Information Transfer in the Trojan Universality Class V: A Transfer Theorem and a Synthesis of Five Tests

This paper states and proves the common result that unifies the four preceding studies. Its master transfer theorem asserts that any two members of the Trojan universality class that share the same gate data—identical resonance vector and Krein signatures—exchange every observable of four classes through a fixed packet consisting of two content numbers, two units, and the protocol parameters expressed in scaled form. The prediction error is bounded by a term proportional to the mismatch of those content numbers plus an amplitude term that vanishes like the square root of the action, or linearly with the action once first-order normal-form coordinates are used. Content observables transfer with an error that does not grow in time; most invariant curves persist for all time on a set of nearly full measure; single trajectories are controlled only on finite scaled windows. Two converse theorems establish that nothing less will do. The pair of content numbers is complete: any conjugacy that preserves the exchange coordinate and the scaled time recovers the content up to a single reflection. It is also minimal: no continuous function of one variable can replace both numbers. The gate itself is necessary: across a signature mismatch only the onset of instability transfers; the size of the subsequent excursion does not. The evidence of the entire series is then set against these statements. A pre-registered blind test, performed on a Hénon–Heiles-type galactic potential never used before, predicted the exchange curve from a frozen nonlinear circuit whose clock was nearly four times faster, achieving a root-mean-square error of roughly five thousandths against more than six tenths for transfer in raw detuning. A deliberate sweep of content mismatch produced an error that grew exactly as the content term of the theorem predicts, with a floor set by amplitude. Across the seven successful transfer tests the logarithmic gain over raw-unit baselines ranged from roughly four to nearly nine bits, and the single transfer predicted to fail—across a mismatched gate—did fail. Within the stated hypotheses of membership, equal gates, small amplitude, two degrees of freedom and one resonance, the transferability claim is thereby a theorem.