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This work presents the Final Conditional Version V4.1 (September 2025) of a resolution of the Riemann Hypothesis based on S-finite adelic spectral systems.
The paper defines a canonical determinant
𝐷
(
𝑠
)
D(s), constructed purely from operator-theoretic principles (double operator integrals, Schatten class estimates, and Paley–Wiener theory), without using the Euler product or the Riemann zeta function
𝜁
(
𝑠
)
ζ(s) as input.
Main results:
𝐷
(
𝑠
)
D(s) is entire of order ≤ 1.
Functional symmetry:
𝐷
(
1
−
𝑠
)
=
𝐷
(
𝑠
)
D(1−s)=D(s).
Asymptotic normalization:
lim
ℜ
(
𝑠
)
→
+
∞
log
𝐷
(
𝑠
)
=
0
lim
ℜ(s)→+∞
logD(s)=0.
Identification:
𝐷
(
𝑠
)
≡
Ξ
(
𝑠
)
D(s)≡Ξ(s) (the completed Riemann xi-function).
The trace formula recovers the logarithmic prime structure
ℓ
𝑣
=
log
𝑞
𝑣
ℓ
v
=logq
v
geometrically as closed spectral orbits.
Numerical validation (errors ≤ 10⁻⁶) confirms rigidity: perturbing
ℓ
𝑣
ℓ
v
breaks the explicit formula.
Core claim: Under the S-finite axioms and spectral regularity conditions, all non-trivial zeros of
𝜁
(
𝑠
)
ζ(s) lie on the critical line
ℜ
(
𝑠
)
=
1
/
2
ℜ(s)=1/2.
This resolution is conditional, pending formal acceptance of the S-finite axioms, and is offered with full transparency and reproducibility.
All appendices detail Paley–Wiener uniqueness (Appendix A), the Archimedean contribution (Appendix B), and uniform Schatten bounds with spectral stability (Appendix C).
Author: José Manuel Mota Burruezo
Instituto Conciencia Cuántica
GitHub repository with code and data: https://github.com/motanova84/-jmmotaburr-riemann-adelic
License: CC-BY 4.0
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Título A Complete Conditional Resolution of the Riemann Hypothesis via S-Finite Adelic Spectral Systems (Final Conditional Version V4.1)
This work presents the Final Conditional Version V4.1 (September 2025) of a resolution of the Riemann Hypothesis based on S-finite adelic spectral systems.
The paper defines a canonical determinant
𝐷
(
𝑠
)
D(s), constructed purely from operator-theoretic principles (double operator integrals, Schatten class estimates, and Paley–Wiener theory), without using the Euler product or the Riemann zeta function
𝜁
(
𝑠
)
ζ(s) as input.
Main results:
𝐷
(
𝑠
)
D(s) is entire of order ≤ 1.
Functional symmetry:
𝐷
(
1
−
𝑠
)
=
𝐷
(
𝑠
)
D(1−s)=D(s).
Asymptotic normalization:
lim
ℜ
(
𝑠
)
→
+
∞
log
𝐷
(
𝑠
)
=
0
lim
ℜ(s)→+∞
logD(s)=0.
Identification:
𝐷
(
𝑠
)
≡
Ξ
(
𝑠
)
D(s)≡Ξ(s) (the completed Riemann xi-function).
The trace formula recovers the logarithmic prime structure
ℓ
𝑣
=
log
𝑞
𝑣
ℓ
v
=logq
v
geometrically as closed spectral orbits.
Numerical validation (errors ≤ 10⁻⁶) confirms rigidity: perturbing
ℓ
𝑣
ℓ
v
breaks the explicit formula.
Core claim: Under the S-finite axioms and spectral regularity conditions, all non-trivial zeros of
𝜁
(
𝑠
)
ζ(s) lie on the critical line
ℜ
(
𝑠
)
=
1
/
2
ℜ(s)=1/2.
This resolution is conditional, pending formal acceptance of the S-finite axioms, and is offered with full transparency and reproducibility.
All appendices detail Paley–Wiener uniqueness (Appendix A), the Archimedean contribution (Appendix B), and uniform Schatten bounds with spectral stability (Appendix C).
Author: José Manuel Mota Burruezo
Instituto Conciencia Cuántica
GitHub repository with code and data: https://github.com/motanova84/-jmmotaburr-riemann-adelic
License: CC-BY 4.0
Tipo de obra Formación, Divulgación
Etiquetas the riemann hypothesis in full. via s-finite adel
-------------------------
Información de registro en Safe Creative
Identificador 2509203122475
Fecha de registro 20 sept. 2025 22:44 UTC
Licencia Todos los derechos reservados
-------------------------
Declaraciones de autoría y derechos inscritas
Autor 100.00 %. Titular JOSE MANUEL MOTA BURRUEZO. Fecha 20 sept. 2025.
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