You need to download the “MODX Data List” booklet and the “Synthesizer Parameter Manual” (both PDFs) from the Official MODX Download Page.
Arpeggio List information is found pages 85-143... in the “Data List” booklet
The Definitions of all Arpeggio related parameters pages 48-51... in the “Synthesizer Parameter Manual”

You need to read what's written on these forums by the posters before attempting to "answer" them.

Where is the information about the number of concurrent notes an arp handles?

Their complexity?

Where they'll pinch notes from when more are played by the player than are within the arp, as the player adds notes?

Where is the "sort arps by length" button?

Sort by complexity button?

Sort by notes used?

Think what it's like to be confronted by 10,000 arps, and nearly zero insight into what's in them.

Use your empathy.

there doesn't seem to be a mapping (that I can find) of the length of each arpeggio.

Arpeggio List information is found pages 85-143... in the “Data List” booklet

No need to be deliberately dense.

Does your considering that to be a mapping negate the rest of what I'm asking for?

Taken from the MODX reference manual documentation on the arpeggio type list (sometimes you have to go fishing):

https://usa.yamaha.com/files/download/other_assets/2/1192582/modx_en_rm_a0.pdf
Pg 12

Length - Indicates the data length (amount of measures) of the Arpeggio type. When the Loop parameter*1 is set to “off,” the Arpeggio plays back for this length and stops.

Original Tempo - Indicates the appropriate tempo value of the Arpeggio type. Note that this tempo is not set automatically when selecting an Arpeggio type.

Accent - The circle indicates that the Arpeggio uses the Accent Phrase feature (see below)

Random SFX - The circle indicates that the Arpeggio uses the SFX feature (see below)

*1 The Loop parameter is set as follows.
[EDIT] -> Part Selection -> Element/Operator [Common] -> [Arpeggio] -> [Common]

Accent Phrase - Accent Phrases are composed of sequence data included in some Arpeggio types, sounding only when you play notes at a velocity higher (stronger) than that specified in the Accent Velocity Threshold parameter.

If it is hard to play at velocities necessary to trigger the Accent Phrase, set the “Vel Threshold” (Accent Velocity Threshold) parameter to a lower value.

Random SFX - Some Arpeggio types feature a Random SFX function which will trigger special sounds (such as guitar fret noises) when the note is released. The following parameters affecting Random SFX are provided.

For turning the Random SFX on/off: Random SFX parameter
For setting the volume of the SFX sound: Velocity Offset (Random SFX Velocity Offset) parameter
For determining whether or not the volume of the SFX sound is controlled by velocity: Key On Ctrl (Random SFX Key on Control) parameter

The reference manual has more "decoder ring" information for ARPs.

If, by "length", you were asking how many measures an arpeggio is - that's documented. I don't see your other questions addressed by the documentation.

I've asked for similar information before (mostly focused on preset Performances) and have been "politely" been given the task to come up with the documentation myself and share it with presumably the handful of other people who would think it's important. At least that's what is inferred by the tone of the response I got back when.

A script (run by Yamaha) could make pretty quick work out of collecting most of the data you want. Unique notes used, total notes used, max trigger key count. I think you could come up with your own measure of "complexity" given that. Once the data is in the data list - it's fairly easy to pull it out and place in a spreadsheet. This would cover sorting.

Sorry to bother you:

How could I get a script to run and get at that info?

What access can we have to the internals of a MODX?

A script (run my Yamaha) could make pretty quick work out of collecting most of the data you want

... I've corrected this typo. I meant to say "run by Yamaha". So this would be something done at Yamaha to provide the information. No idea if they're going to do this or not.

Argh. I read it as "Run on my yamaha"... and assumed there might be some way to peek and poke I didn't know about.

Worse, I think, is that they probably don't need to run a script... they'd have all this info in some kind of spreadsheet, already.

Or data store that could be queried, onsite. And they could relatively easily build a visualiser on the MODX and Montage to reveal the nature of each arpeggio. Kind of like a dictionary of arps 😉

And, to your point about Performances, and their Auditions, completely agree!

These things should be somehow opened up so we can see how things are done in them.

Much of this could be solved ON the Yamaha's if they provided note sequencer style presentations of arpeggios, songs and auditions.

While they're at it, have a shift function that opens up documentation for every single feature, as it's pressed with a shift query combo held.

SEMI SOLUTION TO SPREADSHEET:

Write code to send MIDI notes to a part, and listen to the arps that come back, examining them dynamically for changes. Spit into arrays, store and present for examination.

Would require much theoretical musical knowledge, to explore variations of the 'smart' arps. I don't have this.

Reaper has enough script based plugin codeability to be the sender and receiver, and storer of what's going on without resorting to C++

Turn "ARP MIDI Out" if you're going to do that.

The solution to this would be to have a new step recorder mode screen that also shows what the arp looks like as well the ability to edit it on the fly. We could edit by touch the display to add or remove steps. this one feature would enhance using arpeggios and doing recording of music so much more powerful.

conversely maybe all the Montage/Modx users could combine efforts to contribute to a new online source for mapping and displaying arpeggio patterns. Would Yamaha allow that? Midimondo anyone?

MidiMondo couldn't be anymore unreliable than SoundMondo!