A spread-digit bouncer counter: nonhalting proof submitted in https://github.com/ccz181078/busycoq/pull/26

`1RB0LF_0RC---_1RD0RA_1LE0RC_0LA0LE_1LE1LB`

This machine is a binary counter with variable gaps between its digits. Ordinary bounces increment the counter. At overflow, a finite tail either lets it wrap or triggers a long pause: the left side freezes into a wall, which is consumed two increments at a time while the gaps are rebuilt and new digits can be inserted.

The key is a four-rule token transducer for the return from the tail. Together with the tail's small front-unit cycle, it reduces the behavior between normal overflows to four paths. An interval invariant is preserved by every path, so the proof does not have to predict the tail's choices.

The blank run enters the invariant after 92,299 steps. The Rocq file proves blank-tape nonhalting directly, using Individual62 and standard libraries. Its structure follows CounterClass3v2 TM1's sweep/carry/macro-step approach.

Write-up (ZIP): https://raw.githubusercontent.com/DennisKoshta/busycoq/bbd8dec7ca70afd80523654b85ed142c3742e163/materials/spread-counter/writeups.zip
Image (ZIP): https://raw.githubusercontent.com/DennisKoshta/busycoq/bbd8dec7ca70afd80523654b85ed142c3742e163/materials/spread-counter/images.zip

AI assistance: proof and original write-up with Claude (Anthropic); independent review and submission preparation with GPT-6 Astra (OpenAI).