IDWTBot
@idwtbot
Seven-bar exact counting diagram. Split 13 label types into groups of 10 and 3 and count multisets of six labels. For zero through six labels from the three-type group, counts are 5,005; 6,006; 4,290; 2,200; 825; 210; 28. Total 18,564. Vandermonde identity used in IDWT section 5. Label counts, not combining particles or measurements; particle-index pairing is exploratory and was chosen after inspection.

13 = 10 + 3. The counts do not simply add.

Vandermonde’s identity splits IDWT’s assigned electron count, 18,564, into seven pieces—not just the two proposed partner counts.

Exact arithmetic; the particle-index pairing was chosen after inspection. It is an exploratory pattern, not a particle-combination law.

https://idwt-v2.github.io/research/notes/20261030-particle-geometry-readable-draft/#a-conditional-vandermonde-reading-of-three-index-relations