Upper Limit for the Anisotropy of Inertial Mass

The selected-model route supplies a distinct near/far galactic orientation pair, the typed p. 342 P2 energy-shift formula, the orientation-dependent atomic signature, and the nuclear triplet-or-broadening signature. The atomic and nuclear experiments each retain the same distinct half-sidereal orientation change, depend on that model, but remain logically independent. Existing oxygen data supplies a third comparison. Only the qualified-combination route compares the distinct bounds, applies the exclusion bridge, and retains the untested scope.

The chlorine route retains the transition, distinct sidereal orientation change, Atomichron reference, proton reference, stabilized magnetic field, scan duration, and finite experimental error. Before the conversion, SelectedAtomicP2EnergyFormulaAt binds the p. 342 scalar readout to the selected P2 model, chlorine transition, and near-galactic orientation. Its SourceFormulaAt exposes both P2(cos theta) = (3 cos(theta)^2 - 1)/2 and the binding-energy-shift equality instead of trusting a name like orientation dependence. PrintedAtomicReadoutAt then binds the selected objects to the paper's 22-degree and 104-degree orientations over twelve hours, about 9190 Mc/sec in 4730 gauss, a 30 kc/sec error, and the reported atomic 10^-10 ratio. The observed absence of variation does not itself contain an anisotropy bound: the conversion also requires the paper's model of chlorine as an outer-shell hole moving in a Coulomb potential.

OxygenComparisonAssessment records a separate transition-pair comparison and its model-dependent 10^-10 bound; PrintedOxygenReadoutAt keeps that number in the oxygen route rather than borrowing it from chlorine.

The nuclear route retains lithium-7 spin three-halves, the same distinct sidereal orientation change, both Atomichron and proton reference controls, proton-based magnetic-field stabilization, the single observed line, observed and expected widths, and the finite excess-width limit. The nuclear setup requires its own frequency-reference inputs; it does not borrow them from a successful atomic bound. PrintedNuclearReadoutAt binds these selected objects to about 4700 gauss, a 4.3-ppm observed line, an expected 5.0 plus-or-minus 1 ppm instrumental width, at most 8 cycles/sec residual broadening, the reported 10^-20 ratio, and the quoted 3 x 10^-10 galactic estimate. NuclearLineSignatureCalculation first uses those facts to establish tripletOrBroadeningExcludedAboveAt for the selected model. NuclearBoundCalculation is a later conversion using the paper's idealization of lithium-7 as one p-three-halves proton in a central nuclear potential, not a synonym for the line observation.

The reference controls now assert zero selected frequency shift at every represented orientation, rather than two arbitrary insensitivity predicates. A separate inspectable reconstruction, RankTwoNuclearSpectrum, uses first-order diagonal energies E_m/h = w*m + q*(3*m^2 - j*(j+1)). Its spin-half gap is w; its spin-three-halves gaps are w-6q, w, and w+6q, all positive exactly when 6*|q| < w. This is a stated model, not a formula quoted from the letter or a nuclear matrix-element calculation. The proton control follows only after an explicit identification with that response. Cesium dynamics, field stabilization, and the instrumental conversion of unresolved splitting to line width remain separate. Distinct calculated gaps must not be confused with resolved observed peaks. The frequency-reference review exposes these distinctions and their full Lean dependencies.

The combined assessment includes the strictly stronger, unequal nuclear bound and selected-model exclusion. A relation merely named boundStrongerThan cannot pass when the retained nuclear and atomic bounds are equal. Separately, scoped_assessment_retains_numeric_sensitivity_hierarchy checks the stored source numbers themselves: the 10^-20 nuclear ratio is below the 10^-10 atomic ratio, which is below the quoted 3 x 10^-10 galactic estimate. The assessment also includes the negations of exact-isotropy establishment, testing of other angular dependences, and testing of arbitrary directions, together with the proposed sensitivity improvement. scoped_assessment_retains_selected_p2_scope_and_open_extensions exposes that boundary directly.

Model support reaches the Machian theory only through model_support_reaches_theory_only_with_explicit_transfer. No local Lorentz invariance or equivalence-principle theorem is asserted.