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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English, Middle (1100-1500) |
| Published: |
Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.19885224 |
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Table of Contents:
- <p>This paper demonstrates that Legendre’s Conjecture is a deterministic result of a Bijective Scaling Isomorphism inherent in the distribution of prime numbers. We establish that at the point (k = 1), linear Bertrand scales and exponential architectures share a perfect structural identity. By proving that the Linear Super-System and the Quadratic Reflection both contain exactly 2n+2 members, we define a bijective transformation Φ that carries the proven prime-existence property from the linear domain [2n, 4n + 1] to the quadratic range [n^2, (n + 1)^2]. This symmetry, anchored by the Pronic Center (n^2 + n), necessitates the existence of primes in every square gap as a structural invariant of the number line, effectively satisfying both Legendre’s and Oppermann’s conjectures.</p>