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E01 · F06 · SP-009 — Research for F06 ​

Find, read and record the sources of every story of F06 before its implementation (ADR-0020).

Acceptance criteria ​

  • Given each story of F06, when the spike ends, then every formula and behavior it needs has a verified REF-* or a DERIV-*.
  • Given the sources found, when the spike ends, then the stories cite them, and a research note records what was found and what remains open.

Questions ​

  • The rule of the stretched polygon (research request 0011): a polygon of n corners, its base flat at the bottom, symmetric about the vertical axis, touching the four sides of a w × h box, its sides as even as possible; which measure of as even, a closed form or an algorithm for each n from 3 to 12, and what happens when equal sides are impossible (a triangle or a square have no freedom left).
  • The model: the option stored in the regular polygon, and its effect on the anchor; an ADR if the polygon's model changes.
  • Exact or floating values: the stretched points are derived (ADR-0003); test values computable by hand for at least the triangle, the square and the hexagon.

Tasks ​

One task = one commit, referenced as SP-009.Tn.

    • the aspect grows with λ for each n from 5 to 12, and the sound range is one interval containing λ = 1: proved, or tested exhaustively → tested over 6 001 values of ln λ for each n (step 5), not proved;
    • a read source for a sin φ − b cos φ = c ⇒ φ = atan(b/a) + asin(c / √(a² + b²)) → not needed: the code bisects for every n, and the hand checks substitute the angle;
    • λ_lo and λ_hi computed at run time or tabulated → computed at each call;
    • ECMA-376 read before any citation of the PowerPoint presets (or the citation dropped). → dropped: the presets are context only, REF-ECMA-376 stays unverified and is not cited.