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title: "DFT Automaton — Schematic Specification" description: "Visual schematic and layer topology specifications for the Digital Fabrica Theory relational finite state automaton." layout: doc status: "canonical-figure-spec" claim_boundary: "Visual schematic specification only. Demarcates visual state transition topology from empirical physical validation."

DFT Automaton

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.

Scientific Purpose

Defines the visual and structural requirements for representing the Digital Fabrica Theory (DFT) relational finite state automaton within the formal framework.

Concepts Visualized

• Relational State Automaton · Discrete state machine ${\mathcal{M}}_{\text{DFT}}=(\mathcal{S},\mathrm{\Sigma },\delta ,s_0,\mathcal{A})$ operating on woven lattice configurations.
• Admissibility Indicators · State-local indicator functional $I_{\text{adm}}(s)$ pruning non-admissible transitions.
• Automorphism Invariance · Groupoid transition symmetries preserving trace dual reciprocity.

Symbols Visualized

• ${\mathcal{S}}_{\text{DFT}}$, $\delta (s,\sigma )$, $I_{\text{adm}}(s)$, ${\mathcal{T}}_{\text{inv}}$, ${\mathrm{\Sigma }}_{\text{trans}}$

Equations Referenced

• Digital Fabrica Theory — State space transition dynamics and node automaton cycles.
• Mathematical Invariants — State-local admissibility indicators (thm_state_local_admissibility_composition).

Required SVG Layers

• base-topology: The structural node and state transition graph.
• interaction-vectors: Admissible transition arrows, symbol emissions, and pruning boundaries.
• labels-and-nodes: Mathematical state labels, transition triggers, and admissibility tags.

Caption

Figure: Schematic representation of the DFT Relational Automaton, depicting state-local transition pruning and automorphism preservation.

Construction Notes

Do not use generic raster images. The final SVG must strictly adhere to the mathematical and topological constraints defined in the corresponding route.

Route Bindings

• Primary Theory: Digital Fabrica Theory
• Formal Discipline: Invariant Engineering
• Systems Node: CodexStation Node Architecture

Interpretation Boundary

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.