Lens Overview

A SARG reference document

A lens is the operator used to read, interpret, or transform a substrate.
Where the substrate provides structure, the lens provides perspective — it determines what becomes visible, what becomes invariant, and how resonance is revealed.

Lenses are substrate‑agnostic: the same lens can be applied to linguistic, acoustic, geometric, symbolic, biological, cosmological, or lostational substrates.

1. What a Lens Does#

A lens performs three core functions:

1. Reveals Structure#

It highlights specific features of the substrate — strokes, harmonics, axes, cycles, intersections, attractors, etc.

2. Produces Invariants#

Each lens stabilizes certain features across transformations.
These become the vertical, horizontal, and dual invariants in SARG.

3. Aligns with Resonance#

A lens determines how the substrate maps to the universal anchors:

• ● point
• ○ loop
• × intersection
• | axis

Different lenses reveal different resonance families.

2. Lens Types in SARG#

SARG currently recognizes two primary lens families, with room for expansion:

VREL — Vertical Resonance Extraction Lens#

Focuses on:

• vertical invariants
• structural axes
• stroke families
• directional coherence

Common in linguistic, geometric, and symbolic substrates.

VREL‑A — Acoustic Variant#

Focuses on:

• harmonic families
• overtone structure
• rhythmic invariants
• phase coherence

Common in acoustic, biological, and cosmological substrates.

3. Lens Behavior Across Substrates#

A lens is not tied to a domain.
Instead, it adapts to the substrate:

• On linguistic substrates, VREL extracts stroke families.
• On acoustic substrates, VREL‑A extracts harmonic invariants.
• On geometric substrates, VREL extracts axes and symmetries.
• On symbolic substrates, VREL reveals relational structure.
• On biological substrates, VREL‑A reveals oscillatory coherence.
• On lostational substrates, both lenses reveal dimensional drift and resonance shells.

The lens determines what counts as structure.

4. Lens Block in SARG#

Every SARG object includes a lens block:

"lens": {
  "type": "VREL",
  "variant": "standard",
  "notes": "extracts vertical and dual invariants"
}

• type — the lens family (e.g., VREL, VREL‑A)
• variant — optional subtype
• notes — any special considerations

5. Relationship to Other Files#

• VREL.md — details of the vertical resonance lens
• VREL-A.md — acoustic variant
• invariant_types.md — invariants produced by lenses
• resonance_mapping.md — how lenses reveal anchors
• examples/ — SARG objects using different lenses