Topological Aliasing and Holographic Readout

In the paper's words

URL: https://papers.qnfo.org/papers/topological-aliasing-and-holographic-readout/ Date: 2026-03-23 Version: 1.0 The foundation of modern physical theories relies heavily on the continuous nature of real numbers. This mathematical framework assumes that space and time can be divided infinitely without encountering structural changes. Physicists adopted this continuous metric during the development of classical mechanics to model smooth trajectories.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. Standard metrics calculate separation using the familiar Pythagorean approach extended to multiple dimensions.

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2. They calculate instantaneous rates of change by taking limits as distances approach zero.

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3. An alternative approach suggests that the discrete phenomena are fundamental, and the smoothness is an illusion.

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4. When observational scales approach fundamental limits, the mathematical tools of classical physics lose their predictive power.

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What would falsify it

1. Historical reliance on continuous mathematics originated from observable macroscopic phenomena.

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2. Quantum mechanics developed as a hybrid system utilizing continuous probability waves to predict discrete outcomes.

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3. This termination, known as collapse, forces the system into a single, discrete observable state.

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Where the claim stops

1. This mathematical framework assumes that space and time can be divided infinitely without encountering structural changes.

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2. This extrapolation embedded the assumption of infinite divisibility deep into the core of theoretical physics.

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3. The transition to atomic physics in the twentieth century challenged these continuous assumptions.

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Where to read

1. A22 words · 1 min
2. 1: The4,504 words · 20 min
3. 2: Foundations of3,320 words · 14 min
4. 3: The Mechanics of4,192 words · 18 min
5. 4: Holographic4,603 words · 20 min
6. 5: Emergent4,572 words · 20 min
7. 6: Reinterpreting the3,956 words · 17 min
8. 7: Empirical4,080 words · 18 min