Resonance Families

A SARG resonance reference document

Resonance families describe patterns of anchor dominance across a substrate.
They are the “higher‑order shapes” formed when universal anchors (● ○ × |) combine into stable configurations.

A resonance family is not a geometric shape — it is a behavioral signature that appears across domains.

1. What Is a Resonance Family?#

A resonance family is defined by:

• which anchors dominate
• how they combine
• how the substrate behaves under transformation
• what invariants persist
• what tensions or stabilities emerge

Families allow SARG to compare structure across linguistic, acoustic, geometric, symbolic, biological, and cosmological substrates.

2. Core Resonance Families#

Below are the foundational families that appear across all domains.

●‑Dominant — Point Family#

Signature: ● ● |
Behavior:

• atomic
• discrete
• node‑based
• minimal coherence units

Examples:

• vowel nuclei
• atomic centers
• attractor basins

○‑Dominant — Loop Family#

Signature: ○ ○ ●
Behavior:

• cyclic
• periodic
• self‑enclosing
• rotationally stable

Examples:

• closed curves
• orbital systems
• rhythmic cycles

×‑Dominant — Intersection Family#

Signature: × × |
Behavior:

• tension
• interference
• branching
• dual‑axis alignment

Examples:

• consonant intersections
• geometric crossings
• phase interference

|‑Dominant — Axis Family#

Signature: | | ●
Behavior:

• directional
• vector‑driven
• structural spine
• growth or extension

Examples:

• vertical/horizontal strokes
• frequency sweeps
• biological growth vectors

3. Hybrid Resonance Families#

Many substrates express mixed dominance.

Point–Axis Hybrid#

Signature: ● |
Behavior:

• discrete units arranged along a structural axis
• common in writing systems and symbolic notation

Loop–Intersection Hybrid#

Signature: ○ ×
Behavior:

• cyclic structure with crossing tension
• appears in rhythmic syncopation and geometric knots

Cross‑Axis Family#

Signature: × |
Behavior:

• tension resolved along a dominant axis
• common in branching biological systems

Loop–Point Hybrid#

Signature: ○ ●
Behavior:

• periodic structure with discrete centers
• appears in orbital systems and harmonic cycles

4. Lostational / Supsphere‑Adjacent Families#

These appear in high‑dimensional or inversion‑side substrates.

Supersphere Family#

Signature: ○ ○ ○ ×
Behavior:

• spacious coherence
• boundary‑escape behavior
• dimensional drift

5. How Families Are Used in SARG#

Every SARG object may include:

"resonance": {
  "anchors": ["○", "×"],
  "family": "loop-intersection",
  "notes": "cyclic structure with crossing tension"
}

The family provides the cross‑domain comparison layer.

6. Relationship to Other Files#

• universal_anchors.md — defines the four anchors
• resonance_mapping.md — explains how anchors map to invariants
• invariant_types.md — shows how invariants relate to families
• examples/ — real SARG objects using families