BC XV: Canonical Representatives and Gauge Quotients of Schur/Feshbach Response Classes 2026 06 20

The paper also proves that the minimal hidden support dimension is equal to the rank of the effective response operator, and that minimal whitened factorizations of the same response are unique up to a unitary hidden-frame transformation. On rank-stable parameter intervals, the canonical square-root representative varies smoothly, while rank-changing boundaries are identified as the natural singular walls to be studied in the next module. Boundary Compensation XV therefore converts hidden-lift non-identifiability into a precise mathematical language of quotient classes, gauge redundancies, minimal supports and canonical normal forms. The work is deliberately finite-dimensional and structural. It does not claim reconstruction of a physical hidden Hamiltonian, derivation of particle masses, a Standard Model derivation, a cosmological-constant calculation or an empirical prediction. Its purpose is to complete the regular quotient geometry needed before studying singular rank-changing walls in subsequent Boundary Compensation modules. Boundary Compensation / Zenodo records 18 records, ascending DOI order Community archive: Boundary Compensation: Mathematical Physics and Spectral Response 1. Boundary Compensation and Spectral Sensitivity of the Cosmological Constant DOI: https://doi.org/10.5281/zenodo.20582076 Zenodo: https://zenodo.org/records/20582076 2. BC-TimeEntropy v0.3: Boundary Compensation, Spectral Entropy, Gap-Controlled Response and Relational Internal Time DOI: https://doi.org/10.5281/zenodo.20619751 Zenodo: https://zenodo.org/records/20619751 3. Boundary Compensation and Wavefunction Collapse: Finite-Resolution Readout of Nonzero Boundary Residue DOI: https://doi.org/10.5281/zenodo.20674022 Zenodo: https://zenodo.org/records/20674022 4. BC-Horizon-v0.1 Boundary Compensation and the Black Hole Information Problem DOI: https://doi.org/10.5281/zenodo.20680671 Zenodo: https://zenodo.org/records/20680671 5. Boundary Compensation III: Induced Zero-Mode Splitting and the Microscopic Origin of the Compensation Gap DOI: https://doi.org/10.5281/zenodo.20684264 Zenodo: https://zenodo.org/records/20684264 6. Boundary Compensation IV: Multi-Channel Compensation Mixing and Induced Gap Spectra DOI: https://doi.org/10.5281/zenodo.20694403 Zenodo: https://zenodo.org/records/20694403 7. Boundary Compensation V: Orthogonal Sector Projections and Non-Abelian Compatibility in Zero-Mode Spaces DOI: https://doi.org/10.5281/zenodo.20701903 Zenodo: https://zenodo.org/records/20701903 8. Boundary Compensation VI: Stability of Sector-Projected Gap Labels and Representation-Theoretic Selection Rules DOI: https://doi.org/10.5281/zenodo.20709726 Zenodo: https://zenodo.org/records/20709726 9. Boundary Compensation VII: Coarse-Grained Spectral Access to Induced Boundary Gap Operators DOI: https://doi.org/10.5281/zenodo.20723846 Zenodo: https://zenodo.org/records/20723846 10. Boundary Compensation I: Spectral Sensitivity of the Cosmological Constant DOI: https://doi.org/10.5281/zenodo.20724751 Zenodo: https://zenodo.org/records/20724751 11. Boundary Compensation VIII: Parameter Flow of Induced Gap Spectra and Sector-Weight Transport DOI: https://doi.org/10.5281/zenodo.20735158 Zenodo: https://zenodo.org/records/20735158 12. Boundary Compensation IX: Isotypic Sector Transport and Non-Abelian Compatibility under Parameter Flow DOI: https://doi.org/10.5281/zenodo.20738859 Zenodo: https://zenodo.org/records/20738859 13. Boundary Compensation X: Toy Hidden-Sector Response Models and Finite-Dimensional Access Operators DOI: https://doi.org/10.5281/zenodo.20740570 Zenodo: https://zenodo.org/records/20740570 14. Boundary Compensation XI: The Inverse Isotypic Gap Problem and Finite-Resolution Response Equivalence DOI: https://doi.org/10.5281/zenodo.20748061 Zenodo: https://zenodo.org/records/20748061 15. Boundary Compensation XII: Selection Rules and Admissible Representatives of Finite-Resolution Response Classes DOI: https://doi.org/10.5281/zenodo.20751489 Zenodo: https://zenodo.org/records/20751489 16. Boundary Compensation XIII: Rigidity and Refinement of Finite-Resolution Response Equivalence Classes DOI: https://doi.org/10.5281/zenodo.20760491 Zenodo: https://zenodo.org/records/20760491 17. Boundary Compensation XIV: Structural Identifiability Thresholds and Minimal Refinement Conditions DOI: https://doi.org/10.5281/zenodo.20764827 Zenodo: https://zenodo.org/records/20764827 18. Boundary Compensation XV: Canonical Representatives and Gauge Quotients of Schur/Feshbach Response Classes DOI: https://doi.org/10.5281/zenodo.20767709 Zenodo: https://zenodo.org/records/20767709