Pair-Calibrated Second-Magnus Observability

Abstract

Pair-adapted samples recover four times the finite holonomy energy.

Theorem 1.1 (Exact calibrated reverse observability).

$$(\mathrm{Injective}\left(omega\right)\wedge \forall p,C\left(p,p\right)=0)\Rightarrow \mathrm{Ecal}\left(omega,C\right)=4\times \mathrm{Ehol}\left(C\right)$$

Proof. Machine-checked in Lean as D5/S3/Observer/AgencyHolonomy/PairCalibratedSecondMagnusObservability.pair_calibrated_second_magnus_energy_eq_four_holonomy (✓ std3). ∎

Source. Repository-derived.

Commentary.

For injective frequencies and a curvature field with zero diagonal, each ordered pair is sampled at its own half-turn time separation.

The resulting calibrated second-Magnus energy is exactly four times the finite holonomy energy. The clocks remain pair dependent, so a family-wide common-window frame bound is still separate.

References

• Truth anchor: D5/S3/Observer/AgencyHolonomy/PairCalibratedSecondMagnusObservability.pair_calibrated_second_magnus_energy_eq_four_holonomy
• Dependency: D5/S3/Observer/AgencyHolonomy/FiniteHolonomyEnergy
• Dependency: D5/S3/Observer/AgencyHolonomy/SecondMagnusSwapCurvature