Penetration of Quantum Mechanics by the Differential-Time Principle: Abstract Preprint and Priority Claim

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This record is a priority-claim abstract preprint for the paper: “Penetration of Quantum Mechanics by the Differential-Time Principle:Derivation of the Uncertainty Relation, the Born Rule, the Lamb Shift,and the Schwarzschild Metric from a Single Cross-Window Structure.” The paper claims that a single differential-time structure, ΔT(t)=S(t)−C(t),generates a cross-window effective amplitude A_Δ(x,t) from which multiplefoundational structures of quantum mechanics and gravitational physics arederived without introducing them as independent postulates. The central priority claim is the derivation of the Born rule. In this framework,the probability rule P(n)=|c_n|² is not assumed as an axiom. It is obtained asthe normalized long-time limit of finite-time cross-window projection of A_Δ.For a state |ψ(t)> = Σ_m c_m exp(−iω_m t)|m>, the finite-time projectionamplitude onto channel n is defined through a cross-window weight W_T(t).Off-diagonal channel mixing is suppressed by temporal frequency resolution,using the Riemann–Lebesgue lemma, and the normalized squared projectionweight converges to P(n)=|c_n|². The same cross-window object A_Δ is also claimed to reproduce:(1) the uncertainty relation ΔxΔp ≥ ℏ/2 from spatial finite width via theCauchy–Schwarz inequality;(2) the Lorentzian natural linewidth from temporal finite width via Fouriertransform;(3) the measurement transition as the continuous crossover betweenτ≪τ_× and τ≫τ_×;(4) the Lamb shift from spatial smoothing of the Coulomb singularity;(5) the CHSH violation up to S=2√2 from non-separable joint cross-windowreadout A_Δ^{AB}, without invoking superluminal signaling;(6) a finite vacuum-energy integral from a physical cross-window UV cutoff;and(7) the Schwarzschild metric component g_{00}=−(1−r_s/r) and the structuralform of Einstein’s field equations from spatial modulation of τ_×(x). The quantitative testbed is the uniform residual law n×0.087%, derived fromα_ΔT = 4Ω_b/27 and ε = α_ΔT/α_CODATA − 1 = 0.00087. Across α^n-dependentquantities from α^{-1} to α^5, the residuals are predicted to propagate asn×0.087%. This abstract preprint fixes the priority date and public content of the aboveclaims. The complete English manuscript is held by the author as a LaTeX-generatedPDF and will be disclosed separately. The identity of that manuscript PDF is fixedby the following SHA-256 hash. SHA-256 hash (full English PDF, LaTeX-generated):21603304b76d6073b8588d21fd5f6d41c80534036f79813bb42e1ec60257d785 SHA-256 hash (LaTeX source):f82c82191b46ff53796d9aa9b7109cb6b230d074bf6472f5916cb2d9d2c63369

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.