Joined October 2012
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Sharing a thread on the finite mechanism I’d most like checked in The Dyadic Fabric:
four-lift/two-survivor law → cylinder certification → least-representative escape.
Especially interested in the realized-lift assertion and Section 7→8 quotient passage.
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I am sharing one finite mechanism from The Dyadic Fabric, a manuscript on dyadic residue-pair refinement for the odd perfect number problem:
four-lift/two-survivor law → cylinder certification → least-representative escape.
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I am sharing one finite mechanism from The Dyadic Fabric, a manuscript on dyadic residue-pair refinement for the odd perfect number problem:
four-lift/two-survivor law → cylinder certification → least-representative escape.
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Off-perfect cylinder certification forces least-representative escape. A certified least representative cannot carry its same-first-coordinate perfect-compatible realization; if that realization occurs, it must occur beyond the current modulus.
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Technical feedback welcome on the realized-lift assertion, the Section 7-to-Section 8 quotient passage, and terminology for formal, realized, and perfect-compatible lifts.
doi.org/10.5281/zenodo.20510…
#NumberTheory #OddPerfectNumbers
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Jun 3
Updated v2 of The Dyadic Fabric is now on Zenodo.
The paper studies the odd perfect number problem via dyadic residue pairs. After the Euler gate, the finite post-gate cylinder law is:
|G_{n 1}| = 4|G_n|, |J_{n 1}| = 2|J_n|.
The main result is least-representative escape: once a cylinder is certified off-perfect, any same-first-coordinate perfect-compatible realization must occur beyond the current least representative.
I’d value narrow feedback on the realized-lift assertion and the Section 7–8 passage. #NumberTheory #OddPerfectNumbers
doi.org/10.5281/zenodo.20510…
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Apr 20
On Odd Perfect Numbers - The Dyadic Fabric:
A Deterministic Refinement and Elimination Framework
doi.org/10.5281/zenodo.19656…
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25 Apr 2024
On Odd Perfect Numbers
academia.edu/118018739/Guela…
#perfectnumbers #oddperfectnumbers #numbertheory
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26 Mar 2024
If you love math and thinking outside the box, I hope you will enjoy my take on odd perfect numbers.
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In this thread I present my attempt to prove they cannot be perfect. It is a strange document, but if you give it a chance I believe you will see the merit.
#oddperfectnumbers #perfectnumbers
I posted the original version in October of last year. I added an abstract and appendix as well as fixed a few mistakes and added some extra language.
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