SFR Ontology Map

Status Boundary

This work is part of the authorial PHYSICA / Science of Fabric Reality corpus. It is presented as a research framework, formalization target, computational model, or theoretical synthesis unless explicitly marked otherwise. It is not presented as accepted physics, external consensus, or experimentally confirmed science.

1. Scientific Purpose

Defines the visual, topological, and structural requirements for representing the Science of Fabric Reality (SFR) core ontological taxonomy and relation matrix.

2. Concepts Visualized

• Five Ontological Pillars · The primitive foundation tuple:$${\mathcal{O}}_{\text{SFR}}=⟨\mathcal{R},\mathcal{O},\mathcal{B},\mathcal{I},\mathcal{T}⟩$$where $\mathcal{R}$ = Relation, $\mathcal{O}$ = Observer, $\mathcal{B}$ = Boundary, $\mathcal{I}$ = Invariant, and $\mathcal{T}$ = Transformation.
• Subsystem Projections · Mapping the foundational tuple to Digital Fabrica Theory (DFT), Invariant Engineering, Universal Mesh, and CodexStation nodes.
• Topological Category Functors · Categorical arrows preserving invariant structure across theoretical sub-disciplines.

3. Mathematical Symbols & Grounding

• ${\mathcal{O}}_{\text{SFR}}$: Complete ontological 5-tuple defining the Science of Fabric Reality.
• $\text{Hom}(\mathcal{A},\mathcal{B})$: Admissible morphism space between relational structures.
• ${\mathbf{Cat}}_{\text{SFR}}$: The symmetric monoidal category of relational fabric networks.

4. Required SVG Layers & Coordinate Geometry

• Coordinate System: viewBox="0 0 800 500", responsive container scaling down to 320px mobile viewport.
• Layer 1: base-topology:
  • Pentagon hub-and-spoke layout featuring 5 central nodes for the core pillars.
  • Outer concentric ring containing subsystem applications (DFT, FQFT, KBI, NMF).
  • Background radial grid bound to var(--vp-c-border) with 0.5px stroke.
• Layer 2: interaction-vectors:
  • Bidirectional relational arcs interconnecting the 5 pillars.
  • Outward gradient projection rays colored with var(--vp-c-brand-1) and var(--vp-c-brand-2).
• Layer 3: labels-and-nodes:
  • Node titles, category badges, and mathematical symbol tags bound to var(--vp-c-text-1).
  • Accessible screen reader title and <desc> tags.

5. Caption & Interpretation Boundary

Figure: Global ontological map of the Science of Fabric Reality, illustrating the five-pillar architecture and categorical subsystem projections.

NOTE

This figure serves as a formalization target and visual aid for the authorial model. It must not be interpreted as empirical proof or accepted physics.

6. Canonical Continuations

Direction	Target Resource	Purpose	Formal Code Link
Foundational Root	Science of Fabric Reality	Foundational relational thesis & ontology	Fabrica.Realica
Interactive Graph	Concept View & Taxonomy	Full interactive concept hierarchy	Visual Cartography
Formal Mathematics	Formal Mathematics Root	Axioms, proof registry & Lean 4 modules	Fabrica.InvariantEngineering
Figures Atlas	Visual Cartography Atlas	Figure programs index and taxonomy	Visual Cartography
Formalization Gateway	Formalization Gateway	Lean 4 Interactive Proof Suite	Fabrica.PGP

EXTERNAL REFERENCE