QTT Balanced-Rail Optical Intertwining Theorem

A symmetry-selected pi/8 spinor character and its physical clock test \\[B_* = \\frac{Z+X}{\\sqrt 2},\\qquad U_* Z U_*^\\dagger=B_*,\\qquad U_* = \\exp\\!\\left(-J\\frac{\\pi}{8}Y\\right),\\qquad \\frac12\\operatorname{Tr}U_* = \\cos\\frac{\\pi}{8}.\\] QTT Balanced-Rail Optical Intertwining Theorem, v1.4. In a normalized, exchange-symmetric two-rail source sector, the positive balanced direction is unique and its shortest centered spinor lift fixes the pi/8 character without a fitted angle. Positive additive capacity supplies its square, while a declared reference interaction supplies the detector coherence. A complete memory-partition theorem gives eleven jointly fixed configurations and four-phase detector predictions. This private research edition preserves the fourteen earlier theorems and adds independent-reference kernel composition, calibrated signal identifiability, and higher-order closure from quadratic capacity. It connects the finite model to measured photon-scattering and internal-clock coherence, and independently recalculates two Bell aggregate statistics from published event totals. All four Shalm pulse windows and all nine Kauten response-correction rows are retained. Verification: 284 mathematical, numerical, synthetic and scope checks, including 235 inherited checks unchanged; 50 separate archival aggregate checks. The reconstruction includes source receipts, both supplied PDFs, complete numerical transcriptions, code, figures, preservation records and three diagnostic review passes. These counts refer to software checks, not independent experiments. Scientific scope: the cited observations support shared optical correlations and calibrated reference-coherence structure. They do not provide a new A1-versus-QM likelihood contrast or a measurement of an unprogrammed absolute-clock terminal. The same deliberately engineered apparatus has the same fixed quantum predictions. The separate physical source-to-apparatus transfer remains the experimentally distinguishing question. Detector calibration, target fitting and signal survival are treated explicitly rather than merged into one category. Author: Ali Attar, Independent Researcher, Colombes, France. ORCID: 0009-0008-9931-2691. Published research record with public metadata and restricted files. Access to the manuscript and reconstruction package requires the author's permission. Source dependencies: QTT Main Book, A1-CHSH source-character paper, Born-rule paper, Physical Terminal Reference Framework. Same-author dependencies are not counted as independent evidence.