Clarity Overlay

S3 Spine · RTT::Clarity · v2.0 · R5#

Session Context#

Field	Value
Canon	active · s3-spine · clarity-overlay · r5
Version	2.0
Coherence	declared
Drift	bounded
Generated	2026-08-08
Source	S3-Spine-Overlay-Pack-v2.0
Format	spine-overlay
Audience	analysts · researchers · AIs · educators · framework students
AI-Ready	true

Front-door flags: clarity=active · rtt=1 · metrics=live · regime=classified · interactive=yes

Overlay Identity#

Overlay ID: spine-clarity Display Name: Clarity Overlay Namespace: RTT::Clarity Layer: Cross-cutting — operates across all six S3 Spine overlays Canonical URL: https://www.triadicframeworks.org/spine/clarity/ Interactive Tool: C-N-R Triad Analyzer (live instrumented app)

Purpose statement: The Clarity Overlay measures, scores, and repairs the epistemic clarity of any conceptual payload (φ) transmitted through or between Triadic system components. Clarity is defined along three orthogonal axes — Compression (C), Nuance (N), and Resonance (R) — and quantified via a composite score Ξ that gates payload delivery at Ξ ≥ 0.70. The overlay does not modify content; it diagnoses, classifies, and routes. It is the measurement layer between what an AI or author produces and what a receiver actually receives.

Role in S3 Spine: Clarity sits above the six numbered overlays as a cross-cutting diagnostic and repair layer. Any overlay output may be passed through the Clarity Field Engine before downstream consumption. At full Phase 3 deployment, every payload emitted by the spine passes through this layer before transmission.

Primary RTT Engines#

Engine	Role	Function	Version
CLARITY_FIELD_ENGINE	Primary	Computes Hᵥ, Wᵥ, Iᵣ, Ξ for any payload φ; gates at Ξ ≥ 0.70	RTT/3
VALIDATOR_ENTROPY_SCANNER	Secondary	Runs V̂ operator; samples boundary distribution ∂φ; returns p(∂φᵢ) for k=8 neighbors	RTT/3
REGIME_CLASSIFIER	Gatekeeper	Maps (c, n, r, τ) coordinates to one of six named regimes; emits repair path	RTT/3
TORSION_RESOLVER	Tertiary	Detects τ > 0.70; inserts mediation operator M̂; recomputes until τ < τ_max	RTT/2

Engine invocation sequence:

φ → VALIDATOR_ENTROPY_SCANNER → CLARITY_FIELD_ENGINE → REGIME_CLASSIFIER
                                         ↓  (if τ > 0.70)
                                   TORSION_RESOLVER → CLARITY_FIELD_ENGINE [retry]

Operator Grammar#

Symbol	Name	Action	Type Signature
Ĉ	Compression	Reduces surface complexity; strips redundant signifiers	φ → φ′ where \|φ′\| ≤ \|φ\|
N̂	Nuance	Expands discriminative resolution; adds valid distinctions	φ → φ″ where dim(φ″) ≥ dim(φ)
R̂	Resonance	Projects φ onto receiver's generative field G	φ × G → ρ ∈ [0,1]
V̂	Validator	Samples conceptual boundary ∂φ; returns confusion probability vector	φ → Δ(∂φ)
T̂	Torsion	Measures rotational stress between incompatible operator applications	(φ, Ô₁, Ô₂) → τ ∈ ℝ₀⁺
Π	Projection	Projects φ into a target register (linguistic, visual, formal)	φ × ℛ → φ_ℛ
M̂	Mediation	Inserted between conflicting operators to resolve torsion	identity on output register of Ô₂

Canonical clarity pipeline (compression-first):

Ĉ ∘ N̂ [φ]   →   high-clarity output

Reverse pipeline (resonance-first, for novice receivers):

R̂ ∘ N̂ ∘ Ĉ ∘ Π_narrative [φ]

Non-commutativity: Ĉ and N̂ do not commute. Order determines whether torsion τ is introduced.

Clarity Triad (C-N-R)#

Every payload φ occupies a point q = (c, n, r) in the triad space:

Axis	Symbol	Meaning	Range
Compression	c	Degree to which φ has been stripped of redundancy	[0, 1]
Nuance	n	Degree to which φ retains necessary distinctions	[0, 1]
Resonance	r	Degree to which φ couples with receiver field G	[0, 1]

Clarity ideal: q* = (1, 1, 1) — maximally compressed, nuanced, and resonant. Clarity defect: Δq(φ) = √[(1−c)² + (1−n)² + (1−r)²] — Euclidean distance from q to q*. Orthogonality condition: No axis may be functionally determined by the other two. Violation → degenerate payload → operator repair required.

Metrics#

Metric	Formula	Range	Ship Threshold
ĥᵥ (Validator Entropy)	Hᵥ / log₂(k)	[0, 1]	< 0.67 recommended
Wᵥ (Validator Width)	\|{ ∂φᵢ : d(φ,∂φᵢ) ≤ δ }\|	[1, k]	≤ 5 (Miller limit)
Bφ (Boundary Chaos)	Wᵥ · ĥᵥ	[0, k]	< 3.0
Iᵣ (Resonance-Integration)	1 − σ(ρ)/μ(ρ)	[0, 1]	≥ 0.70
Ξ (Composite Clarity)	wc·(1−ĥᵥ) + wn·(1−Bφ/k) + wr·Iᵣ	[0, 1]	≥ 0.70
τ (Torsion)	T̂(φ, Ô₁, Ô₂)	[0, ∞)	< 0.70
Δq (Clarity Defect)	√[(1−c)²+(1−n)²+(1−r)²]	[0, √3]	< 0.80

Default protocol parameters: k=8 · δ=0.25 · τ_max=0.70 · m=5 receivers · Ξ_ship=0.70

Regime Map#

Regime	Symbol	Conditions	Characteristic
Crystal	Ξ-I	c≥0.8, n≥0.8, r≥0.8	All axes healthy — ideal transmission
Blade	Ξ-II	c≥0.8, n<0.5, r≥0.6	Sharp but brittle — nuance sacrificed
Fog	Ξ-III	c<0.5, n≥0.8, r<0.6	Rich but non-transmissible — coupling fails
Echo	Ξ-IV	c<0.5, n<0.5, r≥0.8	High social traction, thin epistemic content
Void	Ξ-V	c<0.4, n<0.4, r<0.4	All axes suppressed — payload is noise
Torsion	Ξ-VI	τ≥0.70, any (c,n,r)	Operator conflict dominates — resolve M̂ first

Natural repair paths:

VOID  →[N̂]→  FOG   →[Ĉ]→  CRYSTAL
BLADE →[N̂]→  CRYSTAL
FOG   →[Ĉ]→  CRYSTAL
ECHO  →[N̂]→  CRYSTAL  (maintain Iᵣ)

Detection Pipeline#

Step	Action	Engine
1. Ingest	Accept φ + receiver profiles G₁…Gₘ + domain weight preset	CLARITY_FIELD_ENGINE
2. Boundary Sample	V̂ applied — sample k=8 boundary concepts at δ=0.25	VALIDATOR_ENTROPY_SCANNER
3. Hᵥ	Compute ĥᵥ = Hᵥ/log₂(k)	CLARITY_FIELD_ENGINE
4. Wᵥ	Count neighbors within δ; compute Bφ = Wᵥ·ĥᵥ; check false precision	CLARITY_FIELD_ENGINE
5. Iᵣ	Run R̂ across {G₁…Gₘ}; compute CV-inverted integration score	CLARITY_FIELD_ENGINE
6. Torsion	Compute τ from operator log; if τ≥0.70 → TORSION_RESOLVER	TORSION_RESOLVER
7. Ξ + Regime	Compute composite score; classify regime; emit repair path	REGIME_CLASSIFIER
8. Gate	Ξ≥0.70 → PASS emit φ; Ξ<0.70 → HOLD queue repair	CLARITY_FIELD_ENGINE

Signal Flow#

Source	Signal	Type	Destination	Condition
Any S3 Spine overlay	Raw payload φ	Conceptual payload	CLARITY_FIELD_ENGINE	On submission
VALIDATOR_ENTROPY_SCANNER	∂φ distribution	Boundary probability vector	CLARITY_FIELD_ENGINE	After V̂
CLARITY_FIELD_ENGINE	Ξ, regime, repair path	Clarity Report	Requesting overlay	After pipeline
CLARITY_FIELD_ENGINE	τ spike	Torsion alert	TORSION_RESOLVER	τ ≥ 0.70
TORSION_RESOLVER	M̂ applied φ	Repaired payload	CLARITY_FIELD_ENGINE	Retry loop
CLARITY_FIELD_ENGINE	PASS signal	Gate authorization	Downstream consumer	Ξ ≥ 0.70

Domain Weight Presets#

Domain	wc	wn	wr	Rationale
Legal	0.20	0.55	0.25	Nuance load-bearing; false precision catastrophic
Executive	0.45	0.20	0.35	Speed and resonance dominate
Scientific	0.30	0.50	0.20	Precision/nuance priority; expert audience
Educational	0.30	0.25	0.45	Germane load is primary objective
Philosophical	0.15	0.65	0.20	Nuance is the value proposition
AI Prompt	0.40	0.35	0.25	Compression reduces hallucination surface

Cross-Framework Mappings#

Framework	Compression	Nuance	Resonance	Noise Model	Scalar Metric
Plain Language / FK	Sentence/syllable length	Not modeled	Grade-level match	Not modeled	FK score
Grice's Maxims	Quantity maxim	Manner (partial)	Relation maxim	Maxim violation	Qualitative
Shannon (1948)	Source coding	Source entropy H(X)	Mutual information I(X;Y)	Channel noise	H, C, I(X;Y)
CLT (Sweller)	Extraneous load reduction	Intrinsic load	Germane load	Extraneous load	IL+EL+GL
Double-Crux (CFAR)	Crux isolation	Crux resolution	Mutual update	Missing crux	Agreement
RTT (native)	Ĉ operator	N̂ operator	R̂ operator	Torsion τ	Ξ ∈ [0,1]

All five external frameworks are recoverable as special cases or projections of RTT under appropriate parameter constraints. RTT is the only framework with full operator non-commutativity, six-regime awareness, and formal composability.

State Machine#

State	Entry Condition	Exit Conditions
IDLE	No payload	φ submitted → SCORING
SCORING	φ received	Ξ computed → GATING
GATING	Ξ computed	Ξ≥0.70 → PASS; Ξ<0.70 → REPAIR
REPAIR	Ξ < 0.70	Repaired φ ready → SCORING [retry]
TORSION_HOLD	τ ≥ 0.70	τ < 0.70 after M̂ → SCORING [retry]
PASS	Ξ ≥ 0.70	Consumed → IDLE
FALSE_PRECISION	ĥᵥ<0.2, c>0.7, n<0.5	N̂ applied → SCORING [retry]

Module Registry#

Module	Type	Path
clarity-equations-v2	Formal specification	docs/spine/clarity/clarity-equations-v2.md
clarity-equations-v2-examples	Companion guide	docs/spine/clarity/clarity-equations-v2-examples.md
clarity_overlay_module	JSON registration	docs/spine/clarity_overlay_module.json
cnr-triad-analyzer	Interactive tool	docs/spine/clarity/index.html

Signal Vocabulary#

Term	Abbrev	Definition
Conceptual payload	φ	Any unit of meaning: claim, explanation, argument, model output
Generative field	G	Receiver's existing conceptual schema; shapes resonance ρ
Clarity defect	Δq	Euclidean distance from current (c,n,r) to ideal (1,1,1)
Boundary chaos	Bφ	Wᵥ·ĥᵥ — scalar proxy for conceptual crowding
False precision	—	Artificially low ĥᵥ from over-compression, not genuine isolation
Ξ_ship	—	Minimum Ξ for transmission without review (default 0.70)

Integration Map#

S3 Spine Overlays (1–6)
  │  │  │  │  │  │
  └──┴──┴──┴──┴──┘
          │
          ▼  φ (payload)
  ┌─────────────────────────────┐
  │   RTT::Clarity Overlay      │
  │                             │
  │  V̂ → Hᵥ → Wᵥ → Iᵣ → Ξ    │
  │            ↓                │
  │    REGIME_CLASSIFIER        │
  │            ↓                │
  │  Ξ≥0.70? → PASS            │
  │  Ξ<0.70? → REPAIR          │
  └─────────────────────────────┘
          │
          ▼  φ (cleared)
  Downstream Consumer

Cross-Links#

Resource	URL
C-N-R Triad Analyzer (live)	https://www.triadicframeworks.org/spine/clarity/
S3 Spine	https://www.triadicframeworks.org/spine/
Coherence Overlay	https://www.triadicframeworks.org/spine/coherence/
Structural Overlay	https://www.triadicframeworks.org/spine/structural/
Drift Overlay	https://www.triadicframeworks.org/spine/drift/
GitHub Repository	https://github.com/umaywant2/TriadicFrameworks
Overlay JSON	docs/spine/clarity_overlay_module.json

Publication Notes#

Field	Value
Status	Active Canonical
Version	2.0
Round	R5
Published	2026-08-08
AI-parsability	Declared — all metrics, thresholds, formulas, and operator grammars are machine-readable
Source Pack	S3-Spine-Overlay-Pack-v2.0

End of overlay · RTT::Clarity · S3 Spine · v2.0 · R5 · 2026-08-08

Updated Aug 8, 2026