🌀 Fractional Dimensional Ladder (Micro Core)
The Fractional Dimensional Ladder describes how micro‑states shift across fractional dimensions while maintaining coherence.
It is the smallest stable model of dimensional change in RTT Micro Core.
Micro‑scale transitions are subtle:
they do not jump whole dimensions — they slide, compress, expand, or invert across fractional steps.
🔍 What a Fractional Dimension Represents#
A fractional dimension (Dᶠ) captures:
- the structural complexity of a micro‑state
- its available transition pathways
- its resonance capacity
- its boundary behavior
Micro Core uses fractional dimensions because micro‑regimes rarely occupy clean integer states.
Fractional values provide the precision needed to describe micro‑scale behavior without oversimplification.
🔄 How Transitions Work#
A fractional‑ladder transition looks like:
[ Dᶠ_1 \rightarrow Dᶠ_2 ]
Examples:
- 0.7 → 0.9 — micro‑expansion
- 1.2 → 0.8 — micro‑compression
- 0.6 → 0.6 — stable resonance
Each transition must preserve:
- coherence (C ≥ C* )
- bounded drift (δ ≤ δ* )
- structural consistency of the triad
If any condition fails, the transition collapses.
🔺 Triads on the Ladder#
As a micro‑triad moves along the ladder:
- the active node may shift
- the boundary may expand or contract
- the potential node may invert
These changes are reversible as long as coherence remains above threshold.
🧩 Why Fractional Dimensions Matter#
Fractional dimensions allow Micro Core to:
- model micro‑scale behavior precisely
- describe transitions without integer jumps
- capture subtle resonance changes
- support ultra‑low‑power and constrained systems
- bridge micro‑scale and macro‑scale behavior cleanly
They provide the smooth gradient needed for micro‑regime reasoning — a continuous, coherence‑preserving pathway for micro‑state evolution.