Full Monograph

The monograph is the long-form companion to the compact_note. It gives the full proof route, slower exposition, worked examples, and the broader convex-geometric framework around the current theorem package.

Download PDF: project_tesseract_monograph.pdf

Suggested Reading Paths

Fastest Companion Route

If you already know the compact note and want the shortest path through the longer manuscript, read:

1. Introduction
2. Modular hyperbolas in context
3. The basic geometry of MTMN
4. The first-boundary model
5. The second-boundary model

Full Theorem Route

• Introduction — objects, area functions, and the main geometric viewpoint
• Background and notation — terminology and basic tools
• Modular hyperbolas in context — relation to earlier literature
• The basic geometry of MTMN — symmetries, permutation structure, zero-class geometry, and hyperbola-gap theory
• Exact formulas using convex geometry — support-function and exponential reformulations
• The first-boundary model — exact first-boundary formulas and cubic-order growth
• The second-boundary model — exact odd-$N$ second-boundary formulas

Further Exact Extensions

• Using the first two layers together — interaction of the first two boundary layers
• Residue-area polynomials — algebraic packaging of the residue-area profile

What The Monograph Adds

Relative to the compact note, the monograph includes:

• fuller proofs and worked examples
• the support-function and exponential frameworks
• the exact odd-$N$ second-boundary theory
• the two-layer and residue-area-polynomial extensions
• the longer literature discussion around modular hyperbolas

Useful Supporting Pages

• MTMN — project-wide entry point for the main objects
• S_N_a — per-residue convex-hull area
• S_N — total area sum
• zero_class_geometry — solved zero-class geometry
• first_boundary_model — first exact global lower model