PrimeNumberTheoremAnd

Inside dyadic shell k, each height-square term is bounded by 2^(-2k).

Dyadic-shell mass is bounded by shell cardinality times 2^(-2k).

A dyadic shell has no more zeros than the cumulative set below its top edge.

Any RvM estimate gives an absolute-value bound for N(T).

An RvM estimate with Backlund's constants gives the dyadic N(T) bound by the explicit majorant.

The logarithm of a dyadic height is bounded by the dyadic count scale.

The logarithm of a dyadic height is bounded by its dyadic exponent.

Log size of the dyadic main-term denominator factor.

Triangle bound for the RvM main term after writing A = T/(2*pi).

The RvM main term has the dyadic growth needed by the zero-tail route.

The RvM error term has the dyadic growth needed by the zero-tail route.

Main-term dyadic growth gives growth of the full Backlund majorant.

A linear term times 2^(-k) is summable.

A dyadic mass bound gives dyadic-shell height summability.

A cumulative dyadic count source gives the dyadic shell-count source.

The remaining N(T) count source splits into two counting inputs once the finite-strip multiplicity comparison is proved: absolute-height reduction to positive-height zeros, and comparison of N' 0 T to the project N(T).

The same bridge with the finite zero-height bucket preserved as an additive constant.

Conjugation symmetry reduces absolute-height counts to two positive-height buckets plus the finite zero-height bucket.

The N' 0 T comparison with N(T) is sum monotonicity over the rectangle inclusion, once the larger positive-height N(T) series is known summable.

The cumulative dyadic count source follows from a comparison with N(T) and dyadic growth of the explicit Backlund majorant.