The Folman Phase Spine and the Operator-Complete π/8 Reference-Switch Test

Can four atom-interferometric histories expose a clock overlap that ordinary gain calibration would erase? Version: 5.0 Concept DOI: 10.5281/zenodo.20123495 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01, pp. 158-160 and 560-562 The Folman atom-chip programme already supplies full-loop Stern-Gerlach coherence, internal-clock visibility, geometric phase, spinor periodicity, and cubic phase scaling. This paper asks a narrower question: can one physical loop realize four reference histories whose raw quadrature or visibility slopes cancel ordinary channel gain without also dividing out the terminal clock overlap? The source/readout factorization is \[ S_{ab}=\kappa\sqrt{\eta_a\eta_b}\,\Gamma_{ab}, \qquad a,b\in\{\tau,T\}, \] and the operator-complete observable is \[ \boxed{ R_{\rm Gram} = \sqrt{\frac{|S_{\tau T}S_{T\tau}|}{|S_{\tau\tau}S_{TT}|}} }. \] The duplicate histories close the normalization; the cross histories carry the candidate terminal overlap. After an independently passed unprogrammed-access gate, the two fixed branches are \[ \boxed{ R_{\rm Gram}^{\rm standard}=1, \qquad R_{\rm Gram}^{\rm QTT-A1}=\cos\!\left(\frac{\pi}{8}\right) =0.9238795325112867\ldots }. \] The sharpening is algebraic. A calibration that traverses the complete clock-sensitive history divides out the proposed factor and returns unity in both theories. Conversely, deliberately preparing ordinary quantum pointer states with overlap \(\cos(\pi/8)\) makes standard quantum mechanics predict the same value. Version 5.0 therefore forbids both routes and activates the point predictions only when the same hardware control word contains no target angle, the standard device model predicts unit ordinary cross-history overlap, and an independent bypass witness constrains ordinary loss. The exact identifiability equation is \[ \boxed{ R_{\rm Gram}=N_{\rm cross}^{\rm ord}I_{\rm clk}^{q}, \qquad q=0\ \text{(standard)},\quad q=1\ \text{(QTT)} }. \] If \(N_{\rm cross}^{\rm ord}\) is not independently fixed, the packet is ineligible and neither theory is judged. The paper retains the Access-Law trident \[ \boxed{ \mathcal U_X+\left(\frac{V}{V_0}\right)^2=1, \qquad \mathcal U_X:=\frac{2\Delta X\Delta P}{\hbar} }, \] together with the Folman phase spine, \(4\pi\) spinor periodicity, cubic Stern-Gerlach phase scaling, and the Planck-mass-count capacity statement \(B=M/m_A<1\). No observed Folman target number enters the constructor. Sealed lineage: Version 4.0 historical lock: 0812296b3cd13782d81f085d1c8eab16520db0b397090ad9dd9d0e103c1d82d3 Version 5.0 operator lock: d639b046681a60658d375f327541814d801422b1e3c520ac3ec859af0cf4489c Status: SIGMA-FOLMAN-FOUR-CHANNEL-GRAM-OPERATOR-CLOSED SIGMA-FOLMAN-CALIBRATION-ERASURE-NO-GO-CLOSED SIGMA-FOLMAN-PROGRAMMED-OVERLAP-NO-GO-CLOSED SIGMA-FOLMAN-UNPROGRAMMED-ACCESS-HARDWARE-MAP-PENDING SIGMA-FOLMAN-TARGET-DATA-EXECUTION-PENDING Reader routes: QTT Lexicon Two Universes Corpus Tree entry Companion sealed Sagnac test The PDF is the first preview file. The reconstruction archive contains the LaTeX source, both seal generations, four-history packet schema, analyzer, mutation-aware verifier, machine receipt, render audit, and SHA-256 manifest.