Good morning!

I think your observation about the “load-bearing point” is valid, and it is probably the most important aspect to focus on.

You are right that the omega sequence concentrates much of the result: the angular value, the reordering, and the resolution of the letters all pass through that segment. If that point does not hold, the entire structure weakens significantly.

Where I see the difference is in what that concentration implies.

In many structured systems, the most anomalous or information-dense part is precisely where one would expect the signal to be. The fact that multiple constraints converge in a single segment does not automatically make it arbitrary; it may indicate that this is the point where the transformation is concentrated.

The question, for me, is not whether the result depends on that point, but whether the transformations applied there are consistent with the rules of the method, limited in number, and not freely adjustable once defined.

If these conditions do not hold, then your criticism is entirely valid. If they do hold, then the concentration becomes a structural feature rather than a weakness.

On X and Y, to clarify: they are not incomplete or separate outputs, but raw results that are part of the same process. It is precisely through the reordering of the omega sequence that these elements find their place within the overall structure, contributing to the construction of the result and, in a consistent way, also to the possible signature of the author. In this sense, they are not unresolved elements, but intermediate steps within a single transformation.

I understand the purpose of the row-swapping proposal, but there is an important distinction: this is not a neutral variation, because it alters the positional structure defined by the author. In my approach, order is part of the system, not an accessory feature.

That said, I did consider this modification, and it is interesting that the main result does not change: the structure leading to HERCULES and the angular value remain the same. What changes is only a secondary level of the result, related to the possible author signature.

This, in my view, is significant: it suggests that the core of the method is not fragile under this type of variation, while some components are more sensitive to arrangement.

The question then becomes whether it is more appropriate to test the method by altering the original structure, or to evaluate it within the configuration as defined by the author.

In this context, I tend to give more weight to the latter.

Posted by: @lendor-77

↑

I would also like to add an observation that I recently came across while watching a video by David Oranchak about the Z32.

In the video it is noted that, on the envelope associated with the July 26, 1970 letter, the abbreviation “Calif.” (California) appears to have been written in an unusual way, slightly rearranged as “Claif.”

Hello @lendor.77.

Although something of a side point to the main ideas of your thread, I am curious about you bringing this observation up, because I have to admit I had not noticed it before. I would, therefore, like to offer some thoughts about it, in relation to the Z32 cipher and its possible solution, but at the same time being cautious not to hijack your thread.

The envelope in question is, I see, this one:

And, there it is: “Claif.” instead of “Calif.”

For some while now, I have been struck by a couple of apparently non-random similarities between the Z13 and the Z32 ciphers. And the route to these is to begin with a comparison of the symbols that they have in common, as below:

So, the first things that I notice here are:

1. Aside from a repeated ‘A’ and a repeated ‘M’ in the z13, the common symbols appear to be intentionally gathered into two similarly ordered groups that, except for the intervening ‘N’ in the z13 (3rd to last), would likewise be equally spaced, too; and
2. There is a clear symmetry about the z13, around the ‘8-balls’, that can feel highly unlikely to have been achieved at random.

I had done some analysis, several years back now, that brought me to a point where I was forced to consider whether that second ‘N’ in the z13 should be elsewhere in the cipher, having only been moved to this interrupting position to achieve the symmetry that we actually notice. I won’t go into the details of all that here, but it did take me on to a consideration that the z13 has a single transposition (not a swap) in it, and that the last ‘N’ might actually belong in the second position, so:

And this is what your “Claif” reminded me of, where we have the letter ‘l’ (in one way of looking at it), shifted back from it’s expected position to the second.

All the same, just an observation that struck me as interesting.

I think it could therefore be plausibly argued that the common symbols across the two remaining ciphers are intentionally present in both as indicating a common key between the z13 and the z32.

But again, @lendor-77. Apologies for crashing your thread with random thoughts.

All the best.