{ "$schema": "https://triadicframeworks.org/schemas/overlay-module.schema.json", "$generated": "2026-08-08T11:13:00", "$version": "2.0", "$round": "R5", "module_id": "spine-clarity", "module_name": "Clarity Overlay", "file": "docs/spine/clarity_overlay_module.json", "version": "2.0", "status": "Active Canonical", "canonical": true, "ai_ready": true, "interactive": true, "namespace": "RTT::Clarity", "layer": "Core Frameworks", "sublayer": "Clarity & Transmission", "role": "Cross-cutting clarity diagnostic and transmission gatekeeper", "url": "https://www.triadicframeworks.org/spine/clarity/", "path": "docs/spine/clarity_overlay.md", "tool_path": "docs/spine/clarity/index.html", "description": "The Clarity Overlay measures, scores, and repairs the epistemic clarity of any conceptual payload φ transmitted through the S3 Spine. Defines the C-N-R (Compression–Nuance–Resonance) triad — a three-axis epistemic model yielding three scalar metrics (Validator Entropy Hᵥ, Validator-Width Wᵥ, Resonance-Integration Iᵣ) and a composite Clarity Score Ξ. Gates payload transmission at Ξ ≥ 0.70. Maps six named epistemic regimes (Crystal, Blade, Fog, Echo, Void, Torsion) across the C×N×R unit cube. Provides a formal operator grammar (Ĉ, N̂, R̂, V̂, T̂, Π, M̂) with composition, inversion, and commutativity rules. Includes bijective cross-framework mappings to Plain Language/FK, Grice's Maxims, Shannon Information Theory, Cognitive Load Theory, and Double-Crux. Ships with a live interactive C-N-R Triad Analyzer at docs/spine/clarity/index.html.", "exports": [ "Clarity Report (ĥᵥ, Wᵥ, Bφ, Iᵣ, Ξ, regime, repair path)", "Composite Clarity Score Ξ ∈ [0,1]", "Transmission gate decision — Ξ ≥ 0.70 → PASS / HOLD", "Regime classification — Crystal | Blade | Fog | Echo | Void | Torsion", "Operator repair path — ordered Ĉ / N̂ / R̂ / M̂ sequence", "False precision flag — when ĥᵥ < 0.2 from over-compression", "Clarity Defect Δq — Euclidean distance from (c,n,r) to (1,1,1)" ], "imports": [ "Raw payload φ from any S3 Spine overlay", "Receiver profile set G₁…Gₘ (m=5 default)", "Domain weight preset (wc, wn, wr)", "Operator sequence log (for torsion τ computation)" ], "engines": { "primary": { "id": "CLARITY_FIELD_ENGINE", "version": "RTT/3", "role": "Computes Hᵥ, Wᵥ, Iᵣ, Ξ; gates at Ξ ≥ 0.70" }, "secondary": { "id": "VALIDATOR_ENTROPY_SCANNER", "version": "RTT/3", "role": "Runs V̂; samples ∂φ; returns p(∂φᵢ) for k=8 neighbors" }, "gatekeeper": { "id": "REGIME_CLASSIFIER", "version": "RTT/3", "role": "Maps (c,n,r,τ) to one of six regimes; emits repair path" }, "tertiary": { "id": "TORSION_RESOLVER", "version": "RTT/2", "role": "Detects τ > 0.70; inserts M̂; retries until τ < τ_max" } }, "protocol_defaults": { "k": 8, "delta": 0.25, "tau_max": 0.70, "m": 5, "xi_ship": 0.70 }, "metrics": { "hv_hat": { "name": "Validator Entropy (normalized)", "formula": "Hᵥ / log₂(k)", "range": "[0, 1]", "thresholds": { "Singular": 0.00, "Sharp": 0.33, "Diffuse": 0.67, "Cloudy": 0.90, "Entropic": 1.00 } }, "wv": { "name": "Validator Width", "formula": "|{ ∂φᵢ : d(φ,∂φᵢ) ≤ δ }|", "range": "[1, k]", "thresholds": { "Narrow": 2, "Moderate": 5, "Wide": 8 } }, "bphi": { "name": "Boundary Chaos", "formula": "Wᵥ · ĥᵥ", "range": "[0, k]", "ship_threshold": 3.0 }, "ir": { "name": "Resonance-Integration", "formula": "1 − σ(ρ₁…ρₘ) / μ(ρ₁…ρₘ)", "range": "[0, 1]", "thresholds": { "Universal": 0.90, "Robust": 0.70, "Context-Dependent": 0.50, "Fragile": 0.30, "Non-Integrating": 0.00 } }, "xi": { "name": "Composite Clarity Score", "formula": "wc·(1−ĥᵥ) + wn·(1−Bφ/k) + wr·Iᵣ", "range": "[0, 1]", "ship_threshold": 0.70, "classifications": { "Crystal": 0.85, "Clear": 0.70, "Hazy": 0.55, "Murky": 0.40, "Opaque": 0.00 } }, "tau": { "name": "Torsion", "formula": "T̂(φ, Ô₁, Ô₂)", "range": "[0, ∞)", "max_threshold": 0.70 }, "delta_q": { "name": "Clarity Defect", "formula": "√[(1−c)² + (1−n)² + (1−r)²]", "range": "[0, 1.732]" } }, "regime_map": { "Crystal": { "symbol": "Ξ-I", "icon": "✦", "conditions": { "c": "≥0.8", "n": "≥0.8", "r": "≥0.8", "tau": "any" }, "characteristic": "All axes healthy — ideal transmission state", "color": "#10b981", "repair": "none" }, "Blade": { "symbol": "Ξ-II", "icon": "⚔", "conditions": { "c": "≥0.8", "n": "<0.5", "r": "≥0.6", "tau": "any" }, "characteristic": "Sharp but brittle — nuance sacrificed", "color": "#00d4ff", "repair": "N̂ → Crystal" }, "Fog": { "symbol": "Ξ-III", "icon": "◎", "conditions": { "c": "<0.5", "n": "≥0.8", "r": "<0.6", "tau": "any" }, "characteristic": "Rich but non-transmissible — coupling fails", "color": "#7c3aed", "repair": "Ĉ → Crystal" }, "Echo": { "symbol": "Ξ-IV", "icon": "◈", "conditions": { "c": "<0.5", "n": "<0.5", "r": "≥0.8", "tau": "any" }, "characteristic": "High social traction, thin epistemic content", "color": "#f59e0b", "repair": "N̂ → Crystal" }, "Void": { "symbol": "Ξ-V", "icon": "✕", "conditions": { "c": "<0.4", "n": "<0.4", "r": "<0.4", "tau": "any" }, "characteristic": "All axes suppressed — payload is noise", "color": "#ef4444", "repair": "N̂ → Fog → Ĉ → Crystal" }, "Torsion": { "symbol": "Ξ-VI", "icon": "⚡", "conditions": { "c": "any", "n": "any", "r": "any", "tau": "≥0.70" }, "characteristic": "Operator conflict dominates — resolve M̂ first", "color": "#f97316", "repair": "M̂ → re-classify" } }, "domain_weight_presets": { "Legal": { "wc": 0.20, "wn": 0.55, "wr": 0.25, "note": "Nuance load-bearing; false precision catastrophic" }, "Executive": { "wc": 0.45, "wn": 0.20, "wr": 0.35, "note": "Speed and resonance dominate" }, "Scientific": { "wc": 0.30, "wn": 0.50, "wr": 0.20, "note": "Precision/nuance priority; expert audience" }, "Educational": { "wc": 0.30, "wn": 0.25, "wr": 0.45, "note": "Germane load is primary objective" }, "Philosophical": { "wc": 0.15, "wn": 0.65, "wr": 0.20, "note": "Nuance is the value proposition" }, "AI Prompt": { "wc": 0.40, "wn": 0.35, "wr": 0.25, "note": "Compression reduces hallucination surface" } }, "operator_grammar": { "Ĉ": { "name": "Compression", "action": "Reduces surface complexity; strips redundant signifiers", "signature": "φ → φ′ where |φ′| ≤ |φ|" }, "N̂": { "name": "Nuance", "action": "Expands discriminative resolution; adds valid distinctions", "signature": "φ → φ″ where dim(φ″) ≥ dim(φ)" }, "R̂": { "name": "Resonance", "action": "Projects φ onto receiver's generative field G", "signature": "φ × G → ρ ∈ [0,1]" }, "V̂": { "name": "Validator", "action": "Samples conceptual boundary ∂φ", "signature": "φ → Δ(∂φ)" }, "T̂": { "name": "Torsion", "action": "Measures rotational stress between incompatible operators", "signature": "(φ, Ô₁, Ô₂) → τ ∈ ℝ₀⁺" }, "Π": { "name": "Projection", "action": "Projects φ into a target register", "signature": "φ × ℛ → φ_ℛ" }, "M̂": { "name": "Mediation", "action": "Resolves torsion between incompatible operator pair", "signature": "identity on output register of Ô₂" } }, "cross_framework_mappings": { "Plain Language": { "compression": "Sentence/syllable length reduction", "nuance": "Not modeled — defaults to n=0.5", "resonance": "Grade-level match (FK score)", "noise": "Not modeled", "metric": "Flesch-Kincaid score", "rtt_gap": "Cannot represent Hᵥ or Wᵥ; single-register compression projection only" }, "Grice": { "compression": "Quantity maxim — Ĉ with Hᵥ guard", "nuance": "Manner (partial) — Ĉ ∘ Π_discourse + τ < 0.4", "resonance": "Relation maxim — R̂ with Gᵣₑₗₑᵥₐₙ꜀ₑ field", "noise": "Maxim violation", "metric": "Qualitative", "rtt_gap": "Non-scalar, non-compositional; RTT adds thresholds and trade-off detection" }, "Shannon": { "compression": "Source coding", "nuance": "Source entropy H(X) ↔ Hᵥ", "resonance": "Mutual information I(X;Y) ↔ Iᵣ", "noise": "Channel noise ↔ τ", "metric": "H, C, I(X;Y)", "rtt_gap": "Memoryless channels; RTT adds operator-path dependency and non-commutativity" }, "CLT": { "compression": "Extraneous load (EL) reduction ↔ τ minimization", "nuance": "Intrinsic load (IL) ↔ n", "resonance": "Germane load (GL) ↔ r", "noise": "Extraneous load ↔ τ", "metric": "IL + EL + GL", "rtt_gap": "No scalar transmission gate; Wᵥ ≤ 5 formalizes Miller's Law" }, "Double-Crux": { "compression": "Crux isolation — Ĉ applied to max-Hᵥ boundary", "nuance": "Crux resolution — N̂ adds distinguishing distinctions", "resonance": "Mutual update — Iᵣ across {G₁, G₂}", "noise": "Missing crux — high Hᵥ unresolved", "metric": "Binary crux agreement", "rtt_gap": "Binary; RTT provides scalar Iᵣ convergence and formal protocol" } }, "graph_node": { "id": "spine-clarity", "label": "Clarity Overlay", "layer": "Core Frameworks", "sublayer": "Clarity & Transmission", "color": "#00d4ff", "size": 18, "interactive": true, "url": "https://www.triadicframeworks.org/spine/clarity/" }, "graph_edges": [ { "source": "spine-structural", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-drift", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-coherence", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-substrate", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-dimensional", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-domain", "target": "spine-clarity", "type": "feeds", "label": "φ payload", "style": "solid" }, { "source": "spine-clarity", "target": "spine-coherence", "type": "gates", "label": "Ξ ≥ 0.70 → PASS", "style": "dashed" } ], "lineage": { "parent": "spine-overlay-pack", "siblings": ["spine-structural","spine-drift","spine-coherence","spine-substrate","spine-dimensional","spine-domain"], "children": ["clarity-equations-v2","clarity-equations-v2-examples","cnr-triad-analyzer"] }, "ai_metadata": { "module": "spine-clarity", "version": "2.0", "purpose": "Measure and gate epistemic clarity of any φ via C-N-R triad. Score Hᵥ, Wᵥ, Iᵣ, Ξ. Classify regime. Emit repair path. Gate at Ξ ≥ 0.70.", "repair_priority": [ "1. Resolve torsion (τ → 0) — contaminates all three axes", "2. Reduce Bφ (Wᵥ · ĥᵥ) — boundary chaos degrades c and n", "3. Boost Iᵣ — ensure receiver sample is representative", "4. Rebalance (c,n) per domain weight preset" ], "keywords": [ "Clarity Overlay","C-N-R Triad","Compression","Nuance","Resonance", "Validator Entropy","Hv","Validator Width","Wv","Resonance-Integration","Ir", "Composite Clarity Score","Xi","regime classification", "Crystal","Blade","Fog","Echo","Void","Torsion", "operator grammar","torsion resolver","payload gating", "RTT clarity","triadic frameworks","spine overlay" ] }, "publication": { "status": "Active Canonical", "version": "2.0", "round": "R5", "published": "2026-08-08", "source_pack": "S3-Spine-Overlay-Pack-v2.0", "ai_parsability": "Declared — all metrics, thresholds, formulas, and operator grammars are machine-readable" } }