Calculation record

A collective same-field square with a reciprocal geometric response.

This is a stated inverse extension of a finite physical mode projection.
The geometric stiffness and inertia are common model coefficients. Their
microscopic source, and the full spatial extension, are not derived here.

Research context

  • A stationary collective source for the spatial mass operator

    A completed-square collective action makes the occupied geometric source stationary, preserves the finite carrier's frequencies and canonical energy, and has a controlled stable linear response across all maintained sector controls; its physical spatial completion and coupling vertices remain distinct questions.

Interpret numerical checks within the assumptions and limitations documented in these notes.