Theory of Reality / Manuscript

Rotational Complexity of Matrices — Theory and Experimental Results

Reference19 Sept 2026 · saved

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01 / THE QUESTION

Editorial guide

Can any finite matrix be rebuilt from rotating circles (Fourier rotors), and does the number of rotors needed measure pattern or randomness?

02 / WHAT THE RECORD SAYS

Source passage

Every finite real matrix can be reconstructed exactly by a finite collection of these rotors.

03 / LIMITS & OPEN POINTS

Source passage

The rank-one and impulse controls are deliberately simple in other languages but expensive in the Fourier language.

04 / THE NEXT QUESTION

Source passage

The next scientifically meaningful quantity is therefore a two-part description length:

05 / CHECKS IN THE RECORD

Source passage

- Matrix size: 64 × 64 (4,096 values). - Available conjugate rotor groups: 2,050. - Energy targets: 50%, 90%, 95%, 99%, and 99.9%. - Controls: constant, one sinusoid, four sinusoids, checkerboard, and square-wave stripes. - Geometry: Gaussian blob, binary disk, and binary square. - Counterexamples: random rank-one outer product and single spatial impulse. - Randomness: Gaussian noise, random signs, and a short-rule 32-bit LCG. - Random trials: 40 seeds for each distribution at 16², 32², 64², and 128². - Comparator: SVD components needed for the same retained-energy targets.

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Access: Public
Dates declared in the record: Not recorded
Project basis: Editorial topic association
Origin: d0re research collection (snapshot 1 October 2026)
Original path: /THEORY_AND_RESULTS.md
Authorship basis: Collection attribution; original record retains its own credits
Title basis: From the source
Date: 19 Sept 2026 · saved
Status basis: r-350b255f3242 is a standalone lab report that states its own boundary: the idea succeeds as Fourier complexity 'and fails if interpreted as basis-independent complexity or as proof of true randomness.'
Size: 8,242 bytes
Word count: 1,323 words
SHA-256 of indexed source: 350b255f32427d7791569c6055722f4ab7bf1ba8bfaa8c5fc7875380c766eb8d

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Rotational Complexity of Matrices — Theory and Experimental Results
2026-09-19
d0re research record r-350b255f3242
https://www.d0re.com/library/records/r-350b255f3242.html
Authorship basis: Collection attribution; original record retains its own credits
Date basis: saved
Source SHA-256: 350b255f32427d7791569c6055722f4ab7bf1ba8bfaa8c5fc7875380c766eb8d