Abstract

Background

Electrolyte balance is fundamental to neuromuscular function, yet nutritional models often consider sodium (Na⁺), potassium (K⁺), calcium (Ca²⁺), and magnesium (Mg²⁺) in isolation. This hypothesis proposes that physiological coherence depends not only on balance within paired axes (Na⁺:K⁺ and Ca²⁺:Mg²⁺) but also on their interaction — a dynamic captured here by a provisional scalar metric: the Inter-Axial Ratio (IAR), defined as (Na:K) ÷ (Ca:Mg).

Methods

A single daily whole-food meal was designed to explore feasibility of mineral-phase coherence. It employed a fixed base of lentils, legumes, and grains, rotating vegetables, and targeted inclusion of magnesium-rich seeds (e.g., pumpkin, flax). Sodium from salt and stock was buffered with potassium chloride or citrate to maintain a low Na:K ratio. Total intake of Na, K, Ca, and Mg was calculated from ingredient-level data. The IAR was used as an exploratory coherence indicator.

Results

Nutritional modelling yielded a Na:K ratio of ~0.35:1 and a Ca:Mg ratio of ~1.18:1, producing an IAR of approximately 0.30. Subjectively, the protocol was associated with increased breath regularity, decreased somatic tension, and improved emotional clarity. Objectively, blood pressure reduced from 140/90 to 120/75 over several weeks. These results are not presented as clinical proof, but as a proof of feasibility for field-based coherence mapping.

Conclusion

Coherence may arise not from static mineral thresholds but from dynamic, phase-aligned relationships across regulatory axes. The IAR offers a preliminary metric for this interaction, inviting further study into mineral patterning, autonomic rhythm, and embodied regulation. Future research should include controlled trials, HRV tracking, and longitudinal coherence mapping.

The Coherence Hypothesis

This hypothesis proposes that the four principal electrolyte minerals — sodium (Na⁺), potassium (K⁺), calcium (Ca²⁺), and magnesium (Mg²⁺) — are not merely biochemical participants, but field elements in a dynamic, relational geometry. Rather than existing as isolated quantities, these ions interact as phase-bound vectors, shaping the body’s ability to signal, respond, return, and resolve.

Health, in this model, arises not from adequate quantities alone, but from the interrelational integrity of these minerals across time. Their coordination enables coherence — a state wherein breath, nerve, posture, and perception are in functional rhythm.

A Tetrahedral Geometry of Function

This interrelationship can be visualised as a tetrahedral field:

• Na, Ca, and Mg form the base triangle — representing the core structural tensions: excitation (Na⁺), contraction (Ca²⁺), and modulation (Mg²⁺).

• K sits at the apex — not as an independent actor, but as the phase gate that determines whether the field can resolve, invert, and return.

When potassium is sufficient and properly oriented, the system gains dimensionality. The tetrahedron does not merely hold structure — it moves. It breathes. It resolves cycles and permits transition.

In low-potassium states, this triangle collapses inward:

• Calcium accumulates and structure becomes rigid.

• Magnesium’s modulating influence is blocked.

• Sodium overfires, and return is lost.

But with potassium, the system reopens:

• Signal completes, rather than loops chaotically.

• Structure supports breath without clenching.

• Coherence returns — not as a fixed state, but as capacity for cyclical renewal.

Functional Axes of the Coherence Tetrahedron

The tetrahedral model proposed here describes not just spatial geometry, but functional tension. Each triangular face of the tetrahedron represents a specific dynamic axis — a field of opposition, modulation, and potential coherence. The fourth axis, Coherence, is emergent — it arises when all three faces align through the presence of potassium.

These axes are not fixed categories but relational movements, describing how the body navigates expansion, contraction, grounding, and alignment at both physiological and experiential levels.

1. The Signal Axis (Na–Mg–K)

Axis: Excite ↔ Ground

• Na⁺ initiates activity and opens cellular potential

• Mg²⁺ buffers excitation, stabilising membranes and synapses

• K⁺ repolarises and returns the signal to baseline

Function: Governs nerve conduction, stimulus recovery, and emotional reactivity.

Failure Pattern: Excess Na⁺ without Mg²⁺ leads to hyperreactivity or inflammation. Without K⁺, signals loop or spike — coherence cannot return.

Coherent Expression: Clear response, intact regulation, emotional resilience.

2. The Structure Axis (Mg–Ca–K)

Axis: Fix ↔ Soften

• Ca²⁺ contracts tissue and defines muscular form

• Mg²⁺ releases tension and dissolves rigidity

• K⁺ holds rhythmic alignment across contraction and release

Function: Mediates the balance between structural integrity and pliability.

Failure Pattern: Excess Ca²⁺ creates stiffness. Without Mg²⁺, the body cannot release. Without K⁺, alignment collapses or becomes brittle.

Coherent Expression: Stable posture, adaptable structure, breath that flows through form.

3. The Containment Axis (Na–Ca–K)

Axis: Expand ↔ Contract

• Na⁺ drives volume, fluid movement, and systemic expansion

• Ca²⁺ binds and defines spatial boundaries

• K⁺ regulates the integrity of expansion without rupture

Function: Governs pressure, fluid balance, and containment of force.

Failure Pattern: Na⁺ and Ca²⁺ without K⁺ lead to overpressure, volatility, or collapse.

Coherent Expression: Capacity to grow, express, and return safely. Emotional and physiological containment.

4. The Coherence Axis (K at the Apex)

Axis: Align ↔ Fracture

• K⁺ sits at the apex of all faces, acting as the resolving vector for all tensions.

Function: Mediates whether the triadic forces complete a cycle or break apart. Without sufficient K⁺, coherence across systems is lost — nervous signalling becomes erratic, structure becomes rigid or unstable, and containment fails.

Coherent Expression: Breath, posture, signal, and emotion function in harmony. The system not only holds, but remembers how to return.

Mapping Relational Coherence: The Inter-Axial Ratio

To move from metaphor to measurement, this hypothesis introduces a preliminary scalar for interpreting mineral field coherence: the Inter-Axial Ratio (IAR).

The IAR is defined as:

IAR = (Na:K) ÷ (Ca:Mg)

This formulation reflects the relationship between two core axes of regulation:

• Na:K — the Signal Axis, governing excitation, repolarisation, and return.

• Ca:Mg — the Structure Axis, governing contraction, release, and postural tone.

Rather than treating these two ratios independently, the IAR frames them as a relational system. By dividing one by the other, we obtain a single, phase-sensitive value that may reflect the system’s broader coherence potential.

Why This Ratio?

The IAR does not claim to capture the full complexity of mineral interaction — it functions as a flattened projection of a multi-axis field. Its purpose is practical:

• To track changes over time in mineral phase alignment,

• To correlate mineral states with physiological patterns (e.g., HRV, breath regularity, blood pressure),

• And to offer a testable signal for coherence across the two dominant regulatory axes.

At this early stage, the division is not offered as a mathematically optimal operation, but as a conceptual bridge — a scalar simplification of deeper relational geometry. Future modelling may reveal a more accurate formulation involving vector fields, dynamic scaling, or geometric means.

Example Case: Nutritional Trial (Feasibility)

In a proof-of-feasibility experiment, a daily whole-food meal was constructed using:

• A fixed base of lentils, legumes, and grains,

• Rotating seasonal vegetables,

• Sodium buffered by potassium chloride and natural stock,

• Magnesium-rich seeds (e.g., pumpkin, flax),

• And food-based calcium from greens and tofu.

Nutrient intake was calculated to yield:

• Na:K ≈ 0.35:1

• Ca:Mg ≈ 1.18:1

• IAR ≈ 0.30

This low IAR was associated with:

• Improved respiratory coherence (deeper, more stable breath),

• Reduced somatic tension and physiological reactivity,

• A measurable drop in blood pressure from 140/90 to 120/75 over several weeks.

These results do not prove causality — they demonstrate that coherence-directed mineral balance is feasible, testable, and subjectively impactful.

Invitation for Further Research

The IAR is offered not as a final diagnostic tool, but as a starting metric — a way to track coherence from a mineral perspective. Researchers are encouraged to:

• Investigate correlations between IAR values and autonomic function (HRV, BP, sleep depth),

• Explore variations across age, sex, and dietary cultures,

• And refine the mathematical structure of the ratio or its geometric analogue.

Real-World Resonance: Blue Zones and the IAR

Across the five Blue Zones — Okinawa, Sardinia, Nicoya, Ikaria, and Loma Linda — dietary mineral patterns appear to echo the conditions for a low Inter-Axial Ratio (IAR). These populations consume diets rich in potassium and magnesium through greens, legumes, and seeds, with minimal sodium from processed foods. While the IAR is not yet a clinical tool, the coherence observed in these regions suggests that relational mineral balance may underpin long-term physiological stability.

Field Collapse and the Loss of Return

Within the coherence model, disease is not framed as a binary state — healthy or sick — but as a progressive loss of structural rhythm. When mineral tensions fall out of relational alignment, the body’s capacity to return — to resolve excitation, to soften tension, to regulate pressure — begins to degrade.

This can be understood as field collapse: the tetrahedron no longer functions as a dynamic system. Instead, it folds inward. Potassium, the apex vector of coherence, becomes insufficient. Without it:

• Calcium accumulates, often unchecked by magnesium, leading to rigidity and calcification.

• Magnesium is depleted, unable to dissolve tension or restore modulation.

• Sodium over-fires, driving inflammatory reactivity or neurosomatic volatility.

What is lost is not simply balance — but the ability to complete cycles.

For a recent analysis of lifestyle coherence in these populations, see Buettner (2025).

Alzheimer’s as a Collapse Signature

In neurodegenerative conditions such as Alzheimer’s disease, we frequently observe:

• Elevated intracellular calcium,

• Depleted magnesium levels,

• Increased neuronal sodium channel activity,

• And insufficient potassium conductance at the synaptic membrane.

While these patterns vary with disease stage, their cumulative trend resembles the very collapse described above — a locked triangle with no apex. The tetrahedron cannot move. Coherence — as the integration of signal, structure, and return — is lost.

Memory itself, in this model, is not merely a cognitive function but an expression of systemic coherence over time. When coherence fractures, the capacity to return to the past in an integrated way breaks down.

This is not proposed as a singular cause of Alzheimer’s, but as a pattern lens — a way of interpreting the layered biochemical shifts that emerge when coherence deteriorates across domains.

Degeneration as Disrupted Rhythm

This collapse model may also apply to a broader class of chronic and degenerative conditions, including:

• Cardiovascular rigidity (elevated Ca:Mg and Na:K),

• Muscular dystonia (impaired structure axis),

• Panic states or PTSD (signal axis fragmentation),

• Burnout syndromes and adrenal dysregulation (containment loss).

Rather than localising dysfunction in a single organ or symptom, the coherence hypothesis invites us to consider phase failure: the body’s failure to rhythmically realign, resolve tension, and return.

Framing the Hypothesis: Not a Mechanism, But a Map

This is not a reductionist theory — it does not claim Alzheimer’s, anxiety, or rigidity can be solved by adjusting mineral levels alone. Rather, it reframes these patterns as expressions of relational incoherence within a mineral field.

If this pattern proves useful, it may offer:

• A new language for systemic health decline,

• A way to visualise disease as fractal misalignment, not discrete malfunction,

• And a call to support coherence, not just suppress symptoms.

Coherence as Living Tension

This hypothesis has proposed that mineral regulation in the human body is not a matter of isolated sufficiency, but of relational tension and phase integrity. Sodium, potassium, calcium, and magnesium are not merely nutrients — they are participants in a dynamic geometry, each holding functional axes of excitation, structure, pressure, and return.

When aligned, these minerals support a system that breathes, moves, remembers, and resolves.

When misaligned — whether through chronic stress, depleted diets, or unbalanced supplementation — the system loses its rhythm. Structure becomes rigidity, signal becomes noise, and breath loses its landing place.

Coherence, then, is not static. It is a living capacity:

The ability to complete cycles, to return, to remember — and to begin again.

A Testable Pattern, Not a Fixed Theory

The Inter-Axial Ratio (IAR) is introduced here not as a diagnostic endpoint, but as a starting point — a scalar echo of deeper, multidimensional dynamics. It invites further modelling, testing, and refinement.

The tetrahedral geometry is not a mechanistic blueprint, but a pattern-map: a way of seeing. Whether this pattern proves mathematically rigorous or metaphorically instructive, it is offered in the spirit of open-source exploration.

Invitation to Researchers, Clinicians, and System Thinkers

This work does not claim authority — it offers orientation. The patterns described here arose not from proprietary methods or clinical funding, but from lived observation, physiological tracking, and field-based coherence practice.

If any part of this framework resonates:

• As a starting point for clinical pilot design,

• As a template for nutritional modelling,

• Or as a metaphorical lens for systems alignment,

You are warmly invited to build on it. Let this not be a declaration, but a living hypothesis — one that evolves through shared attention, experimentation, and application.

References

Buettner, D. (2025). Lessons from the Blue Zones: There is no silver bullet (or magic pill) for a long, healthy life. American Journal of Lifestyle Medicine, 15598276251334310.

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