Continuous Topology and Discrete Arithmetic

In the paper's words

The tension between the discrete cardinality of prime numbers and the continuous geometry of the complex plane is reconciled by treating primes as spectral residues governed by the explicit formulae of the Riemann zeta function. Sequential enumeration provides a linear coordinate that obscures the underlying multiplicative coherence of the prime number system. While the ordinal ranking assigns a unique natural number to every prime, this additive progression fails to encode the local density variations and long-range correlations inherent in the distribution.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. Under this strict definition, the sequence of prime numbers comprises isolated points in the integer lattice, possessing dimension zero and rendering concepts of intrinsic curvature or metric deformation formally inapplicable.

   from The

What would falsify it

1. Simple enumeration suggests a smooth logarithmic density, yet the actual distribution exhibits irregularities that the scalar index cannot predict.

   from Limitations of Scalar

Where the claim stops

1. While the ordinal ranking assigns a unique natural number to every prime, this additive progression fails to encode the local density variations and long-range correlations inherent in the distribution.

   from Limitations of Scalar

2. Simple enumeration suggests a smooth logarithmic density, yet the actual distribution exhibits irregularities that the scalar index cannot predict.

   from Limitations of Scalar

3. These irregularities are governed by the critical strip of the Riemann zeta function, where the locations of non-trivial zeros dictate the oscillation of the prime count around its logarithmic approximation.

   from Limitations of Scalar

Where to read

1. Limitations of Scalar303 words · 1 min
2. Spectral Vectors as411 words · 2 min
3. The249 words · 1 min
4. Reconciliation via451 words · 2 min