecutive-gap divergences over all circle sequences and the distinct-point subclass, with a passing independent whole-conclusion grade at tier 1; catalog acceptance remains pending.

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