Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2026
|
| Online Access: | https://doi.org/10.5281/zenodo.18115506 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866901347181264896 |
|---|---|
| author | Landin, Kelsy Ansol |
| author_facet | Landin, Kelsy Ansol |
| contents | <p>The Riemann Hypothesis is equivalent to the assertion that the error term in the prime counting function scales as O(√x log x). We present a proof based on the Disjoint Prime-Composite (PC) Decomposition. By defining composite removal strictly by the Least Prime Factor (LPF), we eliminate the overlap inherent in the inclusion-exclusion principle. We demonstrate that the prime sieve is a deterministic, band-limited process in which the active "generators" at scale x are strictly limited to p ≤ √x. By invoking Bernstein's Inequality (band-limiting) and Bienaymé's Identity (additivity of variance for disjoint sets), we prove that the error term is structurally forbidden from exceeding the square-root horizon.</p> <p>Files Included in this Record:</p> <ol> <li>Structural Proof: A concise, rigorous mathematical proof demonstrating the structural band-limit of the error term using Lehmer's Counting Formula and the Disjoint Additivity of Variance.</li> <li>Mirror Symmetry: A comprehensive 42-page monograph detailing the complete theoretical framework, including the "Mirror Symmetry" of prime generation, the definition of the error term as "Quantization Noise," and experimental data tables comparing the discrete "Landin-Euler Sieve" against the Logarithmic Integral Li(x).</li> </ol> <p>Key Contributions:</p> <ol> <li>Disjoint Decomposition: Resolving the sieve into orthogonal "PC Waves" to eliminate constructive interference in the error term.</li> <li>The Square-Root Horizon: Identifying that the "Cause" of composite structure at scale X is strictly limited to generators p ≤ √X.</li> <li>Quantization Noise: Reframing the deviation |π(x) - Li(x)| not as random error, but as the deterministic information loss incurred by smoothing discrete steps.</li> </ol> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18115506 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Structural Proof of the Riemann Hypothesis via Disjoint Sieve Mechanics and the Mirror Symmetry of Primes Landin, Kelsy Ansol <p>The Riemann Hypothesis is equivalent to the assertion that the error term in the prime counting function scales as O(√x log x). We present a proof based on the Disjoint Prime-Composite (PC) Decomposition. By defining composite removal strictly by the Least Prime Factor (LPF), we eliminate the overlap inherent in the inclusion-exclusion principle. We demonstrate that the prime sieve is a deterministic, band-limited process in which the active "generators" at scale x are strictly limited to p ≤ √x. By invoking Bernstein's Inequality (band-limiting) and Bienaymé's Identity (additivity of variance for disjoint sets), we prove that the error term is structurally forbidden from exceeding the square-root horizon.</p> <p>Files Included in this Record:</p> <ol> <li>Structural Proof: A concise, rigorous mathematical proof demonstrating the structural band-limit of the error term using Lehmer's Counting Formula and the Disjoint Additivity of Variance.</li> <li>Mirror Symmetry: A comprehensive 42-page monograph detailing the complete theoretical framework, including the "Mirror Symmetry" of prime generation, the definition of the error term as "Quantization Noise," and experimental data tables comparing the discrete "Landin-Euler Sieve" against the Logarithmic Integral Li(x).</li> </ol> <p>Key Contributions:</p> <ol> <li>Disjoint Decomposition: Resolving the sieve into orthogonal "PC Waves" to eliminate constructive interference in the error term.</li> <li>The Square-Root Horizon: Identifying that the "Cause" of composite structure at scale X is strictly limited to generators p ≤ √X.</li> <li>Quantization Noise: Reframing the deviation |π(x) - Li(x)| not as random error, but as the deterministic information loss incurred by smoothing discrete steps.</li> </ol> |
| title | A Structural Proof of the Riemann Hypothesis via Disjoint Sieve Mechanics and the Mirror Symmetry of Primes |
| url | https://doi.org/10.5281/zenodo.18115506 |