Entanglement, Measurement, and Information in a Topological Vacuum

Abstract

This is the sixth paper in a series developing a topological-medium frameworkfor physics. It is built on the two axioms and one initial condition of theearlier papers and adds none. The paper argues that the simultaneity of entanglement is not an additionalpostulate but a consequence of incompressibility. The compressed degree offreedom is barred from the radiative sector, leaving a single light cone andso permitting Lorentz covariance; the same degree of freedom is transferred toa constraint sector governed by an elliptic equation, which suppliesinstantaneity. One axiom, two consequences — and the worry that a rigid mediummust spoil covariance turns out to run the other way, since rigidity removesthe second light cone that would otherwise appear. The instantaneous channelcarries neither energy nor signal, for two independent reasons that arecomputed rather than stipulated. A closure event triggers both the collapse of the shared mode and the landingof a detection. From it, the discreteness of detection follows fromwinding-number integrality with no new assumption, and the Born rule follows atargument level from whole-quantum delivery together with ledger consistency,with the exponent an output of the energy density rather than an input. Thecircularity self-check is written out explicitly, since circularity is thestandard failure of derivations of this kind. The correlation tables — the full-amplitude cosine, the Mermin signs, thegeneral-angle GHZ correlations for N = 3, 4, 5, and the W-state tables in boththe occupation and the transverse basis — are reproduced by onesequential-collapse rule which was not altered between them. All of thesetargets were known in advance and are marked as correspondence-levelthroughout. An appendix carries one derivation end to end, including theattempt that failed first and why. Finally, the criterion that separates what can be equipartitioned from whatcannot is used to sort information into three layers by difficulty ofthermalisation, placing decoherence and topological protection as two cases ofone mechanism rather than two mechanisms. Relation to existing work is stated explicitly, including where this work isnot first: decoherence as the loss of correlational information is the standardpicture, and a derivation of the Born rule by a quite different route alreadyexists and has been tested. What is owed is listed at the end with itsstrength, and the two largest items are identified as one wall seen from twosides. All new derivations and numerical evaluations were AI-proposed andauthor-adjudicated, consistent with the disclosure practice of the earlierpapers in this series.