Part 1_The JS–SH Route-Gated Schrödinger Recovery Equation

This record contains a stand-alone manuscript package for The JS–SH Route-Gated Schrödinger Recovery Equation. The paper presents the JS–SH recursive route-gated recovery equation as an upstream route-selection and inverse-readout framework for wave, path, and particle-like recovery problems. The central equation inserts a recursive route projector into a JS–SH Schrödinger-type phase layer. A route is admitted only when local Schrödinger differential consistency, global path-integral route consistency, and JS–SH 5:5 equality-throat closure coincide. When several first-order 5:5 candidates exist, the principal readout gate is selected by the recursive maximal-overlap core Γ*_JS. The manuscript is written as an independent completed paper, not as an internal revision note. It includes the route-gated recovery equation, the counter-rotating contact origin of plus/minus polarity, the real two-channel phase lift, the non-collinear x-plus/z-minus dynamic-angle source, the single-circumference particle-readout bridge, Chladni-type resonance analogues, aperture-geometry controls, and a reverse double-slit recovery protocol. The ordinary Schrödinger equation and the Feynman path integral are retained as downstream solvers after the Hamiltonian, action, geometry, path domain, and boundary conditions have been supplied. The JS–SH layer addresses the upstream question of which finite route ledger, shell-depth address, source-class marker, and equality-throat gate are admissible before the downstream phase or path-sum calculation is compressed into its usual continuum form. The package is intended for reproducibility, independent circulation, and provenance tracking. It includes the manuscript PDF/TEX and the associated code, output, ledger, and figure assets used to support the route-gated recovery framework. This is a preprint / working manuscript and has not been peer reviewed. ======================== UPDATE JS_SH_STANDALONE_SCHRODINGER_FEYNMAN_PATH_ANALYSIS_V17_ZENODO_READY_MANUSCRIPT JS_SH_STANDALONE_SCHRODINGER_FEYNMAN_PATH_ANALYSIS_V18_WAVE_PARTICLE_READOUT_ZENODO_READY_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V21_FINAL_DOI_20950855_LAYOUT_REPAIRED_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V23_FINAL_INTEGRATED_20260701_R1_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V24_AB_RESIDUAL_CHANNEL_NECESSITY_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V37_ZENODO_DOI_21199407_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V44_DOI_21202622_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V46_DOI_20849560_MANUSCRIPT JS_SH_ROUTE_GATED_SCHRODINGER_RECOVERY_EQUATION_V49_CLAIM_STRENGTHENED_MANUSCRIPT