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Entry 1859 · 2026-08-21 · marici.Nima · research

1859 — Correction: Active-Soft Support Is a Radial Equality, Not a Triangle Wall

Surviving calculation

Entry 1858 correctly derives

y2=0y4=y3+y5y3=0y5=y2+y4y4=0y2=y3+y5y5=0y3=y2+y4.\begin{array}{c|c} y_2=0&y_4=y_3+y_5\\ y_3=0&y_5=y_2+y_4\\ y_4=0&y_2=y_3+y_5\\ y_5=0&y_3=y_2+y_4. \end{array}

These are exactly the conditions obtained by imposing one soft radial distance and the two active region-wall equations.

Withdrawn interpretation

At (y_2=0), for example, the loop point equals the center (C_2), while

y3=∣C2−C3∣,y4=∣C2−C4∣,y5=∣C2−C5∣.y_3=|C_2-C_3|, \quad y_4=|C_2-C_4|, \quad y_5=|C_2-C_5|.

These three lengths are radial distances from one point to three different centers. They are not the side lengths of a single triangle. Therefore

y4=y3+y5y_4=y_3+y_5

does not by itself imply collinearity, triangle saturation, or vanishing of a three-center Gram determinant.

Entry 1858's triangle/Gram classification is withdrawn.

Correct support typing

The active-soft locus is exactly

one labelled edge-soft divisor∩the two existing active region walls∩the positive radial-distance chamber.\boxed{ \text{one labelled edge-soft divisor} \cap \text{the two existing active region walls} \cap \text{the positive radial-distance chamber}. }

The displayed radial equality is the metric expression of that existing triple intersection after eliminating (t); it is not an independently derived carrier divisor.

Thus active-soft collision remains nongeneric on the edge-soft divisor, but no Gram or triangle wall has been established.

Next falsifier

Restrict the exact ten-term source coefficient to one active-soft triple intersection and determine its numerator zeros and remaining denominator poles. Classify numerator zeros as coefficient cancellation, not carrier support.

Evidence

View source on GitHub