Structured Boolean Factorization

The mathematical tool

Factorization asks when a Boolean function can be expressed as independent parts on disjoint variable blocks. This research studies exact factor extraction from vtree-structured representations, including when a chosen representation exposes or hides the semantic factors.

What the current note establishes

The Phase 5 note gives structural results on vtree alignment and higher-order interaction defects. Later work includes further proofs and bounded computational experiments, but these are not yet integrated into a new manuscript. Pilot runtime work did not establish an algorithmic speedup; the value of the present line is its structural mathematics and precise limits.

Why it matters to The MIND

This is a concrete home for part of the older “gluing” question: which components really are separable, and which interactions require treating a whole structure together? A cognitive reading would require additional definitions relating Boolean factors to concepts or mental processes.

Open work

Integrate the later proofs and negative computational results into a current note, then reassess the best public claim and its relation to the wider MIND programme.