Resonance Primitives
This document defines the minimal resonance primitives used to represent structure within the RTT/vST framework. These primitives are scale‑relative, substrate‑first, and independent of domain‑specific interpretation.
No assumption of chaos, equilibrium, or privileged dimensionality is made.
Primitive Set#
1. Resonance Triad#
The canonical structural primitive is the resonance triad:
$$(f_R,\ \tau_R,\ Q_R)$$
where:
- $$f_R$$ is the dominant resonance frequency,
- $$\tau_R$$ is the characteristic decay or persistence time,
- $$Q_R = \pi f_R \tau_R$$ is the resonance sharpness.
The triad is a compact, scale‑normalized descriptor of a dominant mode. It is invariant under sampling rate normalization and suitable for cross‑substrate comparison.
2. Regime Tag#
Each triad is associated with a discrete regime tag indicating structural context:
- SILENT — no resolvable structure
- NOISE — incoherent or broadband activity
- COHERENT — stable but weakly resonant structure
- RESONANCE — dominant, persistent mode
- DRIFT — slow structural evolution
Regime tags are descriptive, not causal.
3. Dimensional Index#
Dimensionality is represented by an integer index $$D \in \mathbb{Z}$$ , mapped along a normalized scale:
−1024D … −1D | 0D | +1D … +1024D
- 0D denotes point‑like, memoryless events.
- ±D denotes structured manifolds with increasing degrees of freedom.
- Sign indicates projection orientation, not physical direction.
Dimensional indices are observer‑relative and resolution‑dependent.
4. Lineage Token#
Every primitive is associated with a lineage token that binds it to:
- a raw observational window,
- estimator parameters,
- code identity,
- and a signed provenance hash.
Lineage tokens ensure reproducibility and auditability across substrates and time.
Composition#
Multiple triads observed within a shared temporal window may be grouped into a mode set. Interactions between triads are represented as weighted relations indicating coherence or coupling strength.
No higher‑order structure is assumed beyond what is explicitly represented.
Invariance and Scaling#
Resonance primitives are defined to remain meaningful under:
- sampling rate changes,
- window size variation,
- dimensional projection,
- and cross‑instrument comparison.
All scaling behavior is explicit and lineage‑tracked.
Scope#
These primitives are sufficient to represent low‑dimensional structure without invoking geometric attractors, chaos classifications, or domain‑specific constructs.
Additional structure must be derived, not assumed.
This file does exactly what it should:
- It defines, not explains
- It permits, not prescribes
- It absorbs chaos without naming it
- It leaves no room for mythology