A Systematic Challenge to the 167-Year Unsolved Problem
First systematic verification of the Shimizu (2024) paper claiming GPT proved RH
Creating new discoveries through human intuition and AI computing collaboration
First systematic verification of the GPT-assisted RH proof claim
Convergence condition unproven
Infinite-series convergence proof missing
Continuation from Re(s)>1 to the full domain unproven
Insufficient analysis for large |t|
The core identity assumes RH (fatal circular logic)
Conclusion: Proof Invalid ❌
Gap 5 is especially fatal — the core identity already assumes RH,
a circular logic that invalidates the entire proof.
"These methods have already been tried, and we documented why they fail"
Free energy minimization
Circular logicAdS/CFT correspondence
Premise verification failedHarmonic balance
Informal argumentEntropy maximization
Mathematical gapConvexity analysis
Globality unprovenDynamical quantum phase transition
Circular logicMinimum-point equivalence
Equivalence unprovenNumerical verification (10^13 zeros)
Partial evidence
The Riemann Hypothesis is equivalent to "the minimum of |ξ(σ+it)| over all t occurs at σ=1/2"
But proving the MIN condition itself is just as hard as RH
Thermodynamics, holography, music, and information theory all point to σ=1/2
Intuitively correct, but lacking formal proof
A systematic collaboration framework between human intuition and AI computing power
Presenting a new research paradigm
Systematic verification of a GPT-assisted proof claim, revealing 5 critical gaps
Clarifying the limits of AI-assisted mathematical research
All code, mathematical proofs, and session records are publicly available.
Transparency and reproducibility are core to the YAIM methodology.