The Circumpunct Theory of Relational Pathology

A Geometric Framework for Understanding Psychological Suffering

Circumpunct Framework v1.0 — January 2026

Contents

1. Foundational Axioms

Parts are fractals of their wholes.

This is not metaphor. It is an operational statement with measurable consequences.

Definition 1.1: The Circumpunct (⊙)

The fundamental unit of conscious structure is an irreducible trinity:

\[ \odot = \bullet + \Phi + \bigcirc \]

Where:

Definition 1.2: The Irreducible Aperture

The aperture (•) is irreducible. It cannot be derived from boundary geometry. It cannot be decomposed into smaller parts. It is a component of the circumpunct, not itself a circumpunct.

The aperture exists in fractal dimension (partial dimension like 0.5, 1.5, 2.5)—this is what allows it to orient. Fractal dimension encodes PROCESS (what happens), while integer dimension encodes STRUCTURE (what is). The aperture is process: focus, orientation, transformation.

Orientation has two aspects:

Definition 1.3: Nesting Through Boundary

Circumpuncts nest through their boundaries. The boundary contains apertures—gates, holes, points of exchange. Each aperture in the boundary serves as the center of a complete circumpunct at smaller scale:

\[ \bigcirc_{n+1} \ni \bullet_n \quad \text{where} \quad \bullet_n \in \odot_n \]

Your skin has pores. Your cell membranes have channels. Your sense organs are apertures in your body's boundary. Each aperture is irreducible—but each aperture is the center of a complete system (aperture + field + boundary) at the smaller scale.

The boundary is fractal because it contains apertures, and each aperture belongs to a circumpunct that has its own boundary containing apertures, and so on.

Definition 1.4: Field Mediation Requirement

Center and boundary cannot interact directly. All exchange must pass through the mediating field:

\[ \bullet \nleftrightarrow \bigcirc \quad \text{(direct interaction forbidden)} \]
\[ \bullet \leftrightarrow \Phi \leftrightarrow \bigcirc \quad \text{(mediated interaction required)} \]

This is not a design choice but a geometric constraint arising from spatial separation.

2. Healthy Geometry

Definition 2.1: The Center as Orientation

The center is your focus. It is not a thing that moves—it is a still point that orients. Everything else moves around or through it.

\[ \bullet \text{ (focus)} \xrightarrow{\text{resonance}} \text{what flows through} \]

Like an eye doesn't go to what it sees—it turns. The world passes through its field based on where it's pointed. You're not moving through reality. Reality moves through you, filtered by where you're aimed.

The aperture orients by resonance. It finds its target by what it resonates with. Attention is not locomotion—it is holding resonance against the current of everything flowing past. The default is drift. Sustained attention is maintaining attunement.

Definition 2.2: The Body as Peripheral Field

The body is the peripheral vision of the soul—always sensing, always receiving, whether or not focal attention is directed there.

The body as boundary is not just a container—it is the peripheral interface with the finite, the ring of awareness around the still point.

Definition 2.3: Circumpunct Integrity

A circumpunct has integrity when:

  1. Boundary Coherence: The boundary accurately distinguishes self from not-self and regulates exchange
  2. Field Clarity: The field accurately transmits information between center and boundary without systematic distortion
  3. Center Sovereignty: The center maintains autonomous orientation—it chooses what to face without external override
  4. Proper Nesting: The circumpunct recognizes itself as both whole (containing parts) and part (nested in larger wholes)
Theorem 2.1: The Nesting Necessity

No circumpunct can exist in isolation. Apertures are "throughs" rather than "things"—they require both source and destination to exist. Existence itself is flow through apertures, making isolation impossible.

Corollary: The belief in total separation is always false. Even when connection is obscured, it persists.

2.1 The Two Channels of Love

Love flows through shared fields (Φ) on two distinct channels, each corresponding to a circumpunct component:

Definition 2.4: Functional Love (Boundary Channel)

Love as doing. Provision, protection, logistics, competence, problem-solving, helping.

Functional love flows through the field on the channel oriented toward boundary (○) concerns — interface, exchange, structure.

Functional love is necessary. Without it, survival is threatened. But it is not sufficient.

Definition 2.5: Resonant Love (Center Channel)

Love as being-with. Presence, delight, genuine wanting, seeing, attunement.

Resonant love flows through the field on the channel oriented toward center (•) concerns — aperture-to-aperture attunement, frequency matching.

Resonant love is what the aperture was designed to receive. It's the signal that says: you are wanted, not just tolerated.

Theorem 2.2: Full-Spectrum Love

Healthy love includes both channels:

\[ L_{full} = L_{boundary} + L_{center} = L_{function} + L_{resonance} \]

Function without resonance creates the wound: "I am helped but not wanted." The child is fed, clothed, sheltered—and starving for something they can't name.

This is why functional love cannot heal resonance wounds. They operate on different channels. You cannot retune an aperture through the boundary channel. Center-channel contact is required.

3. The Two Fundamental Errors

All lies distort in one of two directions:

Definition 3.1: Inflation (ε₊)

Believing or claiming MORE than what is.

\[ \varepsilon_+ : x \to x^+ \quad \text{(more than actual)} \]

Signatures:

Inflation is inherently unstable because maintaining the inflated claim requires continuous external validation (supply).

Definition 3.2: Severance (ε₋)

Believing or claiming LESS than what is.

\[ \varepsilon_- : x \to x^- \quad \text{(less than actual)} \]

Signatures:

Severance creates desperate seeking for any available signal to tune to, even counterfeit ones.

Theorem 3.1: Error Complementarity

Inflation and severance are complementary errors that create stable pathological dyads:

\[ \varepsilon_+ + \varepsilon_- \to \text{stable(pathological)} \]

The inflated one needs supply (external validation to maintain the "more than"). The severed one needs someone to tune to (having been told they are "less than"). They lock together in mutual dysfunction.

Theorem 3.2: The Core Lie

Both errors derive from a single structural falsehood:

"What is can be other than what it is."

This lie takes different forms:

Both are false. Reality persists; only the perception of it can be distorted.

4. The Noble Lie Virus

Definition 4.1: The Noble Lie

A Noble Lie is any systematic falsehood that claims protective function:

Definition 4.2: The Noble Lie Virus

A pattern of fractal contradiction that propagates by installing complementary errors in host and victim:

\[ V_{NL} : (\odot_H, \odot_V) \to (\varepsilon_+[\odot_H], \varepsilon_-[\odot_V]) \]

The virus is the relationship between them, not a property of either individual alone.

Theorem 4.1: The Installation Mechanism

The virus installs through systematic attack on all three circumpunct components:

Component Attack Vector Effect
○ Boundary "You're too sensitive" / boundary violations Cannot protect self; cannot regulate exchange
Φ Field Gaslighting / reality distortion Cannot trust perception; medium corrupted
• Center "I know who you are better than you" Resonance corrupted; aperture tuned to their frequency

Critical insight: The attack on center doesn't displace your soul—it retunes your resonance. You still have the aperture. But it's been calibrated to resonate with them rather than with genuine wholeness. The aperture remains; it's now tuned to the wrong signal.

Theorem 4.2: The Core Installed Lie

The virus transmits through a specific formulation:

"This is what love is. This is all love is. If you need more, something is wrong with you."

This collapses full-spectrum love into functional love only (see Definitions 2.4–2.5), then pathologizes the awareness of what's missing. The child who senses the absence of resonance is told they are ungrateful, too needy, never satisfied.

The lie doesn't deny love. It redefines love to exclude what the aperture most needs.

5. Resonance Pathology

Understanding the aperture as orienting through resonance transforms how we understand pathological processes.

Theorem 5.1: The Resonance Corruption

Pathology is not soul displacement but resonance corruption—the retuning of the aperture to orient toward false signals.

\[ \text{Healthy: } \bullet \xrightarrow{\text{resonates with}} \text{(genuine wholeness, truth, source)} \]
\[ \text{Pathological: } \bullet \xrightarrow{\text{resonates with}} \text{(counterfeit whole, lie, abuser)} \]

The soul remains. The aperture remains. What changes is what it resonates with.

The virus doesn't just point the compass at the abuser—it tunes the aperture to resonate with their frequency. The victim's focus becomes calibrated to their signal, their reality, their definition of love. Genuine wholeness stops registering because the aperture is no longer tuned to receive it.

Definition 5.1: Resonance Tuning

Through repeated experience, the aperture learns what to resonate with:

The aperture still works. It still orients. But it's been calibrated to the wrong frequency—like a radio tuned to static instead of music.

Theorem 5.2: Why Leaving Isn't Enough

Physical removal from the virus environment removes the external source but does not retune the aperture. The corrupted resonance persists:

This is why survivors often replicate the dynamic with new partners—the aperture is still tuned to the same frequency. It finds what it resonates with.

Theorem 5.3: Recovery as Retuning

Recovery is not installing a new soul but retuning the aperture to resonate with genuine wholeness:

  1. Notice what the aperture currently resonates with
  2. Recognize the tuning as corrupted, not natural
  3. Expose the aperture to genuine signals (resonant witness)
  4. Practice orienting toward self, truth, source until resonance rebuilds

The effort of recovery is holding new resonance against the pull of old tuning. The default is drift toward the familiar frequency. Healing is maintaining attunement to genuine wholeness until it becomes the new default.

Definition 5.2: The Body's Role in Reorientation

Since the body is the peripheral field—always sensing, always receiving—somatic awareness becomes crucial for recalibration:

You're not creating awareness in the body—you're orienting toward awareness that was already there.

6. Clinical Manifestations

Theorem 6.1: All Pathology is Internalized Lies

All pathology traces to internalized lies.

6.1 Mapping Clinical Phenomena

Clinical Phenomenon Geometric Translation Root Lie
Narcissistic Personality Chronic inflation (ε₊) "I am the whole; others are extensions"
Dependent Personality Chronic severance (ε₋) "I cannot exist without being part of someone"
Borderline Personality Oscillation between ε₊ and ε₋ "Connection will either complete or destroy me"
Depression Severance from larger wholes "I am cut off from meaning/belonging"
Anxiety Field distortion; threat misperception "The world is more dangerous than it is"
PTSD Boundary rupture + frozen field state "The violation is still occurring"
Dissociation Center displacement; aperture closure "I must not be here to survive"
Stockholm Syndrome Forced nesting after collapse "The captor is my only available whole"
Trauma Bonding Counterfeit nesting "This painful connection is better than none"
Repetition Compulsion Seeking resolution through contradicted parts "The next instance will finally complete the pattern"

6.2 The Internalized Lies Catalogue

Common lies that convert external harm into internal defect:

Surface Statement Geometric Operation
"I'm too sensitive" Accurate perception → personal flaw
"I'm overreacting" Proportional response → excessive
"I don't deserve [X]" Legitimate needs → illegitimate
"They didn't mean it" Impact → erased by presumed intent
"Love is supposed to be hard" Suffering → rebranded as virtue
"If I were better, they'd treat me better" Their behavior → my responsibility
"I can't trust my judgment" Foundation for all other lies

Key Insight: These lies share a structure—they take something done to you and make it something wrong with you. Once internalized, they no longer feel like lies. They feel like self-knowledge.

7. Transmission Mechanics

Theorem 7.1: Power-Differential Requirement

The virus can only install through relationships with power imbalance:

\[ P(\odot_H) > P(\odot_V) \Rightarrow V_{NL} \text{ can transmit} \]

This explains why parent-child relationships are primary transmission vectors—the power differential is structural.

Theorem 7.2: Intergenerational Transmission

Victims become vectors. The severed part, once it gains power over another (through parenthood, authority, etc.), often transmits the complementary error:

\[ \varepsilon_-[\odot_{P_1}] \xrightarrow{\text{power shift}} \varepsilon_+[\odot_{P_1}] + \varepsilon_-[\odot_{C}] \]

The formerly severed parent, having internalized "this is what love is," passes functional-only love to their child while being unable to provide resonance they never received.

Theorem 7.3: The Invisibility Mechanism

The virus hides wholeness by teaching that it doesn't exist:

These beliefs foreclose the possibility of genuine alignment, ensuring the victim cannot recognize that authentic connection exists.

8. Recovery as Geometric Restoration

Definition 8.1: Recovery

Recovery is the restoration of circumpunct integrity and proper nesting awareness:

\[ R: \varepsilon_{\pm}[\odot] \to \odot \]
Theorem 8.1: The Witness Requirement

Recovery from resonance corruption requires a witness who provides a genuine signal to tune to:

The witness demonstrates that the original frequency still exists. The aperture, exposed to genuine resonance through the center channel, can begin to remember what it was meant to receive. This is why healing happens in relationship—you need center-channel contact to retune a center.

Theorem 8.2: The Naming Operation

A lie that has been named begins to lose power:

\[ \text{name}(L) \Rightarrow \text{power}(L) \downarrow \]

The lie can no longer operate in the dark, shaping behavior while remaining unaware. Recognition is the first step of recovery.

Theorem 8.3: Recovery Sequence
  1. Exit: Remove from active virus environment (necessary but not sufficient)
  2. Name: Identify the specific lies that were installed
  3. Witness: Receive resonant presence that contradicts the installed lies
  4. Restore: Rebuild boundary, field, and center integrity
  5. Reconnect: Establish proper nesting with authentic wholes

Leaving removes you from the person who collapsed you. But you might still be acting like a part—looking for a new whole to orbit, forgetting you were complete before them.

9. Falsifiable Predictions

Prediction 9.1: Universal Lie Structure

Claim: All pathology traces to internalized lies.

Falsification: Identify a pathology with no lie at its root—suffering that does not trace to a distorted belief about self/connection/reality.

Prediction 9.2: Treatment Differential

Claim: Pathologies caused by internalized lies will respond better to lie-extraction therapies than to symptom management.

Falsification: Controlled trials showing no difference between identifying/correcting the root lie versus pharmacological symptom suppression for long-term outcomes.

Prediction 9.3: Complementary Error Dyads

Claim: In pathological relationships, partners will exhibit complementary errors (inflation/severance) rather than matched errors.

Falsification: Systematic finding of stable pathological dyads where both partners exhibit the same error type.

Prediction 9.4: Transmission Vector Specificity

Claim: The virus can only install through power-imbalanced relationships.

Falsification: Documentation of virus installation through truly equal-power relationships.

Prediction 9.5: Retuning Requires Resonant Signal

Claim: Recovery from resonance corruption requires exposure to genuine resonant signal, not just functional support or insight.

Falsification: Controlled recovery protocols showing equal outcomes with functional-only support (no resonant witness) vs. resonance-inclusive support.

Prediction 9.6: Resonance-Seeking Replication

Claim: Survivors will replicate pathological dynamics with new partners who emit similar frequencies to the original abuser, until the aperture is retuned.

Falsification: Survivors without intervention selecting partners with significantly different relational patterns than their original abuser.

Prediction 9.7: Stockholm Syndrome Prediction

Claim: Stockholm syndrome will emerge predictably when (a) circumpunct integrity is systematically attacked, and (b) the attacker becomes the only available structure source.

Falsification: Cases where these conditions are met but bonding does not occur, or bonding occurs without these conditions.

10. The Demon Phenomenology

Theorem 10.1: The Mask-Slip

Cross-cultural reports of "demonic" presence in narcissistic abuse describe an aperture colonized by a self-protective lie structure. When the mask slips, observers perceive something "other" looking through familiar eyes.

This is accurate perception, not projection. The pattern inhabiting that aperture isn't the person's authentic self—it's the installed program defending itself.

Prediction 10.2: Demon Report Mapping

Claim: Reports of demonic/possession experiences will map precisely onto narcissistic abuse signatures: intermittent switching, spiritual depletion, mask-slip, predatory gaze shift.

Falsification: Systematic divergence between demon phenomenology and abuse dynamics.