{"id":7939,"date":"2026-06-04T14:01:23","date_gmt":"2026-06-04T21:01:23","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=7939"},"modified":"2026-06-23T11:08:18","modified_gmt":"2026-06-23T18:08:18","slug":"comparing-the-new-and-older-forms-of-my-e8-to-h4-folding-matrices","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2026\/06\/04\/comparing-the-new-and-older-forms-of-my-e8-to-h4-folding-matrices\/","title":{"rendered":"Comparing the new and older forms of my E8 to H4 folding matrices"},"content":{"rendered":"\n

If anyone is using my E8 to H4 folding matrix in their research, this post provides a bit of context from the original form (2012-2014) as it was improved to the current form. Drop me an email if you are using my work or have questions, or find errors, etc.<\/p>\n\n\n\n

See here<\/a> (Baez), here<\/a> (Castro-Perelman), here<\/a> (Schmidt), here <\/a> (Ruen on WP E8 Polytope D4-E6 “Mox” projections<\/a>) for properly cited examples.<\/p>\n\n\n\n

I am working with a few who are using my work on cryptography, quantum computing, and computation optimization, but they have yet to post or publish results. <\/p>\n\n\n\n

Of course, many authors may or may not be aware of their use of my prior art (so it goes without citation) e.g. here<\/a> (Nielsen) using the fine structure constant \u03b1-n<\/sup> as a hyper-dimensional geometric nD scaling factor for the fundamental constants, such as my definition of a new Unit of Measure (UoM) distinct from Natural Units from 1998-2001<\/a>).<\/p>\n\n\n\n

The image below is also available as a Mathematica notebook (NB<\/a>) or PDF<\/a>. Click the PNG image for the SVG<\/a> version.<\/p>\n\n\n\n

The first part reviews the current Hermitian, centrosymmetric, traceless (Tr=0), and volume preserving (Det = 1) form of the folding matrix (U). <\/p>\n\n\n\n

The last part reviews the traceless Hermitian unitary matrix (uU) of determinant 1 (i.e. A7=SU(8)) with characteristic polynomial |coefficients| of the 5th row of the Pascal triangle (1,4,6,4,1}. This matrix has the same characteristic polynomial as that of the 3-Qubit Hadamard matrix. Both are related to QM Hadamard, CNOT and SWAP gates and Pauli matrices from which it, cmU, and U are constructed.<\/p>\n\n\n\n

Below that is another matrix analysis of the 6 8×8 Dirac matrices (i.e. DiracMatrix[#, Dimension -> 6]&\/@Range@6) with the Identity and +\/- Traceless Identity matrices prepended. These have similar properties to uU with the addition of being (skew)Hamiltonian matrices.<\/p>\n\n\n

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Comparing E8 to H4 folding matrix versions<\/figcaption><\/figure>\n<\/div>\n\n\n
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Matrix Analysis of Identity and Dirac Matrices<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

If anyone is using my E8 to H4 folding matrix in their research, this post provides a bit of context from the original form (2012-2014) as it was improved to the current form. Drop me an email if you are using my work or have questions, or find errors, etc. See here (Baez), here (Castro-Perelman), … Continue reading Comparing the new and older forms of my E8 to H4 folding matrices<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[4,34,14,16],"class_list":["post-7939","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-h4","tag-math","tag-physics"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t