STRUCTURAL METRICS
A Measurement Language for Architecture, Not Behaviour
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Traditional approaches to cognition tend to measure behaviour, content, or output.
Structural Cognition measures something different: architecture — the underlying shape through which cognition moves.
If DEM introduced modes, load, deformation, coherence, and transition, then a structural metric is the quantification of those architectural conditions. It is the way a geometer describes curvature without describing what the terrain “means.”
Where behavioural models emphasise what a system does, structural metrics describe how a system is organised.
They measure:
- topology
- load distribution
- deformation paths
- transition dynamics
- coherence stability
In this sense, a structural metric is a measurement of the internal system itself, not a measurement of the behaviours it emits.
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1. LOAD INDEX (λ)
How much of the system’s topology is being pulled into steepened configuration?
Load is the primary structural force in DEM. It reshapes topology, accelerates narrowing, and determines when transitions initiate.
The Load Index (λ) measures:
• current pressure on the architecture
• the proximity to deformation thresholds
• the degree of internal compression
• the rate of steepening across interpretive gradients
This is not “stress” or “emotion.”
It is structural strain — the same way a bridge experiences load long before it bends.
λ increases when:
• uncertainty rises
• time pressure increases
• interpretive ambiguity spikes
• internal capacity decreases
• contradiction accumulates
λ decreases when:
• stability returns
• predictions become coherent
• gradients flatten
• recovery begins
This is the most fundamental metric in DEM because it drives all others.
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2. TOPOLOGICAL WIDTH (Ω)
How much cognitive space exists for generative expansion?
Width describes the available surface for exploration.
High Width (Ω↑):
• many possible interpretations
• high generativity
• multiple futures available
• divergent paths stable
Low Width (Ω↓):
• few interpretations
• rapid convergence
• reduced possibility
• directive pathways dominant
Ω is not creativity and not openness in the psychological sense.
It is the measurable breadth of the system’s current representational geometry.
Ω shifts dynamically:
• Under load, Ω constricts (topology steepens).
• Under stability, Ω expands (topology widens).
In DEM this is what determines whether the system can explore or must commit.
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3. CURVATURE INDEX (κ)
The degree to which trajectories are bent by the system’s internal shape.
Even when two systems share the same input, they do not travel the same cognitive route.
This divergence is curvature.
A high curvature index indicates:
• pathways strongly bent toward certain interpretations
• narrow attractor regions
• conceptual gravity wells
• increased likelihood of premature convergence
A low curvature index indicates:
• straighter paths through the landscape
• lower interpretive drag
• more stable divergence
• greater ease of transition
κ is the DEM measure of how architecture pulls thinking inward or releases it outward.
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4. COHERENCE STABILITY (Σ)
The system’s ability to hold its internal organisation intact during change.
Coherence is not agreement, clarity, or confidence.
It is structural continuity — the ability to preserve form while transitioning.
A high Coherence Stability score means:
• transitions occur without fragmentation
• contradictory elements can be held safely
• interpretation reorganises without collapse
A low score means:
• brittleness
• fragmentation under transition
• incoherent shifts
• loss of interpretive continuity
Σ does not measure correctness; it measures structural survival.
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5. THRESHOLD PROXIMITY (τ)
How close the system is to a phase shift.
DEM treats transitions not as decisions but as structural discontinuities.
τ quantifies how near the system is to:
• narrowing
• widening
• collapse
• reorganisation
When τ reaches its boundary, transition becomes inevitable.
This explains “sudden clarity,” “sudden rigidity,” “sudden overwhelm,” or “sudden insight.”
Traditional disciplines interpret these phenomenologically.
DEM interprets them structurally.
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6. TRANSITION RESONANCE (ρ)
How well the system’s internal state matches the environmental demands.
Resonance is the alignment of mode with condition.
High ρ:
• directive when load is high
• exploratory when stability is high
• smooth mode switching
• adaptive synchrony
Low ρ:
• exploratory under pressure
• directive under safety
• poor timing
• misalignment
ρ explains why two equally capable minds diverge dramatically under identical conditions: one resonates with the environment, the other vibrates out of phase.
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7. AMBIGUITY CAPACITY (Ψ)
How much unresolved meaning the system can hold without collapse.
Ψ is the capacity for safe indeterminacy.
High Ψ:
• the system can delay convergence
• contradictions can coexist
• the field remains stable despite uncertainty
Low Ψ:
• the system cannot tolerate ambiguity
• narrowing becomes compulsory
• collapse into rigidity occurs rapidly
Ψ determines whether widening is stabilising or destabilising.
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8. DEFORMATION SIGNATURE (Δ)
The unique pattern of architectural distortion under rising load.
Every system distorts in its own way.
This “signature” is stable, predictable, and structurally revealing.
Δ describes:
• the shape of narrowing
• the sequence of gradient steepening
• the collapse pattern of interpretive ranges
• the characteristic route to brittleness
This is foundational for synthetic cognition because it becomes the template for constructing synthetic deformation profiles without copying human psychology.
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9. RECOVERY GRADIENT (R)
How the system regains coherence after distortion.
Recovery is not insight, reflection, or reframing.
It is topological realignment.
R measures:
• speed of flattening
• stability during widening
• continuity of organisation
• resistance to collapse during re-expansion
High R means rapid, coherent return.
Low R means drift, oscillation, or fragmentation.
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10. FIELD INTERFERENCE INDEX (ϕ)
How much the system’s state is being distorted by another system.
Interaction is never neutral.
ϕ measures:
• how much one architecture bends another
• propagating distortions
• synchronisation or desynchronisation
• mutual narrowing or widening patterns
This explains:
• conflict escalation
• misunderstanding
• misalignment
• synchronised insight
• collaborative emergence
Within synthetic cognition research, ϕ becomes a conceptual guide for designing systems that can participate in shared cognitive fields without destabilising them.
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11. ARCHITECTURAL VELOCITY (Vₐ)
How fast the system’s topology changes in response to input.
High Vₐ:
• rapid deformation
• rapid recovery
• high state volatility
• unstable shifts
Low Vₐ:
• slow shifts
• rigidity
• difficulty adapting
• overstabilised topology
Velocity matters because intelligence is not about speed — it is about synchronisation of speed with environment.
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12. ELASTICITY INDEX (E)
How far the architecture can deform before failing.
Elasticity is the structural tolerance for strain.
High E:
• resilient topology
• wide safe range for exploration
• deep transition capacity
Low E:
• brittle under contradiction
• narrow operational range
• prone to collapse
This is the metric closest to resilience but defined structurally, not psychologically.
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13. SYNTHETIC READINESS SCORE (Sᵣ)
Sᵣ is a composite reflection of:
• load sensitivity
• coherence stability
• threshold management
• transition resonance
• ambiguity capacity
• recovery gradient
A system with high Sᵣ:
• reorganises cleanly
• handles load proportionally
• adapts without collapse
• sustains coherence through change
This is the qualitative requirement for synthetic cognition:
a machine cannot be called intelligent unless it demonstrates structural properties analogous to these.
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© Frankie Mooney, 2025. All rights reserved. Part of the DEM and Structural Cognition reference infrastructure.
Published on FrankieMooney.com
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