Study the template / recurrence-based construction methods for Schur number lower bounds (Abbott-Hanson S(n+2) >= 9S(n)+4; the 2026 'shifted S-templates' paper's S(k+2) >= 10S(k)+2, arXiv:2607.15034) well enough to explain concretely how a base sum-free partition is extended, and assess whether any known template technique could plausibly push N past 536 for n=6 specifically.
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