Spatial Representation & Mapping

Primes about how problems and substrates are organized in space or by proxy for space: geometric and topological structure (embeddability, dense sets, topographic maps, spatial indexing), and how representation choices shape what can be found or reasoned about (problem representation, optimization landscape, segmentation, remapping).

18 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Backcasting — Work backward from desired future.
• Cross Cutting Relationship — Reading relative temporal order from intersection geometry — a feature that interrupts or overprints another must be younger than the one it cuts.
• Dense Set — A smaller set reaches arbitrarily close to every point of a larger one.
• Embeddability — Whether a structured substrate admits a conflict-free placement inside a constrained ambient target.
• Explanatory Overlay Masking Structural Debt — An artefact carrying avoidable structural confusion is patched with an informational overlay that makes it locally readable without retiring the underlying problem, and the overlay's local sufficiency quietly crowds out the structural fix that would actually resolve it.
• Geometric Chronology — Read temporal order from the spatial or geometric structure a sequence of events leaves in a preserving medium.
• Layering — Segments systems into levels.
• Located-In Relation — One entity is situated within the region of another at a time, without that entity being a part of, or strictly contained by, the location.
• Navigation — A positioned agent moves through a structured space toward a goal using an incomplete map, staying oriented at each step.
• Non-Locality — Distant elements influence or correlate with each other without a chain of contiguous intervening contact — coupling that jumps the substrate rather than propagating through neighbors.
• Optimization Landscape — The topology of a value function over a configuration space, whose shape predicts which search strategies will succeed or get stuck.
• Precomputation and Materialization — Perform expensive or combinatorial work before demand and store its result as a directly usable artifact, trading build and update cost plus possible staleness for cheap, predictable use-time access.
• Problem Representation — The chosen encoding of a problem fixes which operations and intermediate states are available, and therefore which solutions can be found at all, before any solving begins.
• Remapping — A single substrate holds multiple disjoint, context-keyed representations and switches discretely between them on a context cue, preserving inactive ones for later re-entry.
• Segmentation and Boundary Drawing — Partitioning continuous domain via boundaries concentrates meaning.
• Spatial Indexing — Organizing items by position in a space so retrieval, neighborhood, and range queries become geometric and output-sensitive.
• Substrate-Induced Boundary Dissolution — Substrate-induced boundary dissolution occurs when a shared carrier makes formerly separate kinds mutually expressible, removing the operational basis of their partition and propagating reorganization into layers built on that partition.
• Topographic Map — A source space is laid out on a substrate by a neighbourhood-preserving map with non-uniform magnification, so positions encode relationships and damage to a substrate region predicts a localised source deficit.