Official MEFI Core Formula | Steven Greenmyer
Official MEFI Formula Page

MEFI Theory · Steven Greenmyer

THE OFFICIAL MEFI CORE FORMULA

The canonical local-state equation from which MEFI calculations, nested interactions, propagation analysis, simulations, and observational interpretations begin.

$$ F_{\mathrm{MEFI}}(r,t)= \left[ \frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)} \right] + \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$

The formula evaluates expansion response, compression feedback, coherent difference, and the active Universal Frequency Resonance response together. No individual term, proxy quantity, normalized score, or application-specific diagnostic replaces the complete equation.

Author: Steven Greenmyer
Framework: MEFI Theory
Status: Canonical formula
Contact: info@mefitheory.org
Updated: August 6, 2026
Read the Complete Framework Open Interactive Explorer Earth UFR Mission Control

Official formula status

This page defines the official MEFI core formula and its canonical interpretation. Educational pages may isolate a term to show its mathematical behavior, but every physical state, simulation interaction, node relationship, propagation stage, and observational application must return to the complete equation.

Canonical

1. Canonical Formula Statement

$$ F_{\mathrm{MEFI}}(r,t)= \left[ \frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)} \right] + \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$

The MEFI core formula defines a complete local state through the signed relationship between expansion response and compression feedback, together with signed coherent difference coupled to the active Universal Frequency Resonance response.

The equation is evaluated as one system. Its terms may be displayed separately for teaching, diagnostics, or data mapping, but they do not become independent replacement models.

\(F_{\mathrm{MEFI}}(r,t)\) is the resulting MEFI state at the evaluated relationship \(r\) and time \(t\). It may describe the condition of a matter node, a biological node, a simulation member, a parent structure, an Earth observation state, or another application-specific relationship.

\(F_{\mathrm{MEFI}}\) is not automatically a conventional force measurement. It is the complete MEFI state. A force-like, displacement, velocity, pressure, or other observable must be derived separately and identified as such by the application.
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Exact decomposition

2. Exact Formula Decomposition

The complete equation may be decomposed into named relationships without changing its mathematical meaning.

2.1 Expansion term

$$ E(r)=\frac{k_r}{r^2} $$

2.2 Compression term

$$ C(r)= \frac{k_c}{r^2(1+r)} $$

2.3 Signed expansion–compression relationship

$$ S(r)=E(r)-C(r) = \frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)} $$

2.4 Signed coherent dynamic relationship

$$ U(t)= \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$

2.5 Complete local state

$$ F_{\mathrm{MEFI}}(r,t)=S(r)+U(t) $$

The labels \(E\), \(C\), \(S\), and \(U\) are exact shorthand for relationships already present in the canonical formula. They do not introduce a second MEFI equation.

Expansion \(E(r)=k_r/r^2\)
Compression \(C(r)=k_c/[r^2(1+r)]\)
Static Relationship \(S(r)=E(r)-C(r)\)
Dynamic Relationship \(U(t)=\Delta Q f_{\mathrm{UFR}}\)
Complete State \(F_{\mathrm{MEFI}}=S+U\)
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Definitions

3. Official Symbol Definitions

Symbol Official role Interpretation
\(F_{\mathrm{MEFI}}(r,t)\) Complete local MEFI state The signed result of the complete expansion–compression and ΔQ–UFR relationships evaluated together.
\(k_r\) Expansion response coefficient Sets the active strength of the expansion term for the evaluated node and application.
\(k_c\) Compression feedback coefficient Sets the active strength of the compression term for the evaluated node and application.
\(r\) Local separation or relational radius The positive separation, radius, scale-normalized distance, or other disclosed relational coordinate used by the application.
\(\Delta Q(t)\) Signed coherent difference The time-dependent coherent change driving transition, disturbance, propagation, reorganization, or decoherence.
\(f_{\mathrm{UFR}}(t)\) Signed active UFR response The time-dependent Universal Frequency Resonance response participating in the current local and enclosing relationship.
\(E(r)\) Expansion term Exact shorthand for \(k_r/r^2\).
\(C(r)\) Compression term Exact shorthand for \(k_c/[r^2(1+r)]\).
\(S(r)\) Static signed relationship Exact difference \(E(r)-C(r)\).
\(U(t)\) Dynamic signed relationship Exact product \(\Delta Q(t)f_{\mathrm{UFR}}(t)\).
\(t\) Time or retained event stage The active time coordinate used to preserve phase, propagation, delay, sequence, and state history.
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Complete explanation

4. Complete Explanation of Every Term

\(k_r/r^2\)

Expansion response

Expansion response is the outward or separation-supporting portion of the local MEFI relationship. It regulates how an organized node remains spatially responsive and capable of movement, distribution, circulation, or reorganization.

The \(1/r^2\) dependence causes the expansion response to weaken quadratically as the evaluated separation increases.

\(k_c/[r^2(1+r)]\)

Compression feedback

Compression feedback is the concentrating and structure-retaining portion of the local MEFI relationship. It supports localization, density, folding, collection, and the retention of nested organization.

The additional \((1+r)\) factor causes compression feedback to diminish faster with increasing separation than the expansion response.

\(\Delta Q(t)\)

Coherent difference

ΔQ represents a signed difference from the prior state that remains sufficiently ordered to participate in the surrounding resonant relationship.

ΔQ can be positive, negative, or locally zero. Its physical meaning depends on its sign, magnitude, timing, propagation history, UFR coupling, and the complete state of the receiving node.

\(f_{\mathrm{UFR}}(t)\)

Active UFR response

UFR is the enclosing resonant relationship through which the local node remains coupled to parent nodes, neighboring nodes, retained histories, and larger conditions.

The function \(f_{\mathrm{UFR}}(t)\) represents the signed active UFR response used by the specific calculation. It preserves timing, phase, and the possibility of reinforcement, opposition, reversal, attenuation, or reintegration.

None of these four relationships is the MEFI framework by itself. The complete state exists only when expansion, compression, ΔQ, and UFR are evaluated together.
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Sign conventions

5. Sign Conventions and State Meaning

5.1 Coefficients

In the canonical expression, \(k_r\) and \(k_c\) represent the magnitudes of expansion response and compression feedback. Their opposing relationship is expressed by the subtraction inside \(S(r)\).

5.2 Signed ΔQ

ΔQ retains sign. Converting ΔQ to an absolute magnitude would erase whether the coherent change is acting with or against the current phase relationship.

5.3 Signed UFR response

\(f_{\mathrm{UFR}}(t)\) also retains sign. A negative UFR response is not treated as missing data or converted to a positive strength. Its sign is part of the active phase relationship.

5.4 Dynamic product

$$ U(t)= \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$
ΔQ sign UFR sign Dynamic product Mathematical result
Positive Positive Positive The dynamic relationship adds positively to the complete state.
Negative Negative Positive Two negative signs produce a positive dynamic contribution.
Positive Negative Negative The dynamic relationship subtracts from the static state.
Negative Positive Negative The dynamic relationship subtracts from the static state.
Zero Any value Zero No local ΔQ contribution is present at that instant.
Any value Zero Zero The selected UFR response produces no dynamic contribution at that instant.

5.5 Meaning of the final sign

\(F_{\mathrm{MEFI}}>0\)

The complete evaluated state is positive under the sign convention of the application. This commonly corresponds to an expansion-supporting or positive dynamic condition, but the term breakdown must still be inspected.

\(F_{\mathrm{MEFI}}<0\)

The complete evaluated state is negative under the sign convention of the application. This commonly corresponds to a compression-supporting or negative dynamic condition.

\(F_{\mathrm{MEFI}}\approx0\)

The signed contributions are near cancellation. This does not mean the node contains no activity, no structure, or no internal energy. Large opposing terms may still be present.

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Mathematical behavior

6. Radial Behavior and Balance

6.1 Expansion behavior

$$ E(r)=\frac{k_r}{r^2} $$
$$ \frac{dE}{dr} = -\frac{2k_r}{r^3} $$

For positive \(k_r\) and \(r\), the expansion response decreases as separation increases.

6.2 Compression behavior

$$ C(r)= \frac{k_c}{r^2(1+r)} $$
$$ \frac{dC}{dr} = -\frac{k_c(2+3r)} {r^3(1+r)^2} $$

For positive \(k_c\) and \(r\), compression feedback also decreases as separation increases.

6.3 Large-radius behavior

$$ E(r)\sim\frac{k_r}{r^2}, \qquad C(r)\sim\frac{k_c}{r^3} \quad \text{as }r\rightarrow\infty $$

At large separation, compression feedback falls approximately as \(1/r^3\), while expansion response continues to fall as \(1/r^2\). The expansion term therefore remains longer-ranged within the canonical static relationship.

6.4 Small-radius boundary

Both radial terms increase sharply as \(r\) approaches zero. The canonical formula therefore requires \(r>0\).

A numerical application must define a finite minimum radius, node scale, sensor separation, or regularized relational distance. It must not evaluate the formula at \(r=0\).

6.5 Static balance radius

The static expansion–compression relationship is balanced when:

$$ S(r)=0 $$
$$ \frac{k_r}{r^2} = \frac{k_c}{r^2(1+r)} $$
$$ r_{\mathrm{balance}} = \frac{k_c}{k_r}-1 $$

A positive static balance radius exists when:

$$ k_c>k_r $$

If \(k_c\leq k_r\), the equation does not produce a positive static balance radius under the canonical positive-coefficient interpretation.

6.6 Complete-state cancellation

The complete state is zero when the dynamic relationship exactly opposes the static relationship:

$$ U(t)=-S(r) $$
$$ \Delta Q(t)\, f_{\mathrm{UFR}}(t) = - \left[ \frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)} \right] $$

This is dynamic cancellation, not the absence of an active system.

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Coherent coupling

7. ΔQ and UFR Coupling

The dynamic relationship is not ΔQ alone and is not UFR alone. It is their signed product.

$$ U(t)= \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$

7.1 ΔQ is the coherent change

ΔQ identifies the ordered departure from the previous state. An application may derive ΔQ from direct observations, member-node changes, matter-state transitions, biological measurements, or simulation variables, but the mapping must be disclosed.

7.2 UFR supplies the active response relationship

\(f_{\mathrm{UFR}}(t)\) preserves the active phase and temporal relationship through which ΔQ couples to the surrounding system.

A simulation may use a sinusoidal, damped, pulsed, measured, reconstructed, or numerically propagated UFR response. That selected function belongs to the implementation. It does not redefine UFR universally.

7.3 Phase matters

Two events with the same ΔQ magnitude can produce different dynamic results when their UFR phase differs.

$$ \Delta Q_1=\Delta Q_2 \quad\not\Rightarrow\quad U_1=U_2 $$

The result also depends on:

  • UFR sign,
  • event timing,
  • propagation delay,
  • the complete state of the receiving node,
  • parent and enclosing relationships,
  • retained event history.
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Nested application

8. Nested Node Application

Every local node receives its own complete MEFI evaluation.

$$ F_{\mathrm{MEFI},i}(t)= \left[ \frac{k_{r,i}(t)}{r_i(t)^2} - \frac{k_{c,i}(t)} {r_i(t)^2[1+r_i(t)]} \right] + \Delta Q_i(t)\, f_{\mathrm{UFR},i}(t) $$

The subscript \(i\) identifies the specific member, cell, matter node, sensor location, planet, parent structure, or other evaluated relationship.

Member state

Every member continues to recalculate its own complete state. Membership in a larger node does not erase the member.

Parent state

The parent is reconstructed from the current relationships of its active members. It does not become a frozen average.

Neighbor state

Local neighbors affect the evaluated relationship through disclosed coupling and propagation rules while retaining their own complete states.

Enclosing state

The node remains part of a larger UFR, compression–expansion, temporal, and propagation context.

The official formula must be applied at every interaction. A parent object, average score, visual marker, or aggregate value may summarize a system, but it may not replace the live complete states of its members.
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Event propagation

9. Propagation and Event Identity

A coherent event can propagate through multiple layers while changing expression. The event identity, sign, timing, order, and measurement history must remain retained.

9.1 Origin state

The event begins with a time-stamped source record containing direct observations, the complete local MEFI state, and a unique event identifier.

9.2 Transit state

During transit, the system retains measurements and calculated changes in:

  • ΔQ,
  • density and temperature,
  • compression and expansion conditions,
  • velocity and direction,
  • signed phase components,
  • propagation timing,
  • uncertainty and source health.

9.3 Receiving state

The receiving layer does not simply inherit the source value. It recalculates its own complete state using its current local coefficients, relational radius, incoming ΔQ, active UFR response, and existing nested condition.

$$ F_{\mathrm{receive}}(t_a)= \left[ \frac{k_{r,\mathrm{receive}}}{r_{\mathrm{receive}}^2} - \frac{k_{c,\mathrm{receive}}} {r_{\mathrm{receive}}^2 (1+r_{\mathrm{receive}})} \right] + \Delta Q_{\mathrm{incoming}}(t_a)\, f_{\mathrm{UFR,receive}}(t_a) $$

9.4 Pattern preservation

Propagation is tested through more than a single delayed peak. The retained event may be compared by:

  • onset and arrival time,
  • ordered sub-event sequence,
  • sign and polarity,
  • amplitude relationships,
  • compression and expansion stages,
  • phase reversal,
  • attenuation or amplification,
  • recovery or Phase D behavior.
Native observations remain separate from the MEFI calculation. Correlation can identify a relationship worth testing, but it does not establish propagation or mechanism by itself.
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Coherence boundaries

10. RePhase and Phase D

10.1 RePhase

RePhase is the reorganization of a complete node after coherent change. It is not an additional term added to the formula.

$$ F_{\mathrm{MEFI}}^{\mathrm{old}} + \delta F_{\mathrm{MEFI}} \longrightarrow F_{\mathrm{MEFI}}^{\mathrm{new}} $$

A RePhase state may differ from the prior state while preserving the identity and larger organization of the node.

RePhase involves the complete redistribution of:

  • expansion response,
  • compression feedback,
  • ΔQ,
  • UFR phase and coupling,
  • member-node relationships,
  • parent-node organization,
  • retained propagation history.

10.2 Phase D

Phase D is the condition in which the existing node can no longer retain or rebuild a supported nested relationship.

Phase D is not defined by one coefficient, one sensor value, or one simplified threshold. It requires evaluation of the complete state through time.

The shorthand \(k_c>k_r+\Delta Q_{\mathrm{crit}}\) is not an official complete Phase D criterion. It omits radius, sign, active UFR response, propagation history, member-to-parent relationships, persistence, and RePhase capacity.

10.3 Complete Phase D assessment

An application evaluating Phase D must examine whether the node shows persistent failure across the complete relationship, including:

  • unresolved expansion–compression mismatch,
  • ΔQ that remains unsupported or destructive,
  • UFR coupling that cannot restore or reorganize the state,
  • loss of member-to-parent coherence,
  • failure of RePhase,
  • continued degradation through time.
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Dimensional contract

11. Units and Dimensional Contract

Every implemented term must be dimensionally compatible with the complete MEFI state used by that application.

11.1 Required compatibility

$$ [F_{\mathrm{MEFI}}] = \left[ \frac{k_r}{r^2} \right] = \left[ \frac{k_c}{r^2(1+r)} \right] = \left[ \Delta Q\, f_{\mathrm{UFR}} \right] $$

If \(r\) is dimensionless or normalized, the coefficients must be defined accordingly. If \(r\) carries physical units, the coefficients must carry the compensating dimensions required by the application.

11.2 The \((1+r)\) requirement

The expression \(1+r\) requires \(r\) to be dimensionless or to be normalized to a disclosed reference scale.

$$ \rho= \frac{r_{\mathrm{physical}}} {r_{\mathrm{reference}}} $$
$$ C(\rho)= \frac{k_c} {\rho^2(1+\rho)} $$

An application using a dimensional physical radius should therefore disclose the reference scale used to create the dimensionless relational radius.

11.3 Native sensor units

Direct sensor measurements remain stored in their original units. Any transformation into \(k_r\), \(k_c\), \(r\), ΔQ, or \(f_{\mathrm{UFR}}\) must be:

  • explicit,
  • reproducible,
  • versioned,
  • dimensionally defined,
  • separate from the original observation.
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Interactive calculation

12. Complete-State Calculator

This calculator accepts direct values for the five active formula inputs and evaluates the complete MEFI state. It does not calculate a proxy coherence score, prediction confidence, or Phase D percentage.

Official MEFI Formula Calculator

Enter \(k_r\), \(k_c\), \(r\), ΔQ, and the signed active \(f_{\mathrm{UFR}}\) value. Every result is calculated from the complete canonical equation.

Nonnegative coefficient magnitude.
Nonnegative coefficient magnitude.
Must remain greater than zero.
Positive, negative, or zero.
Active response at the evaluated time.
EXPANSION E 0.040000
COMPRESSION C 0.006667
STATIC S = E − C 0.033333
DYNAMIC U = ΔQ × UFR 0.500000
COMPLETE FMEFI 0.533333
Positive complete state
The current result is positive. Inspect the static and dynamic terms to identify which relationship produces the sign.

This calculator accepts an already determined signed UFR response. It does not define UFR as one universal waveform.

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Implementation requirements

13. Official Application Contract

A page, simulation, sensor system, biological tool, or observational monitor may claim to implement the official MEFI formula only when it follows these requirements.

Complete formula

Every physical interaction evaluates expansion, compression, ΔQ, and UFR together.

Correct coefficients

\(k_r\) always identifies expansion response and \(k_c\) always identifies compression feedback.

Signed inputs

Signed ΔQ and signed phase-sensitive measurements are not converted to absolute magnitude without explicit diagnostic labeling.

Positive radius

The calculation never evaluates \(r=0\). Any minimum radius or normalization scale is disclosed.

Native observations

Direct measurements retain source, timestamp, sign, units, and quality status separately from derived MEFI values.

Disclosed mappings

Every sensor-to-formula transformation is explicit, reproducible, versioned, and dimensionally defined.

No substitute scores

Coherence, confidence, risk, index, or normalized values may summarize a result but may not replace missing formula inputs.

Missing means missing

An unavailable direct input remains unavailable. A response index or unrelated channel is not silently substituted.

Nested members remain live

Composite parents are rebuilt from active member states rather than replacing their members with a frozen average.

Retained propagation

Event identity, timing, sequence, sign, and stage history remain preserved through connected systems.

Derived values are labeled

Any coherence diagnostic, Phase D risk, RePhase potential, or prediction confidence is visibly identified as derived.

Versioned implementation

Formula mappings, source contracts, and numerical changes include a version identifier and revision history.

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Interpretation boundary

14. What the Formula Is Not

  • It is not four independent theories placed beside one another.
  • It is not a compression-only model.
  • It is not an expansion-only model.
  • It is not a ΔQ-only disturbance score.
  • It is not a single chosen UFR waveform.
  • It is not a normalized average of unrelated sensors.
  • It is not automatically a conventional force quantity.
  • It is not a permission to replace missing inputs with response indices.
  • It is not complete when signs, phase, time, or nested context have been removed.
  • It is not fully implemented when a composite parent replaces the live states of its members.
Any implementation that reverses \(k_r\) and \(k_c\), removes the sign of ΔQ or phase-sensitive inputs, treats a diagnostic as a core term, or calculates only one part of the equation is not using the official complete MEFI formula.
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Official wording

15. Official Citation Language

Official equation:

$$ F_{\mathrm{MEFI}}(r,t)= \left[ \frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)} \right] + \Delta Q(t)\, f_{\mathrm{UFR}}(t) $$

The MEFI core formula, developed by Steven Greenmyer, defines the complete local MEFI state as the signed expansion–compression relationship plus the signed coherent ΔQ–UFR relationship.

Suggested citation

Greenmyer, Steven. “The Official MEFI Core Formula.” MEFI Theory, 2026.

Short description

MEFI Theory is a complete resonance–compression framework in which expansion response, compression feedback, coherent difference, and Universal Frequency Resonance are evaluated together across nested systems and retained propagation histories.

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FAQ

Frequently Asked Questions

Is \(F_{\mathrm{MEFI}}\) a conventional force?

Not automatically. It is the complete MEFI state. A specific application may derive a force-like observable, movement, rate, pressure relationship, or other measurable quantity from the state, but that derived quantity must be labeled separately.

Can the expansion and compression terms be studied separately?

Yes, for education and diagnostics. They cannot be interpreted as complete physical models independently of ΔQ, UFR, time, and the nested system.

Is UFR always a sine wave or damped cosine?

No. Those functions may be used in specific interactive or numerical experiments. The official formula requires the active signed UFR response used by the application; it does not define UFR as one universal waveform.

Why must ΔQ retain its sign?

Because the sign determines how ΔQ combines with the signed UFR response. Taking only the magnitude can reverse or erase the dynamic contribution.

Does a zero final result mean nothing is happening?

No. It may indicate cancellation between active static and dynamic relationships. The individual terms may remain large even when the signed total is near zero.

Can the formula be applied to every scale?

MEFI applies the same complete relationship across scale, but each application must define its coefficients, relational radius, ΔQ mapping, UFR response, units, and nested context. Scale use does not permit proxy substitution.

Is Phase D determined by compression alone?

No. Phase D requires persistent failure of the complete nested system to retain or rebuild coherence. Radius, expansion, compression, ΔQ, UFR response, propagation history, member-parent relationships, and RePhase capacity all matter.

How should direct sensors enter the formula?

Each sensor remains in its native units and is assigned to its proper role through a disclosed, reproducible, dimensionally defined mapping. Direct observations remain stored separately from the derived MEFI calculation.

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Official MEFI Core Formula · Steven Greenmyer
Canonical equation, exact decomposition, application requirements, nested propagation, RePhase, and Phase D interpretation.
Updated August 6, 2026.