u/Fearless-AK-1857

I wanted to express my sincere thanks to everyone who has taken the time to read and engage with my work.
Two of my recent papers have now reached:
Reframing P vs. NP via Structural Descent: SBI, Alankar Chains and the Emergence of Temporal Complexity Theory — 1,214 downloads
Complete Detectable Spacetime Geometry: Unified Emergence of Matter, Gravity, and Quantum Dynamics — 514 downloads
Together, they’ve been downloaded 1,728 times.
Whether you agree with the ideas or remain skeptical, I genuinely appreciate everyone who has invested time in reading, questioning, and discussing them. Critical feedback is an essential part of scientific progress.
If you’re interested in computational complexity, quantum foundations, gravity, or attempts at unified theoretical frameworks, I’d be grateful if you took a look at the papers and shared your thoughts. Constructive criticism, questions, and independent analysis are all welcome.
Thank you again to everyone who has supported this research journey.

Rethinking the Riemann Hypothesis: A Structural Framework

For over 160 years, the Riemann Hypothesis (RH) has been treated as an isolated puzzle of complex analysis. In my latest research, I move this problem into the realm of operator theory and spacetime geometry.

To be completely clear: This is not an unconditional proof of the Riemann Hypothesis. Instead, it is a rigorous conditional proof that shifts the foundational burden. It establishes that the truth of RH is an absolute mathematical necessity if and only if our universe obeys the principle of complete detectability.

The Mathematical Mechanics:

The framework, Complete Detectable Spacetime Geometry (CDSG), connects these concepts step-by-step:

The Probe Algebra: Zeros of the Zeta function are mapped to a linear operator spectrum, translating complex roots into geometric parameters.

The Weil Explicit Formula: I use André Weil’s classical 1952 positivity criterion as the primary mathematical bridge. Zeros off the critical line cause Weil's functional to fail, which my framework maps directly to a loss of geometric injectivity.

The Defect Functional (Δ): If RH were false, it would force a non-zero defect functional (Δ > 0). This introduces "hidden spectral defects"—blind spots where information is trapped and completely undetectable.

The Significance:

By linking structural completeness to Weil positivity, the paper proves: If a system is entirely free of hidden defects (Δ = 0), RH follows by logical necessity.Remarkably, enforcing this defect-free condition naturally constrains the system to a minimal four-dimensional spacetime realization.

I invite colleagues across mathematics and physics to review this conditional framework and explore this new dictionary uniting prime numbers and gauge physics.

Preprints are available on SSRN:

https://papers.ssrn.com/sol3/papers.cfm?abstract\_id=6598573

https://papers.ssrn.com/sol3/papers.cfm?abstract\_id=6566300

#Mathematics #TheoreticalPhysics #RiemannHypothesis #QuantumMechanics #AcademicResearch