# Reading guide

Compare the frozen 26 December 2009 arXiv source with the separately frozen Acta typesetting. The received-date external-result cutoff is 29 December 2009. The complete editions have not been collated line by line.

Follow expansion into spectral comparison and lattice-point counts; separately follow transfer operators through constant and nonconstant modes to congruence counting, then the local arithmetic and combinatorial sieve. Record hypotheses and uniformity at every transition. Distinguish rational from geometric irreducibility and fixed from shrinking smoothing widths.

Native labels identify source nodes; selected labels additionally give their Acta counterparts. The graph contains bibliography references and a limited set of explicit proof-input arrows. An indexed reference is not an independently checked proof input. Outdegree zero is relative to this incomplete recorded graph.