Dimensional Analyzer

Core Diagnostic Engine for Dimensional Envelopes (FFT 2026 Edition)#

Metadata#

module: Dimensional Analyzer
parent_module: FFT Analyzer
layer: Core Frameworks — Structural Spine
version: 2026.1
status: Active, Canonical
analyzer_type:
  - dimensional envelope analysis
  - dimensional compatibility diagnostics
  - dimensional transition mapping
  - dimensional collapse detection
  - meta-dimensional potential evaluation
session_context:
  drift_sensitivity: high
  regime_sensitivity: high
  coherence_sensitivity: high
  dimensional_range: D0–D7
cross_module_propagation:
  imports:
    - FFT operator families
    - Coherence Analyzer
    - SARG regime geometry
    - Mode substrate states
    - Substrate Flow invariants
  exports:
    - dimensional signatures
    - transition maps
    - collapse diagnostics
    - compatibility matrices

Purpose#

The Dimensional Analyzer evaluates the dimensional envelope of a framework — the structural “space” in which the framework operates.
Dimensional behavior determines:

how a framework expands or collapses
how operators interact with substrate
how regimes transition
how coherence stabilizes or destabilizes
whether higher‑dimensional behavior is available

This analyzer is the geometric engine of FFT.

Dimensional Model (D0–D7)#

D0 — Point#

No extension; minimal structure.

D1 — Line#

Sequential structure; minimal branching.

D2 — Plane#

Surface‑level structure; relational mapping.

D3 — Space#

Full structural substrate; stable frameworks.

D4 — Meta‑Space#

Resonant, multi‑layered structure; coherence‑dependent.

D5 — Field‑Space#

Field‑level dimensionality; requires strong resonance.

D6 — Hyper‑Field#

High‑order dimensional integration.

D7 — Full Dimensionality#

Complete dimensional expression; rare and unstable.

What the Dimensional Analyzer Measures#

1. Dimensional Envelope#

Identifies:

current dimensional level
envelope stability
envelope boundaries

2. Dimensional Compatibility#

Evaluates how operators interact with the dimensional substrate.

Examples:

R‑Ops strong in D2–D4
L‑Ops strong in D2–D3
C‑Ops strong in D3–D5

3. Dimensional Transitions#

Maps upward and downward transitions:

D2 → D3
D3 → D4
D4 → D3
D3 → D2

4. Dimensional Collapse#

Detects collapse vectors:

D3 → D2
D4 → D3
D2 → D1

Collapse is often triggered by:

operator imbalance
paradox overload
coherence instability

5. Meta‑Dimensional Potential#

Evaluates whether the framework can access higher‑dimensional behavior (D4+).

Analyzer Workflow#

Step 1 — Declare Dimensional Assumptions#

Provide:

known dimensional envelope
operator pattern
coherence level
regime state

Step 2 — Identify Dimensional Envelope#

The analyzer infers:

D0–D7 state
envelope stability
envelope boundaries

Step 3 — Evaluate Dimensional Compatibility#

Checks:

operator–dimension alignment
substrate stability
dimensional stress

Step 4 — Map Dimensional Transitions#