Perturbation Landscapes of the Ghost-Cell Encoding: Convention- Dependence, Channel Independence, and Single-Perturbation Reach in a 25-Point Voronoi Tessellation

Paper II of this series formalised a single geometric transition – the correction of onemislocated seed in a 25-point Voronoi tessellation – as an entanglement between a cell-area register and a ghost-cell ancilla, and from that one instance advanced severalinterpretations: a non-local reading of the 21.1% distinguishable fraction, a possiblystructural invariance of the topological entropy, and a distinguished scale near N = 25. Herewe hold that encoding fixed and apply it to a controlled landscape of perturbations of thesame configuration, generated by symmetry-derived operations (mirror reflection, rotationby 60°, and rotation by 180° – point inversion in the plane), to ask which of those single-instance interpretations survive as measured relationships. Each perturbation is readthrough three channels in parallel – metric/quantum (the entanglement entropy S_E),topological (side-count entropy), and graph-structural (a Ramsey-type ratio) – with ahexatic order parameter and a reflection-odd chiral measure carried alongside. Within thislandscape S_E appears governed, to good approximation, by a single scalar – the magnitudeof the change in the area distribution (correlation ≈ 0.96) – though the relationship iscalibrated to a framing convention rather than frame-independent. The metric and graphchannels are statistically independent. A single perturbation’s disturbance ispredominantly local, refining the earlier non-local reading; accumulated perturbations addsub-linearly. Global symmetry operations leave every channel exactly invariant,reproducing the Bormashenko–Legchenkova–Frenkel paradox at this scale, withhandedness recoverable only through a reflection-odd measure. A recurring theme ismeasure-dependence: a reading inherits the blind spots of the measure it is taken from.