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\title{VMS Electromagnetic Laws}
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\maketitle

A concise set of VMS-first laws for electromagnetism. Each law states its value, minimal math, and practical use. Classical recovery is shown as a limit (bridge).

\section*{Locked Conventions (apply everywhere)}

\begin{itemize}
\item Display-area: $A_d = \pi r^2$ (projected disk), not $4\pi r^2$.

\item Unit bridge: $\alpha$ bridges to SI Coulomb-style forms; e.g., $\alpha = 4/\varepsilon_0 \Rightarrow E = Q/(4\pi \varepsilon_0 r^2)$ when needed.

\item Slowness/index: $n(x, \lambda)$ encodes medium response (closure / route shadow).

\item Acceptance locks: import one dimensional scale $S_0 = h; \mu_0, \varepsilon_0, c$ used only as unit locks (no tunables).
\end{itemize}

\section*{Part I --- Core VMS Laws (Foundational)}

\subsection*{L0 --- Conventions}

\textbf{Statement:} Use $A_d$ and $\alpha$; avoid flux language; set the bridge explicitly when presenting SI forms.

\textbf{How it's not classical:} Classical optics starts from fields + Gauss/flux with $4\pi r^2$ areas.

\textbf{Classical coverage:} Meta-rule; not a numerical prediction.

\subsection*{L1 --- Closure Conservation (inverse-square)}

\textbf{Statement:} Stationary closure $Q$ spreads over display-area $A_d$, giving $1/r^2$ strength.

\textbf{Core math:} $E_{\text{VMS}}(r) \propto \alpha \cdot Q / (\pi r^2)$

\textbf{How it's not classical:} No Gauss-sphere flux postulate; $1/r^2$ comes from projected area, not spherical flux.

\textbf{Classical coverage:} Matches classical magnitudes when $\alpha = 4/\varepsilon_0$.

\subsection*{L2 --- No Sideways Pile-Up (boundary continuity)}

\textbf{Statement:} Tangential transport across boundaries is continuous; determines angles and amplitudes.

\textbf{Core math:} $n_1 \sin\theta_1 = n_2 \sin\theta_2$ \quad (angles)

\textbf{How it's not classical:} Derived as a transport rule, not via Fermat or Maxwell BCs.

\textbf{Classical coverage:} Angles/amplitudes agree with classical results.

\subsection*{L3 --- Route-Phase Superposition (interference)}

\textbf{Statement:} Coherent routes add with phase set by closure comparisons; knob is path difference $\Delta L$.

\textbf{Core math:} $\Delta\phi = (2\pi/\lambda) \Delta L$; \quad bright: $\Delta L = m\lambda$; \quad dark: $\Delta L = (m+\frac{1}{2})\lambda$

\textbf{How it's not classical:} Phase meaning is route-closure comparison rather than field axiom.

\textbf{Classical coverage:} Fringes identical to classical.

\subsection*{L4 --- Eikonal \& Rays}

\textbf{Statement:} Write $U = A e^{\{i k_0 S\}}$; rays follow $\nabla S$; transport fixes $A$.

\textbf{Core math:} $|\nabla S|^2 = n^2$; \quad $2 \nabla S \cdot \nabla A + A \nabla^2 S = 0$

\textbf{How it's not classical:} Assigns VMS meaning to $n$ (closure/``slowness'' budget).

\textbf{Classical coverage:} Same ray paths as classical eikonal theory.

\subsection*{L5 --- Polarization Projection}

\textbf{Statement:} Polarizer drains closure $\perp$ to its axis; surviving field is the projection (Malus).

\textbf{Core math:} $I_{\text{out}} = I_{\text{in}} \cos^2 A$

\textbf{How it's not classical:} Mechanism is closure drain, not field boundary components.

\textbf{Classical coverage:} Malus law unchanged.

\subsection*{L6 --- Diffraction-Fourier Law}

\textbf{Statement:} Finite $A_d$ (pupil) $\Rightarrow$ Fourier weighting; PSF/MTF from aperture transform.

\textbf{Core math:} $\Theta_R \approx 1.22 \, \lambda/D$; \quad $f_c = D / (\lambda \, f)$

\textbf{How it's not classical:} Framed via display-area/routes; math matches Fourier diffraction.

\textbf{Classical coverage:} Airy, OTF/MTF identical.

\subsection*{L7 --- Étendue / Brightness Invariance}

\textbf{Statement:} Paraxial invariants for route cones are conserved in passive systems.

\textbf{Core math:} $q = n\Theta$; \quad $H = x \, q$; \quad $G = n^2 \, A \, \Omega = \text{const}$

\textbf{How it's not classical:} Motivated by route packing rather than radiance postulate.

\textbf{Classical coverage:} Same invariance as classical radiometry.

\subsection*{L8 --- Dispersion \& Achromats}

\textbf{Statement:} $n(\lambda)$ varies with color; two-glass pair cancels first-order axial color.

\textbf{Core math:} $\varphi_1 + \varphi_2 = \varphi^*f$; \quad $\varphi_1/V_1 + \varphi_2/V_2 = 0$

\textbf{How it's not classical:} Interpretation of $n(\lambda)$ differs; design equations are the same.

\textbf{Classical coverage:} Same achromat conditions as classical.

\subsection*{L9 --- DOF-Diffraction Trade}

\textbf{Statement:} Defocus blur shrinks with $f/\#$; diffraction grows with $f/\#$; pick the crossover.

\textbf{Core math:} $c_{\text{defocus}} \propto 1/(f/\#)$, \quad $r_{\text{diff}} \propto (f/\#)$

\textbf{How it's not classical:} Route-cone view adds geometric intuition; same outcome.

\textbf{Classical coverage:} Same trade curves as classical.

\subsection*{L10 --- Interferometric Fringe Law}

\textbf{Statement:} Path change is counted directly by fringes in 2-pass.

\textbf{Core math:} $\Delta L = m \, \lambda / 2$

\textbf{How it's not classical:} Treated as route metrology rather than field-only.

\textbf{Classical coverage:} Identical to classical interferometry.

\subsection*{L11 --- Maxwell-Limit Reduction}

\textbf{Statement:} With SI locks and smooth fields, VMS reduces to Maxwell's equations.

\textbf{Core math:} $F = dA$; \quad $dF = 0$; \quad $d^*F = J$

\textbf{How it's not classical:} Classical starts at Maxwell; VMS reduces to it as a limit.

\textbf{Classical coverage:} By construction, same equations.

\subsection*{L12 --- Measurement-Domain Law}

\textbf{Statement:} Use Jones/eikonal when phase matters; use Stokes/Mueller when intensities add.

\textbf{How it's not classical:} Framed as a modeling-domain law inside VMS, not a separate theory.

\textbf{Classical coverage:} Same practice as classical optics.

\section*{Part II --- Extended Mass-Coupled Laws (New Value Propositions)}

\subsection*{L-M1 --- Mass-Coupled Slowness of ``Vacuum''}

\textbf{Statement:} Nearby mass perturbs slowness $n$ used by routes; unify delay and bending under OPL.

\textbf{Minimal form:}
\begin{equation*}
n(x, \lambda) = 1 + n_0 \cdot \varphi(x) + n_1(\lambda) \cdot \varphi(x) \quad \text{where} \quad \varphi = \Phi/c^2
\end{equation*}

\textbf{Immediate use:}
\begin{itemize}
\item Delay: $\Delta t(\lambda) = (1/c) \int [n(1)-1] \, ds$

\item Bending: $\theta(\lambda) \approx \int \nabla_\perp n \, ds$
\end{itemize}

\textbf{Classical limit:} $n_0 = n_1 = 0$ (EM vacuum); GR corresponds to achromatic $n_0 \neq 0$, $n_1 = 0$.

\subsection*{L-M2 --- Mass-Flow Non-Reciprocity (One-Way Phase Bias)}

\textbf{Statement:} Mass currents bias counter-propagating phases in vacuum loops.

\textbf{Minimal loop form:}
\begin{equation*}
\Delta\varphi_{\text{NR}}(\lambda) = \zeta(\lambda) \cdot (2\pi / (\lambda \, c)) \cdot n^- \cdot \int (\Omega_m(r) \times r) \, dA
\end{equation*}

\textbf{Immediate use:}
\begin{itemize}
\item Additive bias in ring gyros: total phase = Sagnac + $\Delta\varphi_{\text{NR}}$

\item Model $\zeta(\lambda)$ as a fitted coefficient vs rotor geometry/speed
\end{itemize}

\textbf{Classical limit:} $\zeta = 0$ (no mass-flow term).

\subsection*{L-M3 --- Cavity Mode Pulling by Static Mass}

\textbf{Statement:} Nearby mass shifts effective optical length in vacuum cavities.

\textbf{Minimal form:}
\begin{equation*}
L_{\text{eff}}(\lambda) = \int n(x, \lambda) \, ds \quad \Rightarrow \quad \delta f / f = - (n - 1) \, L = -n_0(\varphi) L - n_1(\lambda) (\varphi) L
\end{equation*}

\textbf{Immediate use:}
\begin{itemize}
\item Predict frequency drift sign/magnitude when mass approaches a cavity

\item Treat $(n-1)$ as an environmental term in clock/comb models
\end{itemize}

\textbf{Classical limit:} $n_0 = n_1 = 0$ (no pull beyond mechanics/thermal).

\subsection*{L-M4 --- Mass-Dependent Chromatic Lensing}

\textbf{Statement:} Deflection carries a weak $\lambda$-dependence via $n(x, \lambda)$.

\textbf{Minimal thin-deflector form:}
\begin{equation*}
\alpha(\lambda) \propto \nabla_\perp \int (n - 1) \, dz = \left[n_0 + n_1(\lambda)\right] \nabla_\perp \int \varphi \, dz
\end{equation*}

\textbf{Immediate use:}
\begin{itemize}
\item Add achromatic/chromatic split to lensing kernels; fit $n_0, n_1(\lambda)$ jointly with mass maps

\item Propagate to time-delay: $\Delta t(\lambda)$ picks up the same parameters via OPL
\end{itemize}

\textbf{Classical limit:} $n_1(\lambda) = 0$ (achromatic); $n_0 = 0$ restores EM vacuum.

\subsection*{L-G1 --- Closure-Limited Focusing (Route-Capacity Inequality)}

\textbf{Statement:} Independent of diffraction, route/closure budgets cap peak concentration for a passive pupil.

\textbf{Minimal bound (paraxial):}
\begin{equation*}
I_{\max} \leq K \cdot (A/\lambda^2) \cdot S(\text{NA})
\end{equation*}

\textbf{Immediate use:}
\begin{itemize}
\item Ceiling check: compare predicted PSF peaks against the closure bound; expect plateau if exceeded

\item Guide apodizer/stop choices to approach the bound realistically
\end{itemize}

\textbf{Classical limit:} matches the diffraction-limited scaling when $K \cdot S(\text{NA})$ equals the Airy core constant; any extra saturation reflects the VMS cap.

\section*{Drop-In Forms (for modeling tools)}

\subsection*{Rays/OPL:}
\begin{equation*}
\text{OPL}(\lambda) = \int n(x, \lambda) \, ds; \quad t(\lambda) = (1/c) \, \text{OPL}(\lambda); \quad \text{ray tilt} \propto \nabla n(x, \lambda)
\end{equation*}

\subsection*{Interferometer phase:}
\begin{equation*}
\Delta\varphi(\lambda) = (2\pi/\lambda) \int (n - 1) \, ds + \Delta\varphi_{\text{NR}}(\lambda)
\end{equation*}

\section*{Parameter Legend}

\begin{itemize}
\item $\varphi = \Phi/c^2$ : dimensionless gravitational potential along routes

\item $n_0$ : small achromatic coupling to $\varphi$ (dimensionless)

\item $n_1(\lambda)$ : small chromatic coupling to $\varphi$ (dimensionless, weak $\lambda$-dependence)

\item $\zeta(\lambda)$ : small coupling for mass-flow non-reciprocity (dimensionless)

\item $A$ : pupil clear area; NA : numerical aperture; $K, S(\text{NA})$ : geometry factors

\item $\alpha$ : unit bridge to recover SI Coulomb-style forms when desired
\end{itemize}

\section*{Classical / GR Limits (for comparison)}

\begin{itemize}
\item EM vacuum: $n_0 = n_1 = \zeta = 0 \Rightarrow n = 1$; no mass-coupled effects in vacuum.

\item GR lensing/delay: achromatic effective term only $\Rightarrow n_0 \neq 0, n_1 = 0, \zeta = 0$.

\item Diffraction only: closure bound reduces to standard Airy scaling when $K \cdot S(\text{NA})$ matches the Airy constant.
\end{itemize}

\newpage

\section*{VMS Electromagnetism --- Additional Considerations (Concise List of 40)}

\emph{Claim --- how it is not classical --- measurement signature to look for.}

\subsection*{1) Mass-coupled refraction in vacuum}

\textbf{Claim:} Nearby mass changes local slowness $n(x)$, bending rays and adding phase delay.

\textbf{Not classical:} Maxwell vacuum has $n=1$; GR bending is achromatic with fixed coefficient.

\textbf{Signature:} Tiny extra bending and phase delay vs mass proximity; check for weak $\lambda$-dependence.

\subsection*{2) Mass-dependent chromatic lensing}

\textbf{Claim:} Lensing by mass has a small $\lambda$-dependence through $n(\lambda)$.

\textbf{Not classical:} GR lensing in vacuum is achromatic (plasma aside).

\textbf{Signature:} Differential deflection/time delay vs wavelength after de-plasma correction.

\subsection*{3) Mass-induced polarization rotation / birefringence}

\textbf{Claim:} Torsion/shear budgets near mass impose a feeble polarization bias.

\textbf{Not classical:} GR predicts negligible gravitational birefringence; EM vacuum has none.

\textbf{Signature:} Sub-$\mu$rad rotation in crossed-polarizer nulls near dense/moving mass.

\subsection*{4) Boundary mass-loading shifts interference}

\textbf{Claim:} Slit/mask mass distribution perturbs route closure $\rightarrow$ material-dependent phase.

\textbf{Not classical:} Classical two-slit depends on geometry and optical $n$, not substrate density.

\textbf{Signature:} Fringe center shift/envelope skew with identical coatings but different substrates.

\subsection*{5) Mass-flow optical drag (non-reciprocity)}

\textbf{Claim:} Moving/rotating mass induces a one-way phase bias in vacuum loops.

\textbf{Not classical:} Sagnac is rotation-only; Fizeau requires flowing refractive media.

\textbf{Signature:} Non-reciprocal phase vs rotor speed in a ring after isolating vibrations.

\subsection*{6) Vacuum index map around compact masses}

\textbf{Claim:} $n(x)=1+\delta n(\Phi)$ tracks gravitational potential.

\textbf{Not classical:} EM vacuum has no index; GR uses metric (achromatic).

\textbf{Signature:} Shapiro-like delay in evacuated paths grazing a mass; compare coefficient/sign.

\subsection*{7) Mass-gradient tweaks to Fresnel amplitudes}

\textbf{Claim:} Tangential continuity across mass-graded boundaries yields tiny amplitude corrections.

\textbf{Not classical:} Fresnel set purely by EM boundary conditions.

\textbf{Signature:} Angle-dependent ellipsometric micro-offsets with identical optical stacks on different density substrates.

\subsection*{8) Closure-limited upper bound on focusing}

\textbf{Claim:} Geometric closure budget caps peak concentration beyond diffraction.

\textbf{Not classical:} Classical limits are diffraction + material nonlinearities only.

\textbf{Signature:} PSF core saturates vs apodizations at high NA beyond diffraction expectations.

\subsection*{9) Mass-proximity waveguide dispersion shift}

\textbf{Claim:} Guided modes pick extra phase near dense supports even in vacuum regions.

\textbf{Not classical:} Mode indices depend only on dielectric profile.

\textbf{Signature:} Ring-resonator FSR/frequency shift over heavy vs light pedestals (same dielectrics).

\subsection*{10) Achromat residual tied to areal mass}

\textbf{Claim:} First-order achromat holds; a secondary residual scales with element mass.

\textbf{Not classical:} Secondary spectrum classically from higher-order dispersion only.

\textbf{Signature:} Two identical-glass doublets with different densities show repeatable color focus offsets.

\subsection*{11) Étendue with mass gradients}

\textbf{Claim:} Étendue invariant holds or gains minute corrections under mass gradients.

\textbf{Not classical:} Invariant assumed regardless of mass proximity in classical radiometry.

\textbf{Signature:} Throughput vs cone angle near dense blocks shows strict null or tiny deviations.

\subsection*{12) Polarization-dependent gravitational phase (null)}

\textbf{Claim:} Either strict null (consistent with GR) or tiny split from VMS budgets.

\textbf{Not classical:} GR and EM vacuum: null.

\textbf{Signature:} Dual-pol interferometer skimming mass; improved upper bounds even if null.

\subsection*{13) Mass-tuned speckle statistics}

\textbf{Claim:} Route-ensemble weighting alters speckle contrast in mass-graded cavities.

\textbf{Not classical:} Speckle set by coherence/aperture/scatterers only.

\textbf{Signature:} Contrast changes when introducing/removing dense inserts at fixed optics.

\subsection*{14) Near-field evanescent coupling vs mass}

\textbf{Claim:} Evanescent decay picks up a small mass-dependent term via closure budgets.

\textbf{Not classical:} Decay set by dielectric gaps only.

\textbf{Signature:} Prism-coupler attenuation length shifts with a dense body just outside the optical near field.

\subsection*{15) Parametric phase modulation by oscillating mass}

\textbf{Claim:} Oscillating mass modulates closure $\rightarrow$ route phase/frequency sidebands.

\textbf{Not classical:} No EM-only coupling in vacuum.

\textbf{Signature:} PDH cavity sidebands at the mass drive after acoustic/thermal isolation.

\subsection*{16) Mass-gradient Goos-Hänchen/Imbert-Fedorov shifts in vacuum}

\textbf{Claim:} Lateral/vertical beam shifts appear without dielectric interfaces, biased by nearby mass.

\textbf{Not classical:} GH/IF classically require interfaces and material $n$.

\textbf{Signature:} Tiny centroid shifts when a beam grazes a dense slab in vacuum.

\subsection*{17) Ambient mass-jitter phase-noise floor}

\textbf{Claim:} Random mass motion adds route-phase jitter.

\textbf{Not classical:} EM alone: no such floor; noise is technical/quantum.

\textbf{Signature:} Interferometer noise rises with controlled mass motion independent of acoustics.

\subsection*{18) Cavity mode pulling by static mass}

\textbf{Claim:} Nearby mass shifts optical length in vacuum and pulls cavity modes.

\textbf{Not classical:} EM vacuum gives none; GR effect is too tiny for lab scale.

\textbf{Signature:} Stable cavity frequency drifts with a dense block approach (distance law, achromaticity test).

\subsection*{19) Chromatic knife-edge diffraction vs edge mass}

\textbf{Claim:} Fringe phase offset depends on edge mass even with identical geometry/optical $n$.

\textbf{Not classical:} Classical depends on geometry and optical constants only.

\textbf{Signature:} Offset difference for identical edges on heavy vs light mounts/coatings.

\subsection*{20) Mass-biased Sagnac offset}

\textbf{Claim:} Static mass asymmetry biases loop phase (non-reciprocity) in addition to rotation.

\textbf{Not classical:} Sagnac offset is rotation-only classically.

\textbf{Signature:} Phase bias that flips with swapping heavy/light segments around the loop.

\subsection*{21) Vacuum birefringence near mass (null expectation)}

\textbf{Claim:} VMS allows tiny polarization splitting near dense mass.

\textbf{Not classical:} Classical/QED vacuum needs strong B fields; near mass alone is null.

\textbf{Signature:} Sub-$\mu$rad differential phase/rotation near dense rotor/block; set upper bounds.

\subsection*{22) Path-closure hysteresis}

\textbf{Claim:} Route closure shows slow re-settling after mass relocation (memory).

\textbf{Not classical:} EM has no memory once geometry resets.

\textbf{Signature:} Phase lag/relaxation after moving a mass out/in with reproducible time constant.

\subsection*{23) Spontaneous-emission tweak near mass}

\textbf{Claim:} Emitter lifetime shifts slightly with mass proximity via closure budgets.

\textbf{Not classical:} Purcell shifts need dielectric/EM structures, not neutral mass.

\textbf{Signature:} Narrowline emitter lifetime changes with a dense object behind a vacuum gap.

\subsection*{24) Vacuum impedance Z0 micro-shift in potential wells}

\textbf{Claim:} $Z_0$ acquires a minute $\Phi$-dependence.

\textbf{Not classical:} Free-space impedance is constant in classical EM.

\textbf{Signature:} Free-space antenna S-parameters drift near dense object in anechoic chamber.

\subsection*{25) Waveguide cutoff drift from external mass}

\textbf{Claim:} Hollow-guide cutoff $f_c$ shifts with nearby dense rings (external mass).

\textbf{Not classical:} Cutoff set by geometry and $\varepsilon$, $\mu$ only.

\textbf{Signature:} Measure $f_c$ shift when hugging guide with heavy vs light rings.

\subsection*{26) Pulse-front tilt from mass proximity}

\textbf{Claim:} Route-phase skew induces spatiotemporal PFT changes.

\textbf{Not classical:} PFT classically from angular dispersion only.

\textbf{Signature:} Streak camera observes PFT change as mass approaches the path.

\subsection*{27) Mode-dependent chromatic redshift in cavity}

\textbf{Claim:} Different TEM modes/$\lambda$ feel slightly different mass-induced pulls.

\textbf{Not classical:} GR redshift is achromatic; EM vacuum has none.

\textbf{Signature:} Mode/$\lambda$-dependent frequency offsets beyond dispersion/thermal models.

\subsection*{28) Grating non-reciprocity via mount mass}

\textbf{Claim:} $\pm 1$ diffraction orders imbalance tied to mount density.

\textbf{Not classical:} Classically symmetric if geometry/optic constants match.

\textbf{Signature:} Order imbalance flips when swapping heavy/light mounts.

\subsection*{29) Achromat secondary tied to areal mass (repeat of \#10, imaging focus)}

\textbf{Claim:} Residual chromatic focus depends on element mass beyond glass dispersion only.

\textbf{Not classical:} Classical: higher-order dispersion only.

\textbf{Signature:} Color focus offset repeats with density change, same glass and shape.

\subsection*{30) Étendue stress test in mass gradients (repeat/extension of \#11)}

\textbf{Claim:} Either strict invariance or minute corrections under mass gradients.

\textbf{Not classical:} Classical invariant regardless of mass proximity.

\textbf{Signature:} Throughput vs cone angle near dense block: confirm null or bound deviations.

\subsection*{31) Mass-dependent speckle statistics (extension of \#13)}

\textbf{Claim:} Route weighting in multi-pass cavities alters speckle contrast.

\textbf{Not classical:} Classical speckle from aperture/coherence/scatter only.

\textbf{Signature:} Contrast shifts when dense insert is moved among passes.

\subsection*{32) Near-field evanescent coupling vs mass (extension of \#14)}

\textbf{Claim:} Decay length picks up mass term via closure budgets.

\textbf{Not classical:} Classical decay set by dielectric gap only.

\textbf{Signature:} Coupling length changes with dense body just outside near field.

\subsection*{33) Parametric sidebands from oscillating mass (extension of \#15)}

\textbf{Claim:} Mass motion imposes sidebands through route modulation in vacuum.

\textbf{Not classical:} No EM-only drive in vacuum.

\textbf{Signature:} Sidebands at drive frequency in PDH after ruling out acoustics.

\subsection*{34) Handedness bias near rotating mass}

\textbf{Claim:} RCP/LCP accumulate slightly different phases near a flywheel.

\textbf{Not classical:} No such effect in EM vacuum; GR frame dragging is negligible in lab.

\textbf{Signature:} Differential phase shift between RCP/LCP vs rotor speed.

\subsection*{35) Fiber delay vs altitude/potential beyond GR coefficient}

\textbf{Claim:} Chromatic tweak to gravitational delay in fiber links.

\textbf{Not classical:} GR gives fixed achromatic coefficient; chromatic residuals are dispersion.

\textbf{Signature:} Dual-$\lambda$ time transfer over height baseline shows residual beyond fiber dispersion model.

\subsection*{36) Aperture-stop mass loading on PSF/MTF}

\textbf{Claim:} Stop mass biases route cone beyond geometry alone.

\textbf{Not classical:} Classically only geometry matters (given rigid mechanics).

\textbf{Signature:} Marginal PSF/MTF change at wide aperture with heavy vs light stops.

\subsection*{37) E-B partition bias near mass}

\textbf{Claim:} Plane-wave E/B phase/ratio slightly skewed by mass proximity.

\textbf{Not classical:} Free-space E/B ratio fixed in classical EM.

\textbf{Signature:} Calibrated E and B probes detect tiny phase/ratio drift near dense object.

\subsection*{38) RF-optical cross-phase via shared closure}

\textbf{Claim:} RF and optical interferometers co-vary through common route budgets.

\textbf{Not classical:} Domains independent in classical EM.

\textbf{Signature:} Correlated phase drifts in colocated RF/optical loops when mass moves.

\subsection*{39) Mass-graded thin-film Fresnel micro-offsets}

\textbf{Claim:} Fresnel $\Psi$, $\Delta$ pick up angle-dependent micro-offsets with substrate density.

\textbf{Not classical:} Classical Fresnel depends only on optical $n,k$ of layers.

\textbf{Signature:} Ellipsometry shows tiny, systematic offsets for heavy vs light substrates.

\subsection*{40) Null-boosting checks (global)}

\textbf{Claim:} Many above should be strict nulls under EM+GR; strong bounds still carve parameter space.

\textbf{Not classical:} Classically nulls are expected; any non-zero is new.

\textbf{Signature:} Publish tight upper limits even if no detection; parameterize ($n_0, n_1, \zeta$).

\end{document}
