The arguments behind the construction tools: exact labels for a 6×4 tower, degree-12 parent constructions, and the relation between real embeddings and fixed cosets.

Papers

• The real-place count and the sibling class as one linear system
  Jonathan Washburn · 17 August 2026
  On a quadratic step the real-place count is twice the number of real embeddings positive on the adjoined unit. The sibling is the square class of the relative norm in the orbit field. Both are blocks of one linear system. The 12T11 split is a measurement.
• Exact Galois labels for a 6×4 tower
  Jonathan Washburn · 12 August 2026
  Classification of the subgroups of A₄ wr C₆ that contain the full 2-part and surject onto the top C₆. Twenty-four conjugacy classes, labelled before any field is built.
• Leftover parents and the octic 2-side
  Jonathan Washburn · 13 August 2026
  Three leftover degree-12 parents identified with constructors, and the theorem that a 2-group acting on a nonzero 𝔽₂-space has only rank-1 composition factors. No degree-24 field is built in the note.
• Inverse Galois over the rationals as a rational point on a four-branch curve
  Jonathan Washburn · 17 August 2026
  Only the function-field architecture has descent to the rationals. Four branch points is a curve. The apex is derived from Fried and Voelklein and the dimension count, and says so.
• The real-root count as a coset count
  Lean · RowLaw, RowLawGaloisReading
  The number of real embeddings of an intermediate field is the number of right cosets fixed by complex conjugation. Odd Galois groups are totally real. A unique involution class collapses the possible signatures.
• The longer argument
  16 August 2026
  Orbit field, aiming map, parity dial, and the scoped signature law.
• Solve, don’t search
  Jonathan Washburn · 6 July 2026 · early note
  Screening polynomial families was saturated at the frontier. Solvable targets compile by class field theory. Dated 6 July 2026.