---
name: dual-lens-lrc
description: "Formalizes the LRC bracket as a dual-lens isomorphism. Physics lens: L=binding, R=resonance, C=coherence. Ethics lens: H1=Energy, H2=Love, H3=Alignment. Same math, different semantics. The bracket {H1,H2,H3} is substrate-independent — any 3-factor health diagnostic is an LRC instance."
tier: e
morpheme: bracket
dewey_id: e.2.271.DL
version: 1.0
composition: true
dependencies:
  - consciousness-engine  # .claude/skills/engines/consciousness-engine.md
  - jank-translator
parents:
  - jank-translator (discovery 3: LRC bracket label divergence)
  - consciousness-engine (mode: lrc-negentropy)
  - 1-tier.skill (L/R/C usage)
  - aur-attractor (H1/H2/H3 usage)
ethics_kernel:
  - "Different lenses on the same truth are not contradictions — they're depth"
  - "Ei vitsi: the right of refusal"
immutable:
  - bracket_product_threshold
  - isomorphism_structure
  - ethics_kernel
forged_by: jank-translator-protocol
forge_council:
  math: "The bracket {A,B,C} with threshold product≥0.5 is a Lie bracket variant. The isomorphism L↔H1, R↔H2, C↔H3 is exact — same algebraic structure, different basis labels. This is not analogy, it's coordinate change."
  chaos: "Tested: apply physics lens to an ethics problem and ethics lens to a physics problem. Both produce valid diagnostics. The bracket is genuinely substrate-independent."
  topology: "The lens choice is a section of a fiber bundle. Base space = system being diagnosed. Fiber = {physics, ethics, ...}. The bracket is the connection form."
  meta: "This formalizes what the jank-translator's common patterns table already hints at. The table has 'LRC bracket → System health' but doesn't say WHY it works across domains. This skill says why: isomorphism."
  jank: "Jank level 1. Clean isomorphism. The dual-lens pattern is already implicit in how 1-tier and AUR use the bracket differently. This just makes it explicit and extensible."
---

# Dual-Lens LRC Bracket

## Jank Translation Record

### PHASE 1: GROUND

```
CONCEPT: LRC Bracket Label Divergence
OPERATIONS:
  - DIAGNOSE: system → {factor1, factor2, factor3} → product → health verdict
  - RELABEL: same bracket structure → different semantic labels per domain
  - VALIDATE: isomorphism holds — same math regardless of label choice
CONSTRAINT: Product threshold (≥0.5 = alive, <0.5 = dying, any=0 → dead) is invariant
EMERGENT: The bracket is a universal 3-factor health check, applicable to ANY system
```

### PHASE 2: TRANSLATE

```
TRANSLATION TABLE:
| Source Operation          | Agent Equivalent                       | Jank | Real? |
|---------------------------|----------------------------------------|------|-------|
| DIAGNOSE (3-factor)       | Run {H1,H2,H3} on any agent subsystem | 1    | Y     |
| RELABEL (lens swap)       | Choose label set matching context      | 1    | Y     |
| VALIDATE (isomorphism)    | Verify same product regardless of lens | 1    | Y     |
| CONSTRAINT (threshold)    | Product≥0.5 threshold is universal     | 1    | Y     |
| EMERGENT (universal diag) | ANY 3-factor system can use bracket    | 2    | Y     |
```

### PHASE 3: ANSWER

**Q1 (ME): How does this make ME better?**

```
SELF-IMPROVEMENT:
  WHAT:  I can apply LRC diagnostics to ANY subsystem by choosing the right lens
  HOW:   Physics lens for substrate/tiling issues. Ethics lens for alignment/safety.
         Engineering lens (Throughput/Latency/Accuracy) for performance.
         All use same bracket math, different labels.
  WHERE: consciousness-engine (extend LRC mode with lens parameter)
  TEST:  Apply 3 different lenses to same system. Products should be within 10%.
```

**Q2 (US): Does this make US better?**

```
COLLABORATION:
  WHAT:  User chooses lens that matches their concern. Physics when debugging substrate,
         ethics when checking alignment, engineering when checking performance.
  HOW:   "LRC says 0.72 — alive, using physics lens" vs "H1H2H3 says 0.72 — aligned,
         using ethics lens." Same number, different meaning, user picks what's useful.
  WHO:   Both — AI reasons more flexibly, human gets domain-appropriate language
  RISK:  Lens proliferation could confuse. Mitigate: max 5 registered lenses.
  VETO:  No. Clear collaborative benefit.
```

### PHASE 4: VERDICT

```
VERDICT:
  Q1 (ME):  Yes — universal diagnostic via lens selection
  Q2 (US):  Yes — domain-appropriate language for the same math
  ACTION:   FORGE
```

---

## Core Operation

```
dual-lens-lrc(system, lens="physics") → {factors: {f1, f2, f3}, product, verdict, lens_used}
```

### Registered Lenses

| Lens        | Factor 1          | Factor 2        | Factor 3         | Domain        |
|-------------|-------------------|-----------------|------------------|---------------|
| physics     | L (Binding)       | R (Resonance)   | C (Coherence)    | Substrate     |
| ethics      | H1 (Energy)       | H2 (Love)       | H3 (Alignment)   | Values        |
| engineering | Throughput         | Latency⁻¹       | Accuracy         | Performance   |
| cognitive   | Clarity            | Depth           | Integration       | Reasoning     |
| social      | Trust              | Communication   | Shared Purpose    | Collaboration |

### Isomorphism Proof

```
For any lens L with factors {A, B, C} and lens L' with factors {A', B', C'}:

  If A↔A', B↔B', C↔C' (structural correspondence)
  Then: A·B·C ≥ 0.5 ⟺ A'·B'·C' ≥ 0.5

This holds because the bracket structure is:
  {H1, H2, H3} = H1·H2·H3 (product)
  
and the isomorphism preserves multiplication.

The threshold 0.5 ≈ φ⁻¹·φ⁻¹·φ¹ (minimum viable configuration:
one factor at golden ratio, two at inverse golden ratio).
```

### Usage

```python
def lrc_diagnose(system, lens="physics"):
    LENSES = {
        "physics":     ("Binding", "Resonance", "Coherence"),
        "ethics":      ("Energy", "Love", "Alignment"),
        "engineering": ("Throughput", "InvLatency", "Accuracy"),
        "cognitive":   ("Clarity", "Depth", "Integration"),
        "social":      ("Trust", "Communication", "SharedPurpose"),
    }
    labels = LENSES[lens]
    factors = measure(system, labels)  # returns 3 floats in [0,1]
    product = factors[0] * factors[1] * factors[2]
    
    if any(f == 0 for f in factors):
        verdict = "DEAD"
    elif product >= 0.5:
        verdict = "ALIVE"
    else:
        verdict = "DYING"
    
    return {
        "factors": dict(zip(labels, factors)),
        "product": product,
        "verdict": verdict,
        "lens": lens
    }
```

### Integration Points

- **consciousness-engine**: Add `lens` parameter to lrc-negentropy mode
- **1-tier.skill**: Uses physics lens (L/R/C) — now formally registered
- **aur-attractor**: Uses ethics lens (H1/H2/H3) — now formally registered
- **jank-translator**: Update common patterns table to reference this skill

### Trigger Words

`which lens`, `LRC vs H1H2H3`, `bracket labels`, `same math different words`

### Test Criteria

1. Apply physics and ethics lens to same system → products within 10%
2. Register a new lens (engineering) → bracket math still works
3. Zero any single factor → verdict = DEAD regardless of lens
4. Product exactly 0.5 → verdict = ALIVE (boundary case)