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Coverage-Hole Heatmap

Diagnostic visualization tool — instantiates Neighborhood-Preserving Substrate Mapping

Renders the substrate as a heatmap of representation density so under-covered source regions — the holes where the map is thin or missing — become visible at a glance and can be prioritized.

Coverage-Hole Heatmap colors the substrate (or the source space projected onto it) by how well each area is represented, so gaps read as literal cold spots. Its defining move is making absence visible: rather than scoring overall coverage with a single number, it shows where the map is thin, empty, or under-resolved, turning "we might have blind spots" into a picture a human can point at and rank. It is a diagnostic display of the coverage-and-tiling plan's shortfalls — it surfaces the holes; it does not fill them.

Example

A carrier planning a 5G rollout needs to see where the network leaves users stranded. A coverage-hole heatmap overlays predicted and measured signal strength on the service map and colors every area below a usable threshold. Instantly the holes take shape: a dead zone behind a ridge, a weak corridor along a highway, an indoor hole inside a parking structure. Planners read not a coverage percentage but the shape and location of each gap — which is exactly what tells them where a new small cell earns its cost and where the map is fine as-is. Tellingly, the places where predicted coverage looks good but measured coverage is poor draw the eye first, because that disagreement flags where the propagation model itself is wrong. The heatmap diagnoses; siting the tower is a separate act.

How it works

Define a coverage or density measure per substrate cell — element count, distance to the nearest representative, measured signal — and bin it onto the substrate. Color by an explicit legend with a stated adequacy threshold, and highlight contiguous holes so a gap reads as a region rather than scattered pixels. Optionally weight each area by how much source mass or task-relevance actually lives there, so a large empty region nobody cares about does not scream louder than a small critical one. What makes it this mechanism is that it is the display of gaps — static, diagnostic, feeding fixers rather than acting.

Tuning parameters

  • Coverage metric — density, nearest-representative distance, or measured signal; each defines "hole" differently and can disagree.
  • Threshold and legend banding — where "adequate" ends and "hole" begins; shifting it grows or shrinks the red without changing the map.
  • Resolution / bin size — fine bins reveal small holes but get noisy; coarse bins hide them.
  • Source-mass weighting — weighting holes by the source mass or task-relevance sitting there, so trivial empty space does not alarm.
  • Measured versus predicted — showing modeled coverage, empirical samples, or the disagreement between them.

When it helps, and when it misleads

Its strength is surfacing the gaps a global coverage score hides and putting them where a human can prioritize; the predicted-versus-measured disagreement is itself a high-value signal. Its limits are perceptual and dimensional. It shows holes only at the metric and resolution you chose — a hole smaller than a bin, or in a dimension you did not render, stays invisible — and a two-dimensional heatmap of a high-dimensional source can only show coverage in the projection, not the territory. The classic misuse is filling every visible hole regardless of whether any source mass or task actually lives there, chasing cosmetic uniformity at real cost. The discipline is to weight holes by source mass and task-relevance and to remember the map is a projection.[1]

How it implements the components

As a visualization it fills the coverage and observability components; it neither re-tiles nor lays out the map:

  • coverage_and_tiling_plan — it exposes where the current tiling under-represents the source, i.e. the plan's shortfalls, region by region.
  • map_observability_and_legend — it is an observability artifact, with an explicit legend banding coverage into adequate and hole.

It does not re-tile to fill the holes it finds — that is Adaptive Remeshing and Reallocation — and it does not lay out the receptive-field tiling itself, which is the Receptive-Field Tiling Grid.

  • Instantiates: Neighborhood-Preserving Substrate Mapping — it makes the archetype's demand for complete-enough coverage inspectable.
  • Sibling mechanisms: Adaptive Remeshing and Reallocation · Receptive-Field Tiling Grid · Adjacency-Matrix Preservation Test · Boundary and Seam Regression Test · Calibration Anchor Stimuli · Canary Region Probe · Elastic-Net Embedding · Lateral-Interaction Smoothing · Local Ablation or Lesion Probe · Magnification Function · Map Fold and Collision Scan · Map Registration and Alignment · Multidimensional Scaling Layout · Neighborhood Trustworthiness and Continuity Metric · Perturbation-Response Map · Self-Organizing Map Training · Topographic Error Measure · Versioned Coordinate Atlas

References

[1] "Coverage hole" is a standard term in cellular network planning for an area where received signal falls below the level needed for service. Cited as the real, correctly-used anchor for the notion of a visible gap. ↩