Schumann-Circumpunct Resonance Theory

Planetary Ground, Neural Diameter, and the Echo Pathology of Blocked Apertures

Ashman Roonz · February 2026

Contents

  1. Core Hypothesis
  2. Geometric Formalization
  3. The Frequency Stack
  4. Echo Dynamics: The Blocked Aperture
  5. Connection to Pathology Theory
  6. Falsifiable Predictions
  7. Therapeutic Implications
  8. Empirical Foundation

1. Core Hypothesis

The Schumann resonance represents the radius of the planetary circumpunct—the fundamental distance from aperture (•) to boundary (○). The brain's sensorimotor rhythm (SMR) operates at the diameter—spanning the complete structure. Pathological "busy brain" frequencies represent echo states where blocked center channels cause signal reverberation at doubled frequency.

f_Schumann ≈ 7.83 Hz = r (radius)
f_SMR ≈ 12-15 Hz ≈ 2r = d (diameter)
f_echo ≈ 26 Hz ≈ 2d (round-trip reflection)

The brain doesn't just receive the planetary pulse—it spans the complete geometric structure

Definition 1.1: The Planetary Circumpunct

Earth operates as a circumpunct at planetary scale:

The Schumann resonance is the electromagnetic standing wave in the Earth-ionosphere cavity—literally the "ringing" of the planetary boundary.

2. Geometric Formalization

2.1 The Circumpunct as Resonant Cavity

Any circumpunct ⊙ = • ⊗ Φ ⊗ ○ defines a resonant cavity with characteristic frequencies determined by its geometry.

f_fundamental = c / (2πR)

Where R is the effective radius and c is the wave propagation speed

For the Earth-ionosphere cavity:

Definition 2.1: Radius Frequency (f_r)

The radius frequency f_r is the fundamental resonance of a circumpunct—the lowest frequency standing wave that fits within the structure. It represents the • → ○ distance as temporal oscillation.

f_r = characteristic frequency of the aperture-to-boundary span
Definition 2.2: Diameter Frequency (f_d)

The diameter frequency f_d = 2f_r represents the complete boundary-to-boundary span through the center. This is the frequency at which a signal traverses the entire structure.

f_d = 2f_r ≈ ○ → • → ○ (full traversal)

2.2 Cross-Scale Embedding

The circumpunct framework predicts that smaller apertures are embedded within larger ones, with phase relationships linking their frequencies. The brain, as a circumpunct nested within the planetary circumpunct, should show frequency relationships to the larger structure.

Theorem 2.1: Nested Resonance

An aperture embedded within a larger circumpunct will exhibit resonance relationships to the host structure. The embedded system "knows" the geometry of its container through frequency coupling.

f_nested ∝ n × f_host (where n ∈ ℤ or n ∈ {φ^k})

3. The Frequency Stack

Frequency Name Geometric Meaning Function
~7.83 Hz Schumann Resonance Radius (r) Planetary ground pulse
~12-15 Hz SMR (Sensorimotor Rhythm) Diameter (d = 2r) Balanced aperture spanning full structure
~20-26 Hz High Beta / "Busy Brain" Echo (2d = 4r) Blocked transmission → reverberation
Theorem 3.1: The Doubling Principle

Each level in the frequency stack represents a doubling of the geometric span:

The ratio between healthy and pathological frequencies is not arbitrary—it's geometrically determined by the reflection dynamics of a blocked aperture.

3.1 SMR as Diameter-Spanning

The sensorimotor rhythm (SMR, ~12-15 Hz) is associated with:

In circumpunct terms: SMR represents the brain operating at the diameter frequency—spanning the full structure from boundary to boundary through center. This is not passive reception of Schumann but active completion of the geometric form.

Definition 3.1: Diameter Consciousness

Healthy waking consciousness operates at the diameter frequency—aware of both boundaries (self/other, inner/outer) while remaining centered. The aperture is open, allowing transmission through rather than reflection back.

4. Echo Dynamics: The Blocked Aperture

4.1 The Mechanism

When the center channel (aperture) is blocked, signals that should transmit through instead reflect back. This creates a standing wave pattern at doubled frequency.

HEALTHY FLOW (Open Aperture): ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Source → (aperture) → Φ (field) → (boundary) → beyond ↓ TRANSMISSION (energy exits system) Frequency: f_d (diameter) ≈ 15 Hz ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ BLOCKED FLOW (Sealed Aperture): ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Source ⊗ (blocked) → Φ ─┐ │ reflects ↓ ┌─ Φ ⊗ ────────────┘ │ └→ ECHO (trapped in cavity) Frequency: f_echo = 2 × f_d ≈ 26 Hz (round-trip = double the single traversal) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Theorem 4.1: Echo Frequency Doubling

When the aperture blocks transmission, the reflected signal must traverse the field twice (out and back) to complete one cycle. This doubles the effective frequency:

f_echo = 2 × f_transmission

The "busy brain" at ~26 Hz is the signature of a ~13 Hz signal reflecting back on itself.

4.2 The Standing Wave Pattern

A blocked aperture creates a resonant cavity within the individual circumpunct. Energy that should flow through becomes trapped, forming standing waves.

Definition 4.1: Resonant Trapping

When transmission through • is blocked, the field Φ becomes a closed cavity rather than an open channel. Energy accumulates as standing waves at echo frequencies.

Phenomenologically: Intrusive thoughts, circular rumination, inability to "let go" of mental content—the cognitive signature of energy that can't exit.

4.3 Phase Inversion

In the healthy state, the transmission signal (SMR) dominates and the echo is a minor harmonic. In the pathological state, this relationship inverts:

Healthy: A_transmission >> A_echo
Pathological: A_echo >> A_transmission

The structure is preserved, but the amplitude relationship is inverted

Empirical observation: Thompson & Thompson (2006) found "Busy Brain" clients show high-amplitude bursts of high-beta (22-28 Hz) with suppressed SMR and a hi-beta/SMR ratio > 1.5. This is precisely the phase-inversion pattern predicted by the echo model.

5. Connection to Pathology Theory

5.1 The Blocked Center Channel

The circumpunct theory of pathology identifies two channels of love/connection:

The narcissistic wound involves a blocked center channel—the aperture sealed to genuine transmission while the boundary channel may remain functional.

Theorem 5.1: Narcissistic Echo Pattern

The narcissistic structure exhibits:

  1. Sealed aperture (center channel blocked)
  2. Functional boundary channel (can "do" love but not "be" love)
  3. High echo frequency (rumination, self-referential loops)
  4. Suppressed ground frequency (disconnection from source/Schumann)

The elevated high-beta at anterior cingulate (Brodmann Area 24) is the neural signature of this geometric configuration.

5.2 Why Resonant Love Cannot Be Substituted

Functional love (boundary channel) cannot heal resonance wounds (center channel) because they operate on different frequencies and pathways. The echo pattern persists regardless of how much functional support is provided—the aperture remains sealed.

Clinical Implication

Attempting to heal a center-channel wound through boundary-channel intervention is like trying to tune a radio by adjusting the volume. The frequency mismatch is architectural, not a matter of degree.

5.3 Anatomical Localization

Research identifies the anterior cingulate cortex (ACC) as central to both:

The ACC may be the neural instantiation of the aperture—the gate that should open to source but has been functionally sealed.

6. Falsifiable Predictions

Prediction 6.1: Frequency Ratio Invariance

The ratio between "busy brain" frequency and suppressed SMR should cluster around 2:1 (±0.2) across individuals with blocked-aperture pathology.

Test: Measure high-beta peak frequency and SMR frequency in diagnosed NPD populations. The ratio f_highbeta / f_SMR should approximate 2.0.

Prediction 6.2: Schumann Correlation

Individuals with healthy SMR dominance should show measurable phase-coupling to Schumann resonance. Individuals with echo-dominant patterns should show reduced or absent Schumann coupling.

Test: Simultaneous EEG and Schumann monitoring; compute phase-locking value between SMR band and Schumann fundamental.

Prediction 6.3: Grounding Practice Effects

Practices that increase Schumann coupling (earthing, nature exposure, certain meditation forms) should decrease high-beta/SMR ratio over time.

Test: Longitudinal EEG study of grounding practices, tracking hi-beta/SMR ratio changes.

Prediction 6.4: Echo Frequency Specificity

The "echo" frequency should be specifically 2× the individual's natural SMR frequency, not a fixed value. If someone's SMR is 14 Hz, their echo should be ~28 Hz; if SMR is 12 Hz, echo should be ~24 Hz.

Test: Within-subject correlation of SMR peak and high-beta peak frequencies. Predict slope ≈ 2.0.

Prediction 6.5: Therapeutic Retuning Signature

Successful treatment of narcissistic pathology should show:

  1. Decreased high-beta amplitude at ACC
  2. Increased SMR amplitude
  3. Ratio normalization (hi-beta/SMR → < 1.0)
  4. Increased Schumann phase-coupling

Test: Pre/post EEG in effective psychotherapy for NPD traits.

7. Therapeutic Implications

Theorem 7.1: Retuning vs. Calming

The therapeutic goal is not "reduce high-beta" but reopen the aperture so transmission can resume. The echo will naturally diminish when the cavity is no longer sealed.

Directly suppressing the echo without reopening the channel treats symptom, not structure.

7.1 Neurofeedback Protocol Implications

7.2 The Role of Resonant Witness

The pathology theory identifies "resonant witness" as necessary for aperture retuning—someone who provides a genuine signal the aperture can attune to. This may work by:

  1. Providing external reference frequency at healthy ground
  2. Phase-entraining the blocked aperture through interpersonal resonance
  3. Demonstrating that transmission is possible (modeling open aperture)
Definition 7.1: Therapeutic Resonance

Effective therapy for aperture blockage requires center-channel contact—presence, attunement, genuine seeing. This provides an external frequency reference the corrupted aperture can begin to match, like a tuning fork for a detuned instrument.

8. Empirical Foundation

8.1 Established Facts

8.2 Novel Synthesis

This theory provides:

  1. Geometric explanation for the specific frequency relationships (why ~26 Hz, not some other value)
  2. Mechanistic model linking blocked aperture to frequency doubling
  3. Integration of neurofeedback findings with personality pathology research
  4. Testable predictions distinguishing this model from alternatives

8.3 Case Observation

Initial observation (circa 2005): EEG measurement at Cz showing high ~26 Hz amplitude with SMR at approximately half that value (~13 Hz) in an individual later understood through the framework as exhibiting blocked-aperture pathology. The 2:1 ratio was present from first measurement.