Abstract

Attachment theory describes the early relational patterns that shape how individuals expect, interpret, and regulate connection. AToM reframes these patterns as prototypical coherence geometries—not fixed types, but dynamic attractors describing how a nervous system maintains (or struggles to maintain) relational stability under constraint. This article offers a careful, clinically responsible geometric translation of attachment research, integrating insights from affective neuroscience, developmental psychology, and information geometry. These manifold shapes are intended as conceptual scaffolds, not prescriptions, and are accompanied by limitations, cultural qualifiers, and testable predictions grounded in modern physiological and linguistic measurement tools.

1. Why Geometry Helps (If Used Carefully)

Attachment theory has always been about patterns—patterns of expectation, patterns of regulation, patterns of approach and withdrawal, patterns of staying connected or pulling away. These patterns are developmental, relational, cultural, neurobiological, and experiential all at once. They operate simultaneously in the nervous system, the body, the mind, and the social field. They are dynamic, reciprocal, and often nonlinear. Geometry helps because it gives us a way to see these patterns.

Geometry provides a visual, structural map for complex relational dynamics without claiming that these dynamics are simple. Most clinicians, researchers, and even lay readers can picture smoothness, curvature, tightening, fragmentation, or distance. These are intuitive ways of representing the stability or instability of relational experience. A smooth pathway feels different than a jagged one; a highly curved region feels different than a flat one. These differences already show up in everyday attachment language—“roller coaster relationships,” “stable foundations,” “emotional whiplash,” “walls go up,” “something breaks inside,” “we fell back into sync.” Geometry gives those metaphors structure.

But the usefulness of geometry does not erase the core truth: human systems are high-variance, soft-constraint domains. This phrase from AToM is essential. Human experience cannot be modeled with the tight invariance of physics. There is no single differential equation for intimacy, no Riemannian metric that perfectly captures trust, no single curvature value for heartbreak or repair. People change. Relationships change. Development is path dependent. Trauma reorganizes the internal map in nonlinear ways. Culture bends the manifold in directions that no purely mathematical model could predict. Because of this, any geometric model must be prototypical, not prescriptive.

Prototype means: this is a shape that frequently emerges when relational systems try to maintain coherence under certain constraints. It is a “center of gravity” in the space of possible relational strategies, not a box to inhabit or a diagnosis to carry. It is a useful simplification that captures something structural about the process without pretending that it captures everything. The four canonical attachment configurations—secure, anxious, avoidant, disorganized—already function this way in contemporary attachment science. They are not fixed traits but probabilistic attractors that organize relational expectations and regulatory tendencies. A geometric translation simply makes these attractors visible as shapes.

Geometry also helps because attachment styles are not solely psychological categories; they are regulatory architectures. They are patterned ways of managing prediction error, stabilizing autonomic state, and navigating relational uncertainty. These are inherently geometric ideas: stability, curvature, coupling, bottlenecks, rupture, repair, continuity, and fragmentation. Attachment theory has historically used narrative and behavioral descriptors; AToM adds a structural vocabulary that maps onto emerging neuroscience—vagal regulation, HRV, synchrony, oscillatory coupling, predictive processing, and information-geometric curvature.

Still, it must be emphasized: attachment styles vary by relationship, life stage, culture, and developmental history. A person can feel secure with a sibling, anxious with a romantic partner, avoidant with a parent, and stable-but-defensive with a colleague—all in the same month. Cross-cultural research shows significant variation in attachment expression: collectivist contexts may view proximity-seeking as normative rather than anxious; gender norms may shape avoidance differently across populations; socioeconomic instability may produce behaviors that appear disorganized but are adaptive to chaotic environments. None of this is captured by a single geometry alone.

This variability is not a failure of the model. It is the reason we need geometry. Geometry clarifies constraints without pretending to define identity. It provides a stable language for describing how coherence is being maintained or lost, regardless of the specific content or context. Instead of saying, “this person is avoidant” or “this relationship is chaotic,” geometry allows us to say: “the system seems to preserve coherence by flattening its manifold” or “the system is oscillating between incompatible attractors.” These descriptions are not judgments; they are structural readouts of patterns the person may already feel but cannot articulate.

Importantly, geometry also illuminates plasticity. If attachment is a geometry, it is a geometry that changes through relational repair, secure co-regulation, somatic integration, narrative reconstruction, and safety. Curvature can soften. Bottlenecks can widen. Discontinuous regions can reconnect. Avoidant flatness can lift; anxious steepness can ease; fractured maps can regain continuity through repeated relational safety. Geometry does not imply determinism; it provides a way to understand how change happens when it does occur.

The goal, then, is translation, not reduction. Geometry is not meant to replace clinical intuition, developmental research, cultural context, or lived experience. It is meant to integrate them. It is a bridge—a way to move between narrative language (“I always get scared people will leave me”), physiological language (“my HRV drops when I sense distance”), and structural language (“my internal map spikes in curvature when relational uncertainty rises”). This integrative power is what makes geometry worth using.

Crucially, geometry also supports measurement without overclaiming. Modern tools—HRV, EDA, breathing synchrony, linguistic embeddings, topological data analysis—provide partial windows into coherence dynamics. They do not reconstruct full manifolds, nor should they try. But they can track certain geometric signatures: curvature spikes, synchrony drops, narrative fragmentation, stability gradients. These measurements become meaningful precisely because geometry gives us a framework for interpreting them.

Finally, geometry brings humility. By making the structure visible, it makes the limits visible too. No manifold fully captures a human life. No curvature value expresses the complexity of a relationship. No prototype explains identity, culture, power, trauma, or resilience. Geometry helps not because it simplifies but because it clarifies where simplification ends. It encourages precision in language and care in interpretation.

This is the spirit of AToM: coherence under constraint as a structural lens, not a metaphysical claim. A way of seeing, not a way of replacing. A translation, not a totalizing theory. When applied to attachment, geometry becomes a tool for understanding how relational meaning stabilizes, destabilizes, repairs, and reorganizes—not an attempt to compress humanity into equations. Used carefully, it expands compassion and insight; used carelessly, it risks flattening what it aims to illuminate.

Here, we choose the careful path.

2. The Four Prototypical Coherence Manifolds

(Human → Geometry → Clinically Useful)

Attachment research has always described patterned differences in how people predict relational availability, regulate internal states, and respond to closeness or threat. AToM reframes these differences in coherence geometry: four prototypical shapes that emerge when a nervous system attempts to maintain stability under relational uncertainty. They are not identities, diagnoses, or fates—they are prototypes, structural tendencies, recurrent solutions to an ancient developmental problem: how do I stay coherent when another person matters to me?

Each prototype begins with a direct, human statement—the lived experience behind the geometry.

2.1 Secure — “The Smooth Path”

Plain English: “I expect people to be there when I need them, and they usually are.”

Security is not the absence of struggle; it is the presence of predictable, navigable terrain. The internal manifold of someone with secure attachment is smooth—not because life has been smooth, but because rupture and repair have taught the system that misattunement is survivable.

Coherence Geometry

A secure system lives on a low-curvature manifold:

• Perturbations don’t bend the internal landscape sharply.
• Prediction errors remain small and local.
• Emotional experiences don’t send the system into narrow tunnels or dead ends.

Cross-scale coupling is strong: the person’s body ↔ emotions ↔ cognition ↔ narrative stay connected even under stress. In AToM terms, the system maintains stable, integrated coherence across layers.

Regulatory Profile

Security’s signature is flexibility.

Under load, the system naturally moves through the sequence:

rupture → recognition → repair → reintegration.

The path back to coherence is predictable and well-rehearsed.

Emotions rise and fall without needing suppression or amplification. Conflict is metabolized without overwhelming the system’s geometry.

Developmental & Cultural Shaping

Secure geometry emerges not from perfect parenting but from attuned-enough caregiving:

• reliable return,
• predictable soothing,
• consistent re-engagement after misattunement,
• and a culture that supports responsiveness rather than punishes vulnerability.

Cultures that normalize emotional communication or collective stress-sharing tend to produce more secure-like manifold shapes; cultures emphasizing stoicism, competition, or self-reliance may subtly bend the geometry toward avoidance.

Measurement Signals

Security often expresses itself through:

• High HRV: autonomic flexibility and vagal resilience.
• Stable physiological synchrony during connection.
• Smooth linguistic curvature: narratives flow with coherence, minimal fragmentation, and well-integrated meaning-making.

In conversation, secure individuals modulate tempo, attend to cues, and return to baseline smoothly.

Clinical Notes

Security is not “never stressed” or “always confident.”

Its core feature is repair, not perfection.

In therapy, secure geometry predicts responsiveness to relational interventions, quicker access to reflective states, and greater capacity to hold nuance without collapsing into rigidity or overwhelm.

2.2 Anxious — “The Steep Curve”

Plain English: “I’m terrified the people I love will leave, so I watch them like a hawk.”

Anxiety arises from instability in early relational prediction. When availability is inconsistent, the system evolves a geometry optimized to detect—and preempt—abandonment. It is not “needy”; it is curvature-sensitive.

Coherence Geometry

The anxious manifold is characterized by curvature spikes, especially around uncertainty or ambiguity.

• Small cues bend the internal trajectory sharply.
• The system becomes hypersensitive to micro-signals of withdrawal.
• Dimensionality narrows: attention collapses into the “threat of losing the other.”

Over-entrainment is a defining feature: the anxious system tightly couples its internal state to the partner’s signals. A slight shift in tone, posture, or text timing becomes a significant gravitational pull in the geometry.

Regulatory Profile

Regulation oscillates between:

• hypervigilance,
• protest behavior,
• reassurance-seeking,
• and rapid cycling between hope and fear.

This isn’t emotional volatility for its own sake; it is a regulatory strategy tuned by past inconsistency. Hyperactivation is the nervous system’s attempt to force coherence in a geometry prone to uncertainty.

Developmental & Cultural Shaping

Anxious geometry commonly emerges from:

• unpredictable caregiving,
• inconsistent soothing,
• caregivers oscillating between closeness and disengagement,
• emotional availability contingent on the child’s behavior.

Cultural constructs also matter: in societies where emotional dependence is stigmatized or where social stability is precarious, the anxious geometry may expand or mutely evolve.

Measurement Signals

Anxious attachment often correlates with:

• EDA overshoots (sympathetic spikes),
• mid/low HRV (reduced vagal flexibility),
• “spiky” linguistic curvature—narratives that veer sharply with perceived relational threat,
• rapid synchrony-de-synchrony cycles in interpersonal physiology.

These signals reflect the system’s readiness to absorb and react to micro-perturbations.

Clinical Notes

Anxiety is not immaturity or melodrama—it is the geometry of instability.

The system is exquisitely tuned to detect relational inconsistency because inconsistency was once dangerous.

In therapy, anxious clients often benefit from predictable pacing, clear boundaries, explicit repair, and relational constancy. The task is not to “eliminate anxiety” but to smooth the curvature through repeated safe-regulation experiences.

2.3 Avoidant — “The Flat Plateau”

Plain English: “I’m fine on my own; closeness starts to feel suffocating.”

Avoidance is not emotional absence—it is emotional distance as coherence maintenance. When early closeness overwhelmed rather than soothed, the system learned that internal stability required reducing relational bandwidth.

Coherence Geometry

The avoidant manifold is flattened:

• Low curvature not because life is simple, but because the system minimizes relational gradients.
• Under-entrainment: minimal coupling between partner cues and internal states.
• Wide, sparse attractor basins: emotional distance keeps the system stable and predictable.

This geometry avoids the energetic cost of affective oscillation by decoupling.

Regulatory Profile

Avoidant regulation relies on:

• suppression,
• compartmentalization,
• down-regulation of emotional cues,
• and reliance on autonomy for predictability.

Coherence is maintained by restricting bandwidth, thereby reducing the likelihood of internal overload.

Developmental & Cultural Shaping

This geometry tends to emerge from:

• caregivers who discouraged emotional expression,
• environments where vulnerability was met with criticism, dismissal, or withdrawal,
• cultures that valorize self-reliance or minimize relational interdependence.

These contexts teach the system: connection destabilizes; independence protects.

Measurement Signals

Avoidant attachment often presents with:

• shallow HRV variance (rigidity rather than reactivity),
• weak physiological synchrony with partners,
• reduced alignment between physiological state and narrative content (“I’m calm” while HRV shows strain),
• flat linguistic curvature, with narratives that avoid emotional complexity.

Clinical Notes

Avoidance is not a lack of love or interest.

It is a strategy of coherence preservation developed under conditions where closeness felt overwhelming, confusing, or costly.

Clinically, avoidant clients often need pacing that respects autonomy, non-intrusive curiosity, and long-term relational consistency. Change occurs when connection becomes safe rather than engulfing.

2.4 Disorganized — “The Fractured Map”

Plain English: “People feel both desperately needed and terrifyingly dangerous.”

Disorganized attachment emerges when the caregiver—the source of safety—also becomes the source of fear or unpredictability. The result is not a single geometry but multiple overlapping maps that contradict one another.

Coherence Geometry

The disorganized manifold is fractured, but not permanently or uniformly. It features:

• overlapping, incompatible attractors (approach vs. fear),
• rapid state flips,
• zones of high curvature next to dissociative flatlands,
• discontinuities where predictions cannot smoothly propagate.

This is not a failure of the person—it is the nervous system’s attempt to maintain coherence under impossible constraints.

Regulatory Profile

The regulatory experience often includes:

• approach/avoid cycles,
• sudden shutdowns or dissociative episodes,
• intense but unstable bids for closeness,
• fear-based withdrawal without conscious intention,
• complex internal contradictions (“I need you—don’t come near me”).

State transitions are less predictable because different internal “maps” activate in response to different cues.

Developmental & Cultural Shaping

Fractured geometry typically arises from:

• caregivers who were frightening, frightened, unpredictable, or unresolved,
• trauma or chronic chaos during key developmental windows,
• environments with conflicting cues (love mixed with threat, presence mixed with volatility),
• cultural conditions where identity, safety, or belonging are unstable.

The child’s internal model becomes a patchwork—multiple partial solutions layered atop one another.

Measurement Signals

Disorganized patterns may express as:

• HRV volatility (no stable baseline),
• erratic EDA patterns,
• linguistic discontinuities—narratives that shift abruptly, with gaps or contradictions,
• persistent homology patterns indicating topological fragmentation or bottlenecks.

These are markers of incoherence under overwhelming constraint, not flaw.

Clinical Notes

Language must be gentle: “fractured,” “multiple maps,” “mixed geometry,” “patchwork regulation.”

These are adaptations, not defects.

Disorganized geometry is highly plastic under sustained relational safety. Repair occurs when one map becomes reliable enough to reorganize the others, allowing continuity to emerge where chaos once lived.

Final Integration

These four geometries capture four developmental strategies for maintaining coherence in the presence of another mind. They are not categories but prototypes—recurring solutions to a problem every human nervous system must solve. Geometry provides a way to visualize these solutions, measure aspects of them, and design interventions that respect the underlying structure rather than pathologizing the person.

3. Variability, Context, and Culture

Why No Single Geometry Can Capture a Life

Attachment styles are often discussed as if they were traits—stable dispositions that a person “has.” In reality, attachment is a dynamic regulatory process, continually shaped and reshaped by relationships, culture, developmental stage, identity, and lived experience. The goal of coherence geometry is not to classify people but to describe the structural constraints a system is navigating at a given time. This section integrates variability, culture, intersectionality, and plasticity into a unified AToM-compatible frame.

3.1 Attachment Is Contextual, Not Cartographic

Attachment styles shift dramatically across contexts, partners, and life epochs. A person may feel secure with a friend but anxious with a romantic partner; organized with a therapist but disorganized with a parent; avoidant in dating but secure in collaborative work. Geometry helps because it makes these shifts structurally visible: the manifold may be smooth in one relational field and curved or fractured in another.

Why? Because attachment is the nervous system’s attempt to maintain coherence under relational constraint, and each relationship imposes different constraints. With a reliable partner, the manifold expands; with an unpredictable one, curvature spikes; with a controlling one, bottlenecks may form; with a frightening one, maps may fragment into overlapping, contradictory attractors.

This means coherence geometry must always be interpreted relationally, not as a personality map. People do not “have” a single geometry; they navigate changing geometries across time and context.

3.2 The Influence of Developmental Phase

Attachment geometry evolves across the lifespan:

• Infancy: The manifold is highly malleable; regulation comes primarily from the caregiver. Coherence depends on external scaffolding.
• Childhood: Increasing self-regulation emerges, but the caregiver’s patterns still shape the curvature landscape.
• Adolescence: Peer relationships begin to reshape the manifold; new social hierarchies add curvature and new attractor basins.
• Adulthood: Romantic partners, chosen families, work structures, and cultural role expectations introduce new constraints and new possibilities for repair or rupture.
• Later life: Attachment patterns can reorganize again as social networks shrink or expand, caregiving reverses direction, or vulnerability increases.

The geometry is developmental—alive, not static.

3.3 Intersectionality Shapes Coherence Geometry

Every nervous system grows inside a social world, and that world exerts massive influence on geometry. The manifold doesn’t only encode interpersonal patterns; it encodes structural realities.

Racism

Chronic racialized threat conditions create persistent curvature spikes around authority, belonging, and safety. The system may remain in a semi-hypervigilant geometry even in ostensibly safe interactions.

Economic instability

Resource unpredictability mimics inconsistent caregiving at scale. The nervous system learns that stability is fragile, bending the manifold toward anxious or avoidant strategies depending on cultural norms.

Gender norms

Cultural scripts shape which regulatory strategies are acceptable:

• In many cultures, men are rewarded for avoidance and punished for visible anxiety.
• Women are often socialized into hyper-attunement, bending the manifold toward anxious or appeasing geometries.

These aren’t dispositions; they’re structurally imposed constraints.

Disability

Chronic medical stress, sensory differences, or mobility disparities influence how safe or predictable the relational world feels. Disabled individuals often develop attachment strategies designed to manage both relational and environmental volatility.

Trauma exposure

Trauma reorganizes geometry at the deepest level. Curvature increases, bottlenecks narrow, attractors become deeper. But even trauma-induced geometry is plastic.

Migration & displacement

Leaving one cultural coherence system and entering another destabilizes the manifold. Predictive models of belonging, safety, and community often require deep remapping.

Intergenerational stress

Attachment maps are inherited through behavior, physiology, narrative, and culture. A caregiver with their own fractured geometry passes on more than behavior—they pass on curvature, expectations, and constraints.

Intersectionality means attachment geometry is never “just personal.” It is always embedded in the lived reality of larger systems.

3.4 No Geometry Captures Lived Relational Complexity

AToM’s value is its explanatory power, not oversimplification. But even the best geometry cannot capture:

• the nuances of cultural meaning,
• the idiosyncrasies of temperament,
• the unpredictabilities of life events,
• the unique biographies of individuals,
• the small but pivotal emotional moments that reshape a relationship.

Human connection is too rich, too historically situated, too culturally embedded to be compressed into a single mathematical object. The manifold is an abstraction, a conceptual tool that highlights structure while acknowledging that real relational life is always richer.

Geometry clarifies—but it does not totalize.

3.5 The Danger of Reification

One of the pitfalls in attachment discourse is the tendency to reify styles as identities: “I am avoidant,” “They are anxious,” “She is disorganized.” AToM explicitly resists this.

Geometry must be used as a dynamic map, not a label.

• A person with an avoidant geometry in romantic relationships may have secure geometry with children.
• A disorganized map around intimacy may coexist with a smooth manifold around friendship.
• Someone with anxious patterns early in life can develop flat, avoidant regions after relational trauma.
• Someone who was avoidant in youth may move toward security in stable adulthood relationships.

People do not “have” these geometries—they move within them, and the geometry itself reshapes in response to experience.

Reification freezes a moving system. Geometry reveals the motion.

3.6 Attachment Plasticity: The Nervous System Can Rebuild Maps

Perhaps the most important insight from AToM and attachment research alike is this: attachment is plastic.

Even fractured maps can heal; even steep curves can flatten; even flat plateaus can gain dimensionality; even rigid regions can soften. Coherence geometry is not destiny—it is adaptation to past constraints.

What enables plasticity?

1. Relational Repair

Repeated, reliable co-regulation gradually smooths curvature. This is the essence of corrective emotional experience—new data reshaping the manifold.

2. Somatic Integration

Body-based therapies widen bandwidth, restore synchrony, and reduce curvature spikes. The system gains new degrees of freedom.

3. Narrative Reconstruction

Language reorganizes the manifold. Coherent storytelling reduces fragmentation, bridges discontinuities, and builds new attractors.

4. Trauma Processing

Processing unresolved fear reduces high-curvature zones and opens closed regions of the map. EMDR, SE, and other trauma modalities widen bottlenecks.

5. Cultural Belonging

Being “held” by a community—identity affirmation, collective meaning-making, ritual, shared emotional experience—restabilizes the manifold at a cultural scale.

6. Agency & Intentional Practice

Attachment literacy helps individuals navigate their geometry more intentionally, reducing reactivity and increasing coherence.

Plasticity is the nervous system’s superpower.

3.7 The Geometry of Hope

If the fracturing of geometry explains suffering, the rebuilding of geometry explains healing.

Attachment change does not require perfect partners or ideal circumstances. It requires repeated, stable moments of coherence:

• Someone shows up when the system expects absence.
• Someone stays calm when the system expects volatility.
• Someone apologizes when the system expects blame.
• Someone listens when the system expects dismissal.
• Someone repairs when the system expects rupture to be final.

In AToM’s language, every act of attunement adds smoothness. Every moment of repair builds connectivity. Every stable relationship adds dimensionality. Every culturally safe space recalibrates curvature.

The geometry remembers.

Human systems bend, but they do not break irreversibly. The nervous system wants coherence, and given the smallest opportunity, it moves toward it.

This is the heart of attachment science:

No geometry is fixed.

No shape is final.

Every map can be remade.

4. The Developmental Origins of Coherence Geometry

Attachment does not arise from conscious beliefs or learned rules. It emerges from developmental physics—the internal geometry the infant’s nervous system forms in response to patterns of regulation, misattunement, repair, and threat. Long before a child can articulate reasons or narratives, the brain and body are already learning the shape of relational coherence.

In AToM terms, early relationships provide the boundary conditions that shape the infant’s coherence manifold. Those conditions—predictability, chaos, fear, delight, repair, neglect—exert topological pressure on the developing system, nudging it toward smoothness or curvature, dimensionality or collapse, integration or fragmentation. Attachment styles, then, are not categories or traits; they are developmental geometries, each reflecting the nervous system’s attempt to maintain stability under relational constraint.

4.1 Early Co-Regulation as Manifold Smoothing

Before self-regulation is possible, infants rely entirely on caregivers to stabilize physiological and emotional states. Feeding, rocking, mutual gaze, warmth, vocal prosody, and proximity are not “nice-to-have” interactions—they are synchronizing events that bring the infant’s internal oscillations into phase.

Every moment of successful attunement—when the caregiver accurately perceives and responds to the infant’s signal—creates a tiny local smoothing of the manifold:

• bodily discomfort resolves,
• emotional escalation de-escalates,
• prediction errors shrink,
• the internal world becomes more navigable.

The repeated experience of “I feel something → someone helps me → I return to calm” is the developmental core of secure attachment:

coherence is restored through the caregiver.

Over time, these micro-repairs accumulate into a globally smoother information manifold. The infant learns that internal turbulence can be regulated, and the world becomes predictable enough that the system does not need to flatten, curve, or fragment in self-defense.

In this sense, secure attachment is the result of successful manifold smoothing across thousands of small relational events.

4.2 Misattunement as Curvature Spikes

No caregiver is perfectly attuned, nor is perfection required. Misattunement is normal—delays in response, misread cues, competing needs, temporary unavailability. What matters is the pattern of response.

When misattunement is brief and predictably followed by re-attunement, the system experiences a manageable curvature spike:

• stress rises (curvature increases),
• the caregiver re-engages (curvature decreases),
• the system regains smoothness (repair).

This teaches the infant:

“Curvature spikes are survivable. The world returns to coherence.”

But when misattunement is chronic or poorly repaired, curvature spikes become persistent geometrical features:

• attention narrows,
• emotional oscillations increase,
• internal mapping becomes more energetically expensive,
• predictions become volatile or hyper-reactive.

This is the seed of anxious attachment: a manifold where relational gaps produce sharp, destabilizing curvature rather than temporary deviations.

The nervous system learns to track the caregiver obsessively because the landscape becomes too steep to ignore.

4.3 Threat or Chaos as Bottlenecks and Fragmentation

Chaos—unpredictable caregiving, volatile emotional climates, inconsistency punctuated by intrusion—imposes deeper geometric transformations. The system tries to maintain coherence but finds itself operating in a relational environment lacking stable structure.

The resulting geometry includes:

Bottlenecks

Certain emotional states or relational contexts become extremely narrow corridors. The system can enter them but struggles to exit. In behavioral terms:

• rumination,
• cling–collapse cycles,
• repetitive bids for connection,
• or patterned shutdowns.

These are not psychological quirks; they are topological bottlenecks formed when the system must funnel many experiences through a small set of strategies to preserve coherence.

Fragmentation

When chaos rises beyond the system’s capacity to regulate, the manifold may split, producing disconnected or weakly connected regions. In behavioral terms:

• inconsistent responses,
• contradictory behaviors,
• sudden affective shifts,
• confusion about the caregiver’s intentions.

This is the developmental origin of disorganized attachment:

a manifold shaped by incompatible constraints.

The system is forced to develop multiple partial maps—none of which fully covers the terrain.

4.4 Dissociation as Temporary Boundary Formation

Dissociation is often misunderstood as absence or numbness. AToM reframes it as a boundary operation—a dynamic topological defense that isolates highly curved or unstable regions of the manifold to prevent global collapse.

In infancy and childhood, dissociative tendencies arise when overwhelming emotional or sensory load exceeds available co-regulation:

• the child cannot flee,
• cannot fight,
• cannot rely on the caregiver for stability.

The nervous system responds by partitioning experience:

• certain emotional states become unreachable,
• certain memories become disconnected,
• certain relational signals no longer propagate across the manifold.

This boundary formation prevents catastrophic coherence failure.

But it does so at the cost of integration.

Dissociation is thus an early form of protective geometry, not pathology—a way for the system to survive an environment too demanding for its current capacities.

Importantly, these boundaries are reversible. With safety, stability, and co-regulation, the manifold can reintegrate previously isolated regions.

4.5 Trauma as Large-Scale Coherence Collapse

AToM’s trauma geometry provides a powerful unifying model for the developmental effects of severe threat:

• collapse (loss of dimensionality),
• curvature concentration (hypervigilance),
• bottlenecking (narrowed pathways),
• hysteresis (irreversibility without supportive scaffolding),
• boundary formation (dissociation).

These are not abstract mathematical metaphors—they are developmentally grounded processes observable in behavior, physiology, and narrative.

Collapse

When a caregiver is frightening or unable to regulate the child, the system reduces degrees of freedom:

• fewer emotional states feel safe,
• fewer relational strategies seem viable.

This leads to rigidity or “shutdown,” a collapse of the manifold.

Curvature Concentration

Threat clusters create high-curvature regions where predictions become hypersensitive. The child’s system becomes exquisitely attuned to danger cues—useful in chaos, costly later.

Hysteresis

Even when threat lifts, the geometry does not automatically revert. The child may continue using survival strategies long after they cease to be adaptive. This is the developmental foundation of “triggered states” in adulthood.

Boundary Formation

Dissociation and compartmentalization become necessary to contain internal conflict. Different “maps” activate in different contexts—approach in one moment, fear in the next—creating the hallmark discontinuity of disorganized attachment.

AToM’s trauma geometry aligns seamlessly with decades of developmental research: trauma does not just change behavior; it reshapes the geometry of relational coherence.

4.6 The Infant’s Problem: Maintain Coherence with an Unpredictable Other

The entire nervous system learns through a single overarching developmental problem:

“How do I remain coherent when another mind controls my survival?”

Each attachment pattern is a different solution to this problem:

• Secure: rely on the caregiver; the system internalizes stable repair.
• Anxious: hyper-track the caregiver; the system internalizes instability.
• Avoidant: decouple from the caregiver; the system internalizes self-reliance.
• Disorganized: oscillate between contradictory maps; the system internalizes unpredictability mixed with threat.

The shapes differ, but the function is the same: maintain coherence under constraint.

4.7 The Good News: Geometry Is Plastic

Even deeply shaped developmental manifolds remain profoundly malleable. The brain continues integrating, pruning, remapping, and smoothing throughout life. Attachment is not cemented; it is continually updated.

Repair is possible at any stage.

Coherence can be restored long after collapse.

Curvature can soften long after spikes form.

Disconnected regions can reconnect long after fragmentation.

The nervous system remembers—but it also rewrites.

5. What We Can Actually Measure Today (Modest & Precise)

One of the central promises of the coherence-geometry approach is that it translates psychological phenomena into patterns that are, at least in principle, measurable. But this promise can only be fulfilled if we stay grounded in the actual capabilities and limitations of current tools. Modern sensing technology—physiological, linguistic, behavioral—provides partial but meaningful windows into how coherence forms, breaks, and repairs. What we can measure today are glimpses of coherence geometry, not the geometry itself.

This section identifies what can be measured now, what each signal tells us, and why these signals must be interpreted as indicators, not reconstructions. The goal is intellectual integrity: to show how AToM’s conceptual framework connects to real data without overstating what the data can deliver.

5.1 Heart Rate Variability (HRV): A Window into Autonomic Flexibility

HRV is one of the strongest and most robust physiological indicators of coherence. High vagal tone and flexible HRV patterns correlate with:

• adaptive emotional regulation,
• quick recovery from stress,
• capacity for social engagement,
• and resilience under relational load.

In coherence-geometry terms, HRV gives us a single-axis reading of the manifold’s flexibility.

• High HRV → smoother manifold, low curvature, broad bandwidth for relational perturbation.
• Low HRV → narrower bandwidth, rigidity, susceptibility to curvature spikes.

But HRV cannot tell us the shape of the manifold. It does not indicate where bottlenecks lie, how curvature distributes across contexts, or which relational cues trigger steep gradients. HRV is an invaluable coherence proxy—but it is still only a proxy.

5.2 Electrodermal Activity (EDA): Arousal and Curvature Reactivity

EDA measures skin conductance, which corresponds to sympathetic nervous system activation. It tells us how readily a system “spikes” under load.

In attachment terms:

• Anxious systems often show rapid EDA overshoots in anticipation of relational cues.
• Avoidant systems may show blunted EDA patterns, masking internal load.
• Disorganized systems frequently show erratic EDA oscillations, reflecting unstable coupling.

In geometric terms, EDA reveals local curvature reactivity—how sharply the manifold responds to incoming signals.

But EDA cannot distinguish:

• predictive fear vs. genuine threat,
• cultural suppression vs. physiological quiet,
• dissociation vs. calm.

It measures arousal, not meaning.

5.3 Breathing Synchrony and Microtiming: Coupling and Coherence Between Systems

Relational coherence is not just internal—it is interpersonal. Breathing synchrony, subtle shifts in microtiming (e.g., turn-taking, speech pacing), and physiological resonance (heart–heart coupling, respiration–respiration alignment) reveal whether two systems are entraining to each other.

This is crucial for attachment geometry:

• Secure dyads show steady synchrony with flexible rebounds after rupture.
• Anxious–avoidant dyads show coupling mismatches, where one system accelerates while the other flattens.
• Disorganized interactions often show fragmented synchrony, where alignment breaks suddenly and unpredictably.

Microtiming is thus a relational coherence measure: a way to detect how two manifolds temporarily align or diverge.

However:

Synchrony data do not show internal experience, motives, trauma history, or meaning-making. Synchrony is a signal, not a story.

5.4 Linguistic Curvature: Embedding-Based Measures of Narrative Coherence

Modern language models (LLMs) allow us to track coherence in spoken or written narratives using semantic embeddings. These embeddings—high-dimensional vectors representing the meaning of sentences or phrases—can be analyzed for:

• curvature spikes (sharp shifts in meaning or emotional tone),
• fragmentation (disconnected narrative islands),
• repair sequences (return to smoother semantic paths),
• looping attractors (repetitive patterns or stuck states).

For attachment geometry:

• Secure narratives tend to have smooth embedding trajectories, even when describing painful events.
• Anxious narratives show sharp curvature around uncertainty.
• Avoidant narratives show flat curvature and low emotional density.
• Disorganized narratives show discontinuities—sudden shifts, gaps, contradictory statements.

However, linguistic curvature is context-dependent:

• Education level affects narrative form.
• Neurodiversity influences linguistic patterns.
• Cultural norms shape emotional expression.
• Trauma affects what is narratable.

Embeddings measure structure, not truth, and must be interpreted with nuance.

5.5 Rupture–Repair Cycles in Conversation: The Microdynamics of Coherence

Rupture–repair is the heartbeat of attachment. Tools like sequential pattern analysis, turn-taking modeling, prosodic analysis, and micro-affect coding allow researchers to track:

• when attunement breaks,
• how quickly partners notice,
• whether repair attempts occur,
• and if repair is accepted or rejected.

From a coherence perspective:

Rupture–repair cycles reveal how a relational system moves between curvature spikes and re-smoothing. They are miniature coherence events, and they map directly onto manifold dynamics.

Secure dyads show short, responsive cycles.

Anxious dyads show frantic repair attempts.

Avoidant dyads show suppressed rupture signals.

Disorganized dyads show unpredictable rupture patterns and inconsistent repair attempts.

These tools provide temporal slices of coherence geometry in action.

But they do not reveal whole-manifold topology—only surface dynamics.

5.6 Limited Exploratory TDA (Topological Data Analysis) for Narrative Fragmentation

TDA methods—persistent homology, mapper graphs, simplicial complexes—can detect “holes,” bottlenecks, and discontinuities in high-dimensional data. Applied to narratives or behavioral sequences, TDA can identify:

• persistent gaps (emotional or narrative absences),
• narrow transition pathways (bottlenecks),
• multiple attractors (different states the person flips between),
• dimensional collapse (rigidity or narrowing of narrative range).

This is directly aligned with AToM’s trauma geometry, where fragmentation, bottlenecking, and curvature distortion are structural signatures of constraint.

However, TDA is in experimental infancy for psychological and clinical use.

The signal-to-noise ratio is unclear, sample sizes must be large, and individual-level interpretation is non-trivial. TDA can spot patterns, but cannot yet be used as a clinical decision tool.

Still, it represents a promising frontier for mapping the shape of coherence in a person’s lived narratives.

5.7 What These Measurements Actually Are: Partial Windows, Not Structural Maps

It is essential to maintain epistemic humility:

none of these tools reconstruct the full coherence manifold.

At best, they give us:

• one physiological dimension (HRV),
• one arousal dimension (EDA),
• one relational dimension (synchrony),
• one linguistic dimension (semantic curvature),
• one developmental dynamic (rupture–repair),
• one structural probe (TDA).

Each measurement is a shadow, a projection of a higher-dimensional structure onto a lower-dimensional plane.

To mistake the shadow for the manifold would be to repeat the very reductionism AToM warns against.

Current technology gives us glimpses, not geometries.

We see the ripples, not the ocean floor.

And yet—these glimpses matter.

Together, they allow us to infer structural tendencies, identify collapse zones, observe curvature spikes, detect fragmentation, and witness repair. They help clinicians track change, help researchers quantify patterns, and help individuals understand their coherence landscape with more accuracy and compassion.

These tools do not complete the map.

But they allow us to see the terrain more clearly than we ever could before.

6. Predictions Framed as Hypotheses (Not Claims)

AToM deliberately positions attachment geometry as a hypothesis-generating framework, not a closed explanatory system. The value of a geometric translation lies not in the elegance of its metaphors but in its ability to produce falsifiable predictions—patterns that should emerge repeatedly across physiology, behavior, and narrative if coherence geometry is capturing something real.

Below are four core hypotheses that connect attachment prototypes to measurable coherence patterns. Each prediction is modest, testable, and explicitly falsifiable, with attention to confounders such as culture, neurodivergence, trauma history, and temperament.

H1: Secure attachment shows smoother physiological synchrony curves under relational load.

Why the Model Predicts It

Secure attachment corresponds to smooth, low-curvature manifolds where relational perturbations cause only small deviations. When two secure individuals interact—or when one secure partner interacts with a less secure one—AToM predicts:

• quicker recovery from ruptures,
• more stable heart–heart coupling,
• smoother respiration synchrony,
• and consistent autonomic alignment during stressful or emotionally charged exchanges.

The secure system’s regulatory geometry relies on efficient coherence restoration. Thus, physiological synchrony should:

• rise with engagement,
• dip briefly during rupture,
• then return to baseline through predictable repair.

This produces smooth, sinusoid-like synchrony curves rather than jagged or fragmented ones.

What Data Would Falsify It

The hypothesis would be challenged if:

• secure individuals consistently fail to show smoother synchrony than anxious/avoidant/disorganized individuals,
• secure dyads show equal or greater volatility than insecure dyads under stress,
• or synchrony metrics correlate strongly with a factor unrelated to attachment (e.g., personality traits like extraversion or agreeableness), eliminating the incremental predictive value of attachment.

If secure attachment does not reliably predict smoother synchrony in any relational context, the geometry would need major revision.

Confounders to Control For

• Culture: Some cultures norm emotional restraint; synchrony may look flatter or subtler even in secure dyads.
• Neurodivergence: Autistic individuals may show atypical synchrony patterns despite secure attachment, due to sensory or timing differences.
• Temperament: High-reactivity infants or adults may display heightened physiological fluctuations regardless of attachment status.
• Context: Conflict discussions evoke different synchrony patterns than warm bonding contexts.

H2: Anxious attachment shows curvature spikes in linguistic embeddings during uncertainty.

Why the Model Predicts It

Anxious attachment exists on a high-curvature manifold—small cues create large internal shifts. Linguistically, this should appear as:

• rapid topic shifts triggered by perceived relational threat,
• abrupt changes in emotional tone,
• intensifiers (“always,” “never,” “too much”),
• escalation markers under uncertainty (“why didn’t you reply?”, “did I do something wrong?”),
• and repetition patterns (looped attractors) around abandonment themes.

When processed through embedding-based analysis or narrative curvature modeling, these features manifest as curvature spikes—points where the semantic trajectory bends sharply relative to the baseline trajectory.

These spikes should occur particularly when:

• discussing ambiguous relational moments,
• anticipating loss,
• or describing unmet needs.

What Data Would Falsify It

The hypothesis would be undermined if:

• anxious individuals do not show higher linguistic curvature spikes than secure or avoidant participants,
• curvature spikes occur more often in avoidant or secure groups,
• curvature spikes appear unrelated to uncertainty or relational content,
• or linguistic curvature correlates more strongly with unrelated variables (e.g., ADHD-related tangentiality, education level).

If anxious attachment does not predict any distinctive linguistic curvature profile—especially around uncertainty—the “steep-curvature” model for anxious attachment would require revision.

Confounders to Control For

• Education/literacy: Higher linguistic skill may smooth curvature artificially.
• Neurodivergence: ADHD, ASD, and other profiles can produce nonlinear narrative trajectories unrelated to attachment.
• Cultural narrative norms: Some cultures use circular, indirect, or high-context storytelling.
• Language modality: Spoken vs. written narrative reveals different curvature patterns.

H3: Avoidant attachment shows reduced physiological–linguistic coupling.

Why the Model Predicts It

Avoidant attachment corresponds to a flattened manifold where internal coherence is preserved by minimizing relational bandwidth. The system suppresses emotion, down-regulates arousal, and decouples physiological states from external cues.

AToM therefore predicts a decoupling between:

• physiology (HRV, EDA, respiration)
• and linguistic expression (affect labeling, emotional vocabulary, tone shifts)

In practice:

• individuals may report calmness while physiology shows stress,
• narratives may avoid emotional content despite elevated EDA,
• linguistic curvature remains flat even as HRV decreases.

This mismatch is the coherence signature of avoidance:

the system maintains stability not by aligning internal and external signals, but by dampening expression and minimizing integration.

What Data Would Falsify It

The hypothesis fails if:

• avoidant individuals show equal or greater physiological–linguistic coupling than secure or anxious groups,
• physiological reactivity reliably matches narrative expression,
• or avoidant individuals demonstrate consistent synchrony with relational partners.

If emotional expression and physiological state align normally for avoidantly attached individuals, the flattened-plateau model loses explanatory value.

Confounders to Control For

• Cultural emotional norms: In some cultures, emotional restraint is normative, not avoidant.
• Gender norms: Men may show reduced coupling due to socialization rather than attachment.
• Alexithymia: Reduced emotional awareness can mimic avoidant decoupling.
• Neurodivergence: Autistic individuals may show atypical emotion labeling unrelated to avoidance.

H4: Disorganized attachment shows inconsistent patterns and discontinuity in multi-modal coherence data.

Why the Model Predicts It

Disorganized attachment arises from fractured, overlapping maps—contradictory relational strategies encoded in different regions of the coherence manifold. This should manifest as inconsistency across modalities:

• physiology: unstable HRV, volatile EDA, erratic synchrony, sudden shifts
• language: discontinuous narratives, contradictory statements, abrupt tone changes
• behavior: irregular turn-taking, unpredictable repair patterns
• microtiming: inconsistent pacing, alignment, and entrainment

The key signature is not high reactivity, low reactivity, or flatness—it is inconsistency, unpredictability, and dynamical incoherence across signals that normally covary.

The model predicts:

• periods of hypervigilance alternating with dissociation,
• physiological spikes without narrative acknowledgment,
• narrative collapse or jump-cuts around traumatic content,
• and disjointed rupture–repair patterns.

What Data Would Falsify It

The hypothesis collapses if:

• disorganized individuals show stable, coherent cross-modal coupling,
• their narrative patterns are as continuous as secure individuals,
• physiological measures show typical coherence curves,
• or their synchrony profiles resemble anxious or avoidant groups rather than forming a distinct pattern.

If disorganized attachment does not predict multi-modal inconsistency, the entire “fractured-map” geometry fails.

Confounders to Control For

• Trauma history: Not all trauma leads to disorganized attachment, and not all disorganization stems from trauma.
• Dissociation disorders: May amplify discontinuity beyond attachment-specific effects.
• Neurodivergence: Autistic or ADHD individuals may show cross-modal inconsistency unrelated to attachment.
• Cultural communication norms: High-context cultures may appear discontinuous to outside evaluators.
• Social anxiety: May mimic fragmentation under observation.

Why These Hypotheses Matter

Each hypothesis is:

• specific,
• testable,
• falsifiable,
• and anchored in measurable signals (HRV, EDA, synchrony, embeddings, TDA).

Success would support the coherence-geometry translation.

Failure would refine or overturn specific geometric claims without invalidating the overall framework.

This is theory behaving as science should:

ambitious enough to generate insight,

humble enough to be disproven.

7. Clinical & Practical Implications

Geometry as a Compassionate, Actionable Lens for Healing

The goal of coherence geometry is not simply to conceptualize attachment in elegant mathematical language. Its practical value lies in how it clarifies, de-pathologizes, and guides clinical work. Geometry makes visible the underlying patterns that clinicians already sense in the room—the smoothness of some clients’ regulatory paths, the steepness of others’, the flatness or fragmentation of still others. It provides a structural vocabulary for describing what clients are experiencing internally, and why certain relational or therapeutic dynamics recur.

Below are the major clinical implications of viewing attachment through coherence geometry.

7.1 Geometry Explains Why Attachment Feels Stable Yet Changeable

Clients often experience attachment patterns as paradoxical:

• “This is just how I am,” and simultaneously,
• “Why do I become someone else with certain people?”

A coherence manifold resolves this contradiction.

Stability

 comes from the 

structural geometry

 formed early in development.

• A smooth manifold tends to stay smooth.
• A high-curvature manifold tends to remain sensitive.
• A flat manifold tends to maintain distance.
• A fractured manifold tends to exhibit discontinuities.

These shapes reflect deeply learned regulatory strategies, not conscious choices.

Changeability

 comes from the fact that geometry is 

not fixed

—it is relationally and contextually plastic.

• Another person’s nervous system can smooth curvature.
• A safe relationship can widen bottlenecks.
• Self-regulation can expand dimensionality.
• Trauma processing can reduce curvature concentration.
• Deeper integration can reconnect fractured regions.

This duality—stability + plasticity—is one of the most clinically hopeful aspects of attachment geometry. It tells clients:

“Your system learned a shape that made sense at the time. And that shape can change.”

7.2 Geometry Helps Clinicians Visualize Rupture and Repair

In traditional therapy, rupture–repair is often described narratively (“a misattunement occurred, then trust was restored”). Geometry gives clinicians a dynamic visualization of the underlying process.

Rupture

A rupture corresponds to a curvature spike—a sudden increase in internal prediction error. Clients may feel:

• overwhelmed,
• misunderstood,
• abandoned,
• attacked,
• disengaged,
• or emotionally destabilized.

Each of these is a shift in geometry, not just a shift in story.

Repair

Repair corresponds to local smoothing—a reduction in curvature, reconnection of fragmented regions, or restoration of synchrony. It is not primarily about apology or cognitive reframing; it is about restoring coherence across layers of the system.

Therapists can therefore conceptualize repair as:

• widening a bottleneck,
• reducing curvature intensity,
• re-establishing cross-scale coupling,
• re-opening closed areas of the manifold,
• or softening rigid attractor patterns.

This allows ruptures to be reframed as expected geometric events, not failures of therapy. Clinicians gain a clearer sense of how to intervene: with pacing, presence, regulation, attunement, and re-engagement rather than persuasion or advice.

7.3 Geometry Broadens and Enriches Couples Work

Couples therapy is essentially the study of two manifolds attempting to entrain. Geometry clarifies why certain pairs struggle and why others stabilize.

• Anxious–avoidant pairs often show complementary but incompatible geometries: one steep and one flat. The anxious partner’s curvature spikes trigger withdrawal in the avoidant partner; the avoidant partner’s flatness intensifies curvature in the anxious partner. Geometry provides a way to explain this pattern without assigning blame.
• Secure partners act as smoothing agents, reducing curvature in their partners’ manifolds and stabilizing synchrony during conflict.
• Disorganized partners may flip between approach and fear states, confusing the partner who expects continuous geometry. Making the “fractured map” explicit helps couples depersonalize the volatility.

Couples therapy becomes the practice of co-manifold regulation, where partners learn to track each other’s signals, modulate tempo, respect thresholds, and stabilize synchrony across sessions. It shifts the focus from “fixing conflict” to learning the geometry of each partner’s system.

7.4 Trauma Therapy Gains a Structural Map of Collapse and Rebuilding

Many trauma modalities—EMDR, Somatic Experiencing, sensorimotor psychotherapy, polyvagal-informed approaches—operate implicitly on geometric principles: widening constricted states, reconnecting dissociated regions, restoring movement through previously blocked experiences.

AToM makes these principles explicit.

Trauma therapy often involves:

• reducing curvature in high-sensitivity zones,
• restoring dimensionality lost to collapse,
• reconnecting topologically isolated states,
• widening bottlenecks between cognitive–affective regions,
• and rebuilding pathways between fragmented self-states.

This geometric clarity helps therapists anticipate when trauma work will destabilize the system, when dissociation may arise as boundary-formation, and when the client requires additional stabilization before continuing.

Geometry also provides clients with a non-pathologizing explanation:

“Your system isn’t broken; it learned to survive curvature that was too sharp at the time.”

7.5 Somatic Therapy and Body-Based Work Gain a Coherence Framework

Somatic work is fundamentally about restoring physiological coherence. Geometry offers new language for what body-based practitioners already see:

• Restricted breath patterns = narrowed dimensionality.
• Fight/flight surges = curvature spikes.
• Freeze/dissociation = boundary walls isolating high-curvature zones.
• Tremoring/shaking = attempts to reopen closed regions of the manifold.
• Grounding = re-establishing smooth baseline curvature.

This framework allows somatic and attachment work to integrate seamlessly. Therapists can map somatic interventions to geometric outcomes:

• breathwork smooths curvature,
• grounding expands bandwidth,
• co-regulation widens attractors,
• movement reopens collapsed dimensions.

7.6 IFS, DBT, and Parts-Based Models Gain Geometric Precision

Internal Family Systems (IFS) already treats the psyche as composed of multiple “parts” that emerge under different conditions. In coherence geometry, these “parts” correspond naturally to:

• local attractor basins (steady states),
• curvature regions (sensitive states),
• disconnected submanifolds (dissociated parts),
• boundary-protected regions (exiles),
• and regulatory control states (managers, firefighters).

IF S’s concept of “Self” as a calm, coherent internal presence aligns with AToM’s notion of global manifold smoothness.

DBT’s focus on distress tolerance, emotional regulation, and interpersonal effectiveness corresponds to modulating curvature, expanding available dimensions, and improving synchrony with others.

Geometry strengthens these models by giving them a structural interpretation.

7.7 Geometry Reduces Pathologizing

One of the most powerful clinical implications is how geometry reframes behaviors typically interpreted as “dysfunctional.”

Anxious

 = “My system became steep because safety was inconsistent.”

Avoidant

 = “My system flattened because closeness once overwhelmed me.”

Disorganized

 = “My system fractured because the source of safety was also the source of fear.”

Secure

 = “My system learned flexible repair through repeated smoothing.”

This de-pathologizes clients without trivializing their struggles.

A therapist can say:

“Your system is using the geometry that once worked. It’s not wrong—it’s adaptive. And it can change.”

This reduces shame, increases self-understanding, and opens the door to transformation.

7.8 Clinical Precision Without Reductionism

Geometry adds precision without collapsing complexity:

• It clarifies why certain patterns recur.
• It helps clinicians anticipate rupture points.
• It guides interventions toward the relevant layer (physiological, emotional, relational, narrative).
• It helps clients externalize patterned responses.
• It complements—rather than replaces—existing models.
• It protects against false certainty or over-generalization.

AToM’s core promise is not mathematical reduction but structural clarity: a map that respects lived experience while helping therapists see where coherence is being maintained, where it is breaking down, and where it can be restored.

Below is a ~1300-word, publication-ready expansion of Section 8: Relationship to Existing Theory, written in the same density and tone as the preceding sections. It situates the attachment-geometry model within contemporary attachment science, affective neuroscience, interpersonal neurobiology, predictive processing, trauma theory, and developmental psychology—showing continuity, novelty, and domain-appropriate caution.

8. Relationship to Existing Theory

A Structural Synthesis, Not a Replacement

AToM’s geometric translation of attachment does not emerge in a vacuum. It stands on the shoulders of decades of research across developmental psychology, neurobiology, attachment theory, trauma studies, and cognitive science. Rather than presenting a new “school” of thought, coherence geometry functions as a unifying scaffold—a formal language capable of integrating strands of theory that are often described separately but behave as if they were parts of a single structure.

This section situates the geometry within the broader scientific landscape, clarifying what is continuous, what is extended, and what is genuinely novel in the approach.

8.1 Continuity with Classic Attachment Theory (Bowlby, Ainsworth, Main)

John Bowlby framed attachment as a biologically rooted system for maintaining proximity, regulating fear, and ensuring survival through predictable caregiving. Mary Ainsworth demonstrated systematic behavioral patterns—the secure base, exploratory confidence, protest, avoidance—that emerged across cultures. Mary Main and Judith Solomon later identified the disorganized pattern and emphasized the importance of unresolved fear in shaping contradictory behaviors.

Coherence geometry extends this foundational work by:

• treating each attachment pattern as a regulatory geometry,
• mapping consistency/inconsistency of caregiving onto curvature,
• mapping avoidance onto flattened coupling,
• mapping disorganization onto fractured or overlapping maps,
• emphasizing repair cycles as the source of manifold smoothness.

In essence, the geometry provides a structural language for what Bowlby saw functionally, what Ainsworth observed behaviorally, and what Main documented narratively and behaviorally.

It does not replace these traditions—it crystallizes their core insights into a formal framework.

8.2 Alignment with Interpersonal Neurobiology (Siegel)

Daniel Siegel’s interpersonal neurobiology (IPNB) centers on integration—the linking of differentiated parts of the nervous system to produce flexibility, stability, and well-being. Siegel conceptualizes integration as the defining feature of mental health and uses metaphors like “harmony,” “coherence,” and “rigidity vs. chaos.”

AToM aligns closely with IPNB:

• Integration maps to low-curvature, high-dimensionality geometry.
• Chaos maps to curvature spikes and inconsistent attractors.
• Rigidity maps to flattened or narrowed manifolds.
• Health maps to smooth, flexible coherence under constraint.

The novelty here is that AToM provides information-geometric structure to IPNB’s metaphors. “Integration” and “coherence” become measurable patterns rather than metaphorical descriptors.

8.3 Convergence with Affective Neuroscience (Schore)

Allan Schore’s decades of research emphasize how early dyadic regulation shapes the right-brain circuits governing affect, arousal, and relational engagement. He argues that:

• attuned caregiving fosters coherent right-brain networks,
• misattunement creates nonlinear stress reactivity,
• trauma yields fragmented regulatory pathways,
• and attachment style emerges from these regulatory circuits.

Coherence geometry is essentially a spatial-temporal reformulation of Schore’s core claims:

• Right-brain integration → manifold smoothness
• Hyperarousal/hypervigilance → curvature concentration
• Dissociation → boundary formation and fragmentation
• Unresolved trauma → inconsistent attractor dynamics
• Repair → re-smoothing of regulatory pathways

Where Schore uses neurodevelopmental language, AToM offers geometric structure—the same truth, in a formalized register.

8.4 Polyvagal Theory and Physiological Coherence (Porges)

Stephen Porges’ polyvagal theory describes the autonomic nervous system as a hierarchical system whose flexibility (vagal tone) underpins social engagement and emotional regulation.

AToM builds directly on this physiological logic:

• Secure attachment = robust ventral vagal engagement → smooth geometry.
• Anxious attachment = hypersensitive sympathetic spikes → curvature.
• Avoidance = damped vagal–sympathetic coupling → flattening.
• Disorganization = mixed sympathetic + dorsal vagal oscillations → fractured geometry.

Polyvagal theory thus provides the biological substrate for coherence geometry’s structure. The geometry does not supersede polyvagal thinking; it visualizes it.

8.5 Predictive Processing and Active Inference (Friston, Clark, Hohwy)

Predictive processing models the brain as a hierarchical prediction engine minimizing surprise (free energy). Attachment becomes a system of learned generative models about relational availability.

AToM maps these ideas into geometric form:

• Secure = generative models with low prediction error and stable updating.
• Anxious = models with overweighted uncertainty → curvature spikes.
• Avoidant = models that reduce prediction variance by restricting relational input → flattening.
• Disorganized = models with incompatible priors → discontinuities.

This alignment is critical: coherence geometry echoes the mathematical shape of predictive error across relational time.

AToM contributes novelty by extending predictive processing into multi-scale relational contexts and by providing measurable curvature interpretations (e.g., linguistic embedding curvature, HRV reactivity patterns).

8.6 Trauma Science and Fragmentation (Herman, van der Kolk, Brewin)

Judith Herman, Bessel van der Kolk, Chris Brewin, and others have shown that trauma disrupts the integration of memory, affect, and bodily experience. Trauma produces:

• fragmentation,
• narrowed behavioral repertoires,
• dissociation,
• difficulty with narrative coherence,
• and unstable relational engagement.

These findings directly map onto AToM’s trauma geometry:

• trauma → manifold collapse (loss of degrees of freedom),
• trauma → bottlenecking (restricted pathways between states),
• trauma → curvature concentrations (hyper-reactivity),
• trauma → boundary formation (dissociation),
• trauma → hysteresis (difficulty returning to baseline after activation).

The novelty is not the insight that trauma disrupts regulation—that is well-established.

The novelty is describing how that disruption organizes itself structurally.

8.7 Behavioral and Computational Models of Attachment

Recent computational and network-based models of attachment (e.g., Sbarra & Hazan, Mikulincer & Shaver’s regulatory models, Coan’s social baseline theory) treat attachment patterns as:

• regulatory strategies,
• adaptations to relational constraints,
• and cost-minimization systems.

Coherence geometry integrates these approaches by offering a universal representational space where these strategies become visible as geometric patterns rather than purely conceptual descriptions.

Coan’s “social baseline theory” (the idea that humans outsource regulatory load to others) fits naturally into AToM’s cross-scale coherence logic: secure individuals maintain low curvature through load sharing, while insecure strategies arise when load-sharing is inconsistent or unsafe.

8.8 What Is Genuinely Novel About the Geometric Approach

While coherence geometry aligns with several existing frameworks, it introduces four true innovations:

1. A single formal language

Attachment, trauma, neurobiology, narrative, and interpersonal synchrony are described using the same structural constructs: curvature, coupling, dimensionality, bottlenecks, fragmentation.

2. Cross-modal measurability

Unlike metaphorical models, coherence geometry connects directly to measurable quantities:

• HRV,
• EDA,
• synchrony,
• linguistic embeddings,
• and exploratory TDA.

It does not claim to fully map the manifold—but it offers operationalizable bridges.

3. Prototypical rather than categorical thinking

Traditional attachment theory sometimes risks reification. Coherence geometry explicitly frames attachment as:

• dynamic,
• context-dependent,
• relationally plastic,
• and multi-regional (different geometries for different people and settings).

4. A unifying structure for therapy

Geometry links somatic therapies, trauma modalities, relational approaches, and parts-based frameworks into a single conceptual scaffold. Each can be described as modifying curvature, widening bottlenecks, or reconnecting fractured regions.

8.9 A Theory That Honors Complexity Without Becoming Unfalsifiable

Many grand integrative models collapse under their own ambition, becoming so universalized that they lose predictive power. Coherence geometry avoids this by:

• offering specific hypotheses (Section 6),
• grounding itself in measurable signals (Section 5),
• retaining domain-appropriate humility,
• and focusing on structural invariants, not content.

It is not a theory of everything—it is a theory of coherence, and attachment is its most natural early application.

9. Limitations, Risks, and Ethical Safeguards

Why Geometry Must Be Used Gently, Precisely, and With Relational Humility

Every powerful framework carries risks. The coherence-geometry model has the potential to clarify and unify—but also to mislead, oversimplify, or be misapplied if interpreted with more certainty than the evidence allows. This section outlines the major limitations, ethical concerns, domain boundaries, and safeguards that must guide responsible use of AToM in attachment and clinical work.

The goal is intellectual honesty: geometry is a lens, not a verdict.

9.1 Geometry Is a Translation, Not the Territory

Coherence geometry reframes attachment patterns as topological tendencies rather than static traits. But even the most elegant geometry is an abstraction—a simplification of lived relational complexity.

What geometry can show:

• relative smoothness or curvature in regulation
• coupling or decoupling across systems
• fragmentation or continuity in experience
• bottlenecks that restrict adaptive movement
• dynamic responses to relational constraint

What geometry cannot show:

• the lived meaning of these patterns,
• the client’s inner world,
• the cultural stories shaping their experience,
• the psychological or existential significance of their relationships,
• or the specific narrative reasons behind their adaptations.

The geometry is not the person.

The manifold is not the life.

It is a map, and all maps simplify terrain.

9.2 Risk of Over-Reductionism

One of the greatest dangers in any systems-theoretic model is the temptation to treat the abstraction as the full explanation. This can lead to:

• Overconfidence in geometric interpretations,
• Diagnostic inflation (“you’re disorganized because your manifold is fractured”),
• Misclassification when geometry substitutes for relational nuance,
• Premature inference that ignores developmental and cultural context.

AToM explicitly warns that human meaning systems are high-variance, soft-constraint domains. The geometry is meant to describe patterns under constraint, not dictate universal rules or label individuals permanently.

As soon as geometry becomes an identity—“I am anxious because my manifold is steep”—we have strayed from its scientific and ethical purpose.

9.3 The Danger of Reification and Labeling

Traditional attachment discourse already suffers from reification:

• “I’m avoidant.”
• “They’re anxious.”
• “She’s disorganized.”

Geometry must avoid becoming a new vocabulary for the same error.

People do not have geometries; they navigate geometries.

Using geometric language incorrectly can:

• harden transient states into personality categories,
• obscure relational and cultural origins of patterns,
• and shame people for adaptations they formed under duress.

Ethical application requires constant reminders that geometry is contextual, plastic, and relational. It describes how systems behave under certain constraints—not who someone is.

9.4 Measurement Limitations: Partial Windows, Not Structures

As described in Section 5, our tools can measure:

• HRV
• EDA
• synchrony
• breathing patterns
• linguistic curvature
• rupture/repair sequences
• limited TDA for narrative fragmentation

But none of these reconstruct the full manifold. They provide:

• glimpses,
• shadows,
• projections,
• statistical tendencies.

If clinicians or researchers over-interpret these signals as definitive proof of geometry, we risk replicating old errors in new language.

Ethical safeguard:

Measurements must be interpreted as indicators, not absolute structures.

9.5 Cultural Misapplication and the Problem of Normativity

Attachment patterns are profoundly shaped by culture:

• collectivist vs. individualist norms,
• gender expectations,
• emotional expressiveness vs. emotional restraint,
• socio-political instability,
• oppression or marginalization,
• religious or community structures,
• intergenerational narratives.

If geometry is applied without cultural understanding, clinicians may pathologize culturally normative behaviors (e.g., emotional restraint, indirect communication) as “avoidant flattening” or “narrative sparsity.”

Similarly, anxiety or fragmentation may reflect structural oppression, not individual adaptation.

Ethical safeguard:

Geometry must always be nested within cultural, economic, and political context.

There is no universal “smoothness,” “curvature,” or “fragmentation”—only relational meanings within a culture.

9.6 Neurodivergence as a Confounder, Not a Defect

Autistic, ADHD, and other neurodivergent individuals often have:

• different sensory processing,
• different arousal reactivity,
• different narrative styles,
• different microtiming and synchrony patterns,
• different emotional communication norms.

These differences may mimic curvature, flatness, or fragmentation without being attachment-based.

Misinterpreting neurodivergence as attachment pathology is a major clinical risk.

Ethical safeguard:

Geometry must differentiate regulatory strategy from neurodevelopmental profile.

Atypical synchrony does not equal disorganization; monotonic narrative does not equal avoidance; hyperfocus does not equal anxious curvature.

9.7 Trauma Cannot Be Inferred Solely From Geometry

While disorganization and trauma geometry overlap, they are not equivalent. Some individuals with high curvature or fragmented narrative patterns may not have relational trauma; conversely, many trauma survivors show highly integrated regulatory geometries after years of healing.

Ethical safeguards:

• Geometry should never be used to infer trauma history.
• Fragmentation signals may indicate many factors—stress, fatigue, cultural storytelling forms, dissociation, or simple emotional overwhelm.
• Clinicians must ask, not assume.

9.8 Attachment Is Dynamic: Geometry Changes Across Relationships

Another risk is assuming that a measured signal reflects global attachment style. But attachment is relationship-specific, varying across:

• caregivers,
• partners,
• children,
• friends,
• coworkers,
• therapists.

An individual may show a steep, anxious geometry in romantic relationships but a smooth, secure geometry with close friends; or a fractured map with parents but stable flatness at work. Geometry can also change within a single relationship over time.

Thus:

• No single measurement defines a person.
• No single relationship defines attachment.
• No session defines the client’s geometry.

Ethical safeguard:

Geometry must be understood as a shifting landscape, not a diagnostic snapshot.

9.9 Overgeneralization Across Scales

AToM emphasizes that coherence is a cross-scale invariant—but this does not mean all scales behave identically. Individuals, dyads, families, groups, institutions, and cultures each have their own constraints, rhythms, and regulatory dynamics.

The danger is scope creep—assuming that a curvature spike in an individual predicts coherence breakdown at a cultural or geopolitical level, or vice versa.

Ethical safeguard:

Geometry applies analogously, not literally, across scales.

Boundaries between levels must be respected to avoid conceptual inflation.

9.10 Therapeutic Power Dynamics and Interpretive Authority

Geometric explanations can sound authoritative. A therapist describing a client’s geometry may inadvertently impose meaning rather than collaborate in meaning-making.

Risks include:

• the therapist becoming the “expert” on the client’s geometry,
• the client internalizing geometric descriptions as identities,
• misalignment between geometric language and the client’s lived experience,
• power imbalance magnifying the interpretive sway of the clinician.

Ethical safeguards:

• Geometry should be offered as an optional lens, not a truth.
• Clients should co-interpret signals; therapists should never dictate meaning.
• Explanations should be reversible, flexible, and provisional.
• Language must remain human-first, geometry-second.

9.11 Avoiding Determinism: The Plasticity Principle

Attachment geometry is profoundly plastic. The nervous system actively reorganizes in response to:

• safety,
• repair,
• stable relationships,
• embodied practices,
• emotional expression,
• narrative integration.

The greatest risk is that clients or clinicians use geometry to justify inevitability (“my map is fractured, so I’ll always be this way”). This is the opposite of AToM’s intent.

Ethical safeguard:

Geometry should always be framed as describable, not destiny; adaptive, not immutable.

The nervous system can re-smooth, re-open, reconnect, and re-dimension its manifold at any point in life.

9.12 Transparency and Humility in Research and Practice

Finally, the geometry must be held with explicit humility:

• It is early-stage theoretical scaffolding.
• Empirical validation is underway, not complete.
• Measurements are partial and noisy.
• Interpretations must be tentative, iterative, and collaborative.
• The model complements—rather than replaces—existing frameworks.

This humility is not a weakness of the model—it is its integrity.

A theory of coherence must be coherent with ethical practice, not merely elegant in abstraction.