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  "counts": {
    "unique_circuit_generators": 6,
    "regular_coordinate_trials": 2238,
    "source_preserving_inputs_across_maps": 6,
    "nonfixed_source_images": 0,
    "preserved2K_or17K_spans": 0
  },
  "positive_circuit_reduced_denominator": "For p P-circuits and j J-circuits, D=3^max(p-j,0)*13^j*529^(p+j). The numerator contains no factor23. For p+j>=2, D>=529^2, already beyond all source displacements; the one-circuit denominators1587/6877 also exceed them.",
  "K_lattice_condition": "For the P generator, c+Kn maps to another c+K integer point iff1587 dividesn; for J iff6877 dividesn. Both conditions require20631=39K dividesn. This is a domain sublattice, not preservation of the entireK lattice.",
  "minimum_nonzero_common_K_lattice_displacement": 10913799,
  "interpretation": "Every nonempty positive circuit preserves exactly its selected basepoint in the frozen regular coordinate menu. The local source-path grammar is valid, but its affine extensions are not actions on the whole source field or the original529 lattice. Formal large lattice displacements are arithmetic diagnostics, not dates or source endpoints."
}