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This work isolates and defines various branches of Dirichlet F1-Lite variance transduction, aiming to simplify specific mathematical constructs.

May 16, 2026Open Access

F1-Lite Dirichlet Variance Transduction and the Subconvexity–GUE Interface: Diagonal-Safe Theorem, Support-Enlarged Obstructions, Stable Secondary Targets, and Model Divisor-Branch Closure

Key Points

This work isolates and defines various branches of Dirichlet F1-Lite variance transduction, aiming to simplify specific mathematical constructs.
Introduced the conditional variance–kernel–energy interface, delineating several mathematical frameworks.
Formulated a diagonal-safe variance-discrepancy bridge under specific coefficient support conditions.
Developed a model divisor-branch closure theorem based on smooth shifted-divisor inputs.
The diagonal-safe theorem corresponds to conditions where σ < 1, eliminating problematic off-diagonal terms.
For σ > 1, established product-congruence obstructions, highlighting significant changes in mathematical behavior.
Demonstrated that under a smooth shifted-divisor input, a deterministic shifted-product component can be absorbed into stable targets.

Abstract

This record contains a five-paper core set for the F1-Lite Dirichlet variance-transduction branch of a conditional Subconvexity–GUE interface framework. The package does not claim a proof of GUE universality, subconvexity, the Riemann Hypothesis, or a zero-density theorem. Its purpose is more specific: it isolates the Dirichlet-family F1-Lite bridge into a restricted diagonal-safe theorem branch, a support-enlarged product-congruence obstruction branch, a stable secondary-target package, and a conditional model divisor-branch closure under a smooth shifted-divisor input. The uploaded PDFs are: 1. **Energy Interfaces between Subconvexity Bounds and GUE-Type Pair-Correlation Statistics: A Conditional Variance–Kernel Transduction Framework**, Version v4. 0r2. This parent manuscript formulates the conditional variance–kernel–energy interface. It separates the forward explicit-formula variance bridge, the variance–kernel comparability gate, the reverse obstruction package, threshold matching, and loss compatibility. 2. **A Diagonal-Safe Explicit-Formula Variance-Discrepancy Bridge for Dirichlet Families**, F1-Lite Restricted Theorem Note, Version v3. 7r2. This note extracts the restricted theorem-level branch for coefficient support below the prime modulus threshold, \ (1: -congruence obstruction and stable secondary-target branch, \] \^ EF=1: model divisor-branch closure under a smooth shifted-divisor input. \ The main remaining mathematical tasks after this release are: proving or importing sufficiently uniform shifted-product asymptotics for broader coefficient classes, proving centered product-congruence residual saving after secondary-target subtraction, handling endpoint/Type-I ledgers, extending the model divisor branch to the full EF/VHB coefficient-local setting, and establishing the separate variance–kernel comparability gate needed for GUE-facing kernel-energy conclusions.

F1-Lite Dirichlet Variance Transduction and the Subconvexity–GUE Interface: Diagonal-Safe Theorem, Support-Enlarged Obstructions, Stable Secondary Targets, and Model Divisor-Branch Closure

Key Points

Abstract

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