About the work
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
π·
(
π
)
D(s), constructed purely from operator-theoretic principles (double operator integrals, Schatten class estimates, and PaleyβWiener theory), without using the Euler product or the Riemann zeta function
π
(
π
)
ΞΆ(s) as input.
Main results:
π·
(
π
)
D(s) is entire of order β€ 1.
Functional symmetry:
π·
(
1
β
π
)
=
π·
(
π
)
D(1βs)=D(s).
Asymptotic normalization:
lim
β‘
β
(
π
)
β
+
β
log
β‘
π·
(
π
)
=
0
lim
β(s)β+β
β
logD(s)=0.
Identification:
π·
(
π
)
β‘
Ξ
(
π
)
D(s)β‘Ξ(s) (the completed Riemann xi-function).
The trace formula recovers the logarithmic prime structure
β
π£
=
log
β‘
π
π£
β
v
β
=logq
v
β
geometrically as closed spectral orbits.
Numerical validation (errors β€ 10β»βΆ) confirms rigidity: perturbing
β
π£
β
v
β
breaks the explicit formula.
Core claim: Under the S-finite axioms and spectral regularity conditions, all non-trivial zeros of
π
(
π
)
ΞΆ(s) lie on the critical line
β
(
π
)
=
1
/
2
β(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 PaleyβWiener uniqueness (Appendix A), the Archimedean contribution (Appendix B), and uniform Schatten bounds with spectral stability (Appendix C).
Author: JosΓ© Manuel Mota Burruezo
Instituto Conciencia CuΓ‘ntica
GitHub repository with code and data: https://github.com/motanova84/-jmmotaburr-riemann-adelic
License: CC-BY 4.0
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Title 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
π·
(
π
)
D(s), constructed purely from operator-theoretic principles (double operator integrals, Schatten class estimates, and PaleyβWiener theory), without using the Euler product or the Riemann zeta function
π
(
π
)
ΞΆ(s) as input.
Main results:
π·
(
π
)
D(s) is entire of order β€ 1.
Functional symmetry:
π·
(
1
β
π
)
=
π·
(
π
)
D(1βs)=D(s).
Asymptotic normalization:
lim
β‘
β
(
π
)
β
+
β
log
β‘
π·
(
π
)
=
0
lim
β(s)β+β
β
logD(s)=0.
Identification:
π·
(
π
)
β‘
Ξ
(
π
)
D(s)β‘Ξ(s) (the completed Riemann xi-function).
The trace formula recovers the logarithmic prime structure
β
π£
=
log
β‘
π
π£
β
v
β
=logq
v
β
geometrically as closed spectral orbits.
Numerical validation (errors β€ 10β»βΆ) confirms rigidity: perturbing
β
π£
β
v
β
breaks the explicit formula.
Core claim: Under the S-finite axioms and spectral regularity conditions, all non-trivial zeros of
π
(
π
)
ΞΆ(s) lie on the critical line
β
(
π
)
=
1
/
2
β(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 PaleyβWiener uniqueness (Appendix A), the Archimedean contribution (Appendix B), and uniform Schatten bounds with spectral stability (Appendix C).
Author: JosΓ© Manuel Mota Burruezo
Instituto Conciencia CuΓ‘ntica
GitHub repository with code and data: https://github.com/motanova84/-jmmotaburr-riemann-adelic
License: CC-BY 4.0
Work type Education, Informative
Tags the riemann hypothesis in full. via s-finite adel
-------------------------
Registry info in Safe Creative
Identifier 2509203122475
Entry date Sep 20, 2025, 10:44 PM UTC
License All rights reserved
-------------------------
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Author 100.00 %. Holder JOSE MANUEL MOTA BURRUEZO. Date Sep 20, 2025.
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/
Registration: 2509203122475
