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Equation 105 · A Horizon Is a Toll Booth, Not a Loophole

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N⊥[Γ]N_\perp[\Gamma]

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N⊥N_\perp

Symbol N_perp

NpN_perp is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Γ\Gamma

Symbol Gamma

Gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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What the article says around this equation

Collect the ledger. N⊥N_\perp[Γ\Gamma] , the cumulative orthogonalization count, is an exact and dimensionless consequence of the Levitin-Toffoli bound integrated over proper time, valid without approximation in the quasi-static driving regime and bounded above by the sharper Deffner-Lutz result outside it — that piece is DERIVED. The identity ElocE_{\rm loc}\,dτ\tau=E∞E_\infty\,dt is an exact consequence of the definition of Killing energy in a static spacetime, proven here for the specific case of N⊥N_\perp[Γ\Gamma] rather than asserted by analogy — also DERIVED. That no energy-convention bookkeeping can extract a net gain from this identity is a direct corollary, not an assumption.

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