Intrinsic regularity: the current proof sequence

This reading guide joins the completed local components. The full course remains unfinished.

  1. Frequency amplitudes and iterated regularity proves both directions of the exact graph criterion, retaining the endpoint Besov norm and finite-rank systems.
  2. Conic frequency coordinates supplies the base-coordinate construction of a graph. Coordinate and directional localization proves transport, wavefront covariance and proper conic cutoffs.
  3. Parametrices and intrinsic localization supplies the full elliptic-test converse and independence of sufficiently small cutoffs and Lagrangian extensions.
  4. Prescribed nondegenerate and clean phases supplies every ordinary-symbol remainder, the amplitude right inverse, the excess correction and the leading-symbol lower-order criterion.
  5. Sobolev improvement and the strict threshold supplies the separate Sobolev-to-symbol theorem, its fully localized counterexample and five worked checks of orders, systems, operator reordering and phase normalization.
  6. Phase signatures and the geometric Maslov line proves the reduced quadratic forms, signature comparison through rank changes, global line construction and phase-chart identification, with three complete examples.
  7. The global principal symbol proves the critical density transformation, all phase and Fourier normalization factors, the exact kernel and surjectivity. Its explicit partition has locally finite base supports, including on a noncompact manifold. Three solved examples check coordinate changes, stabilization and the point mass.

The linked analytic prerequisites give the actual earlier proofs of measure and Fourier facts, dyadic estimates and ordinary operator calculus. Each retains its own author and licence notices.

The tangent lesson and its Gaussian-symbol identification now complete the tangent comparison, including every Gaussian rank and the nonlinear coordinate law. Their exact prerequisite edition is included.

The remaining course includes Fourier-integral composition, propagation, hyperbolic and boundary problems and complex phases. General symbol-class variants, topology/completeness and the separate involutivity statement are not certified by these ordinary-symbol components.