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May 6, 20260 citationsOpen Access

Ambient Schur Landing and Observable Classification in Q5 Transport

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CHCraig Edwin Holdway

Abstract

This Theorem derives the ambient Schur landing of complement-sector feedback and establishes its complete observable classification. The complement block of admissible form Hcc = aI + bJ (J² = I) is invertible for a² ≠ b² with Hcc⁻¹ = (aI − bJ) / (a² − b²). The Schur correction ΔH = Hᵣc·Hcc⁻¹·Hcr decomposes into: ΔH = (a/ (a²−b²) ) ·Δ₀ − (b/ (a²−b²) ) ·ΔJ where Δ₀ = Hᵣc·Hcr and ΔJ = Hᵣc·J·Hcr. Five lemmas establish the landing structure. The helicity-twisted term satisfies Pₛc·ΔJ·Pₛc = 0, J is odd under scalar projection, so the twisted feedback contributes nothing to the scalar channel. The transverse projection of ΔJ lands in spanI, σᵦ, σₓ, J anticommutes with R = iσᵧ, so the twisted component has no R-component and lies entirely in the symmetric transverse sector. A critical bridge identifies ΔJ as the operator-level origin of the T30 spectral deformation: both the Schur denominator (a² − b²) and the T30 discriminant (p² − 4a²) arise as discriminants of two-level systems with identical admissible commutant structure. Four observable consequences: scalar channel protected (μ invariant) ; helicity-twisted correction annihilated by extraction functional L before readout; T30 spectral deformation identified as Schur correction; sole observable manifestation is spectral redistribution between channels at p and ω = √ (p² − 4a²). Two independent protection mechanisms operate: local null-class annihilation (scalar observables) and global mirror-orbit cancellation via T38 (embedded observables). Status: Commutant inversion, Schur decomposition, scalar nullity given J odd under scalar projection, and transverse symmetric landing given anticommutation of J with R, all solid by direct computation. T30 spectral bridge structural, identification of denominator with p² − 4a² is a leading-order structural identification, not a derived equality. Scalar invariance and λₑff = 1 solid given lemmas and T38. Orbit preservation solid via T34–T35. Admissible form Hcc = aI + bJ is a structural assumption; derivation from the full ambient T12/T16 block structure is the primary remaining open step. Dependencies: T12, T16, T26, T29, T30, T34, T35, T37, T38, T54.

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Craig Edwin Holdway (2026) studied this question.

synapsesocial.com/papers/69fa989404f884e66b53257fhttps://doi.org/10.5281/zenodo.20017638
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