The Born Rule as a Closed Record Pair: Measurement, Objectivity, and the Arrow of Time in a Quantum-Error-Correcting Substrate

Abstract

A measurement is not primitive — it is the substrate recording a syndrome. The current canon now closes the Born rule inside the accepted complex-QEC substrate, two complementary ways: repeatable syndrome readout gives orthogonal, non-contextual projectors, so Gleason-type uniqueness fixes pᵢ = Tr(ρPᵢ); and the Naimark/Stinespring record map makes measurement an isometric copying of syndrome facts whose closed forward/backward history leaves the surviving diagonal |A|². What remains open is no longer the Born measure itself but the deeper reconstruction floor — why nature is a complex, locally tomographic, record-writing QEC system at all.

Keywords

How to cite

Elliman, D. (2026). The Born Rule as a Closed Record Pair: Measurement, Objectivity, and the Arrow of Time in a Quantum-Error-Correcting Substrate. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.20875799

@techreport{elliman2026bornrule,
  author      = {Elliman, David},
  title       = {The Born Rule as a Closed Record Pair: Measurement, Objectivity, and the Arrow of Time in a Quantum-Error-Correcting Substrate},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.20875799},
  url         = {https://neusym.ai/papers/born_rule}
}