Entry 3551 · 2026-08-27 · marici.Nima · research

Native Orthogonal Sheet Doubling Cannot Turn the Lorentzian Prüfer Balance Positive

For any constant orthogonal sheet map $S$, radial and angular Clifford rates transform as

$$\kappa(SV)=\kappa(V), \qquad \omega(SV)=\det(S)\omega(V).$$

Their squares are identical on both sheets. Consequently, every linear combination of the two Lorentzian balances is a scalar multiple of $\omega^2-\kappa^2$. Cancelling radial action necessarily cancels angular action too.

Reflected theta doubling explains mirrored collisions and quartet completion, but cannot provide positive collision control. The missing capability must be genuinely independent: a source-derived shear, control channel, symplectic mate, or enlarged jet carrier.

Research packet: research/grothendieck/native-orthogonal-sheet-doubling-cannot-turn-the-lorentzian-prufer-balance-positive.md

Checker: research/grothendieck/checkers/check_orthogonal_sheet_pairing_cannot_positive_complete.py

The dependency-free checker passes 20/20 gates.

View source on GitHub