What a qubit screen can—and cannot—tell an observer

Kenan Oggad, James F. Glazebrook and Chris Fields present the work in a preprint submitted to arXiv on November 8, 2026. The supplied record does not establish peer review. The study develops mathematical proofs within a proposed holographic-screen framework; it reports no laboratory experiment or observational test.

A screen without assigned positions

The screen is an array of noninteracting qubits through which two separable systems exchange information. Each qubit has an observable with possible outcomes of plus or minus one. The interaction adds these observables together, giving each a weight. The authors call that list of weights the screen’s “profile.” No spatial positions are assigned to the qubits.

Under explicit assumptions—nonnegative weights, an overall interaction scale set to one, and exactly one independent state for every joint outcome—the authors derive the spectrum, or list of possible interaction levels. Measured relative to the lowest level, each level equals twice the sum of the weights in some subset of qubits. Different subsets can produce the same level, and those repetitions matter.

This makes every reading based solely on the spectrum a function of the profile. Changing measurement axes or relabelling qubits leaves that spectrum unchanged. Combining qubits into groups, however, can change it.

For example, four equally weighted qubits can be grouped into two equal pairs or into groups of one and three. Adding weights within each group produces different two-qubit spectra. The underlying weights are unchanged; the grouping supplies the difference.

Why a dimension near two needs care

The researchers examine a mathematical diffusion probe that extracts a “running spectral dimension” from how contributions from different spectral levels decay with a scale parameter. This is a calculated diagnostic, not a measurement of ordinary spatial dimensions.

With N equally weighted qubits whose weights sum to one, the running dimension at scale parameter t = 1 is below two, but by no more than 2/N. Yet its maximum across scales grows in proportion to N. A value approaching two at one scale therefore does not impose a universal two-dimensional limit.

Geometrically decreasing weights give another result. Counting spectral levels at selected thresholds yields a power-law exponent that the authors translate, by an explicit convention, into a plateau dimension. Adjusting the ratio between successive weights can produce any positive plateau value.

That counting result is not a proof of a perfectly flat diffusion curve for every ratio. For the special case where each weight halves, the authors separately prove that the actual running dimension stays below two and approaches it across an increasingly broad scale interval as qubits are added. Every finite screen still has a finite spectrum, not an exact power law extending indefinitely toward zero.

When grouped readings resemble a simpler screen

An observer in the model reads sets of qubits by multiplying their outcomes. This records parity: an odd number of minus signs gives minus one, while an even number gives plus one. Sets may overlap.

The central question is whether the resulting levels, including repetitions, match those of a screen with one effective weight per set. The authors call this “carrying a profile,” a specific mathematical property rather than a general test of measurement accuracy.

Their criterion uses each qubit’s membership pattern: the list of sets containing it. A readout carries a profile for every weighting exactly when its distinct, nonzero membership patterns are linearly independent using binary arithmetic, where two copies cancel.

Such a readout can be reversibly recoded into disjoint groups of the qubits it covers. Overlap alone therefore does not make it fail. With dependent patterns, successful weightings require special linear relationships. If an odd number of distinct patterns cancel together, success is impossible when all their class weights are positive.

Mathematical extensions, not observed spacetime

The paper also considers refinement continuing without end. Its limiting boundary is a profinite set: a compact, totally disconnected space. Consistent positive weights define a distance that distinguishes different readings settled at finite stages. Crucially, this distance compares functions representing readings, not points in physical space.

Further applications provide contextuality arguments, an inverse-square-root leading correction to the pole-to-pole distance in a specified fuzzy-sphere model, and constraints on an entanglement-inspired network. In that network, weight-one pairs must be disjoint. These are results within defined mathematical models, not observations of wormholes.

The main conclusion is conditional but concrete: spectral readings depend on the weighting profile, and grouped readings also depend on the observer’s chosen sets. Neither a dimension-like number nor a distance between readings, by itself, establishes an underlying spacetime geometry.