Selection: Why This Polynomial?
MDL doesn't just pick any rule — it eliminates 10290 candidates and arrives at one polynomial in 19 bits. This path explains every step of that elimination, why GF(7) is the only field that works, and how to read level labels on any result in the theory.
What you'll understand after this path
How MDL's five-step elimination funnel uniquely forces
p = C+R−CR−LCR from an astronomically large candidate space.
Why 7 is the smallest prime where chirality (ℤ₂) and color (ℤ₃) are both algebraically derivable at zero extra cost.
How to place any result on the Level 0–3 ladder, and why conflating a discrete algebraic fact (Level 2) with a continuum claim (Level 3) is an error.
This path assumes you know what the polynomial p(L,C,R) = C+R−CR−LCR does
(L03), what MDL and PSC mean (L02), and what the GTE orbit structure looks like (L06).
If those are unfamiliar, start with Path 1.
Lessons
How MDL Selects the Polynomial
The five-step elimination funnel: from 7343 candidates down to one rule, step by step, with the orbit interpolation that pins the 8th constraint.
Why GF(7): The Minimal Prime Theorem
An exhaustive check of every prime below 7 — each fails a specific test. GF(7) is the unique smallest field where chirality and color are derivable for free.
The 19-Bit Accounting
What "19 bits to specify" means in practice. A step-through of the 8+3+5+1+2 breakdown versus the 963-bit lookup table alternative. The polynomial wins by 50×.
The Four Levels of the Theory
The Level 0–3 ladder: raw polynomial, PSC-orbit map, CMCA tape, continuum field. How to read level labels, and why conflating them is a precision error.