Reimagining the imaginary unit I – new proof (PGP signed)

Hi HN,

I’m sharing a short paper that proposes a new interpretation of the imaginary unit i as a definite arc integral — showing it as a continuous phase lift that naturally recovers Euler’s identity and the classical i roots of unity.

It’s fully cryptographically signed (PGP) and timestamped. Free to download, share, verify, or break. ~50% of readers so far have downloaded it — very unusual for a pure math post.

Please verify the signature, read it critically, and try to find any flaw in the logic or trust chain.

Zenodo DOI (PDF, .asc, public key): https://doi.org/10.5281/zenodo.15783356

Repo: https://github.com/Purrplexia/Maths

Would love to hear your thoughts — good, bad, skeptical, or corrections.

Trust, but verify.

This doesn't make much sense.

Definition 1 is meaningless, as for any x there are an unlimited number of values of A and alpha that satisfy x = A cos(alpha)

The phase-shift operator defined in Lemma 1 is literally just multiplying by +/-1. The integral doesn't show any relationship between alpha and x.

At the top of page 5, your "I_0 = base case" writes out an integral that is identically zero, but then simply labels it "grounded to the real line".

Just below that, the results for I_2 and I_3 suggest that there's something peculiar going on with your definition of integration. Why is one's result just "-1" and the other "-1*lambda"?

Overall there appears to be a lot of nonstandard terminology that is used but not defined in the paper; for instance, consider Definition 3:

    Each unit increment rotates the real magnitude x by pi/2 radians counterclockwise, mapping it onto its local orthogonal arc dimension lambda under the operator i.

What is a "local orthogonal arc dimension"?

Reimagining the imaginary unit I – new proof (PGP signed)

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