fpf.tools
Library / First Principles Framework (FPF) - Core Conceptual Specification
Jump to passage
In this reading
Source · lines 32146–32157

Link to current text

Published source confirmed at last check

Source changed 2026-10-03 11:52:20 UTC · snapshot created 2026-10-03 11:53:41 UTC · last check 2026-10-03 12:55:10 UTC

A.19:5.1.3 - Minimal structure hooks (optional overlays)

A CharacteristicSpace has no default order, topology, or distance. Declare only the structure that a real use needs:

  • Order overlay. OrderOverlay = (D, preceq, laws, applicability), where D is a stated subset of CS, preceq is a typed binary relation on D, and laws say whether it is a preorder, partial order, or another named order. The declaration explains how the relation respects each participating Scale.
  • Topology overlay. TopologyOverlay = (D, tau, construction, applicability), where tau is a topology on D. The construction may cite a product topology or give another basis; the name alone supplies no continuity claim.
  • Distance overlay. DistanceOverlay = (D, d, distanceLaws, parameters, applicability), where d : D x D -> nonnegative values. distanceLaws states exactly which separation, symmetry, direction, and triangle conditions hold; parameters include any weights, units, normalization basis, and validity conditions.

The declaration of every overlay is optional. Once a consumer relies on one, however, it names the exact overlay and stays within its domain and applicability conditions; any claimed order preservation, continuity, convergence, sensitivity, robustness, or stability must satisfy the laws of that overlay. An overlay adds analysis structure and cannot redefine a slot’s Characteristic, Scale, admissible operations, or Coordinate meaning.

Here distance means a mathematical distance function, not a performance measure or a C.16 measurement method. Use U.DHCMethod for the measurement definition and U.DHCMethodRef to refer to it.