Reciprocal Internal Complementarity and the Conditional Construction of Lorentzian Twistor Incidence: Typed Carriers, Positive Records, and Faithful Transport

Abstract

We distinguish the construction of an incidence geometry from its realization by operations on positive records. An admitted two-complex-dimensional carrier, an independent anti-dual summand and a specified cross-evaluation form give a signature-$(2,2)$ Hermitian space. Its transverse totally null two-planes are labelled by Hermitian $2\times2$ matrices, with their intersections governed by the Lorentzian determinant. A separately positive readout metric admits rank-two records from which the incidence label can be reconstructed. We prove that faithful support transport for six specified plane records by one common completely positive operation forces every Kraus amplitude to be proportional to the desired incidence isometry. Exact deterministic transport in this fixed encoding is therefore restricted to the positive-unitary incidence subgroup; noncompact transformations admit bounded success operations with retained failure outcomes. We then separate exact certification of a specified unitary from unrestricted tomography. As a code-subspace application of an established connected-spanning input criterion, complete restrictions on two nonorthogonal spanning codes identify the stipulated unitary channel. Yet all null-supported probes span only a fifteen-dimensional operator hyperplane and cannot distinguish an explicit pair of different channels. Finite-label recovery additionally requires output transversality to the chosen affine chart. The results are conditional on the carrier, forms, preparation, calibration and common-process model. They do not derive a physical record apparatus, primitive spacetime or gravitational dynamics, and do not prohibit passive Lorentz covariance or other encodings.

Where it sits in the release

RIC-TI is Wave B’s incidence-and-operations paper. It separates preservation of abstract Lorentzian incidence from deterministic implementation on positive records. Its standard twistor ingredients are imports, and the result does not derive a physical apparatus, primitive spacetime, or gravitational dynamics.

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