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FQFT · Microscopic ArchitectureMICRO-25

FQFT-MICRO-25 — Local/Global Split Compiler

Typed Hilbert-bundle refinement compiler, tensor sum kinetic operators, and scale separation.

Candidate Revision Architecture

The candidate revision architecture resolves the metric-collapse obstruction by factoring the field carrier into two decoupled components:

CLG=RXF,

where:

  1. RX is a global spacetime Dirichlet refinement whose metric and Laplacian converge to (ΔX,L2(X,mX)).
  2. F=(HF,LF) is a fixed internal spectral fiber with dimension NF=dimHF.

Hilbert Bundle and Kinetic Operator

At each refinement level n:

Hn=L2(Vn,mn;HF)L2(Vn,mn)HF.

The combined kinetic operator is the tensor sum:

LnLG=LnXIF+μF2IXLF,

where μF>0 is a dimensionful internal mass/energy scale.


Scale Separation Architecture

Spacetime Scale (n0)Governs IR/UV continuous diffusion and fractal dimension DHInternal Scale (μF)Governs discrete mass splittings and internal fiber charges

This resolves MIC-T01: the global Dirichlet form provides the non-trivial Hausdorff metric space, while the internal fiber retains the exact Ramanujan / Kesten–McKay spectral data without topological collapse.