The complete framework, step by step
MEFI, explained without making your brain hurt.
Start with one system at one moment. One part pushes outward, one part presses inward, a new change enters, and the system responds to that change. MEFI puts those pieces together to describe the system’s current relationship.
01 · Start with the equation
Every mark in the formula, in plain English.
No advanced math is required. First read the sentence underneath the equation, then open any symbol in the component dictionary.
In ordinary words: final relationship = outward push − inward squeeze + new change × the system’s resonance response.
kc acts through the singular r² denominator.
This positive term represents expansion response at the current relationship radius. The coefficient kc is divided by r² only. It does not receive the (1+r) compression bracket.
Imagine a breathing, springy ball.
The ball has an outward push and an inward squeeze. Its size changes how strong those two effects are. Now tap it: that tap is the new change, ΔQ. The ball may strongly respond to the tap or barely respond; that response is represented by fUFR. MEFI combines all of this into one final relationship value.
This is only an analogy. It helps explain the roles in the equation; it is not a claim that every MEFI system is literally a ball or spring.
FMEFIThe final relationship valueWhat the whole equation produces+
Plain meaning: the net result after the outward, inward, and changing parts are combined.
Important: it is not automatically a force, frequency, prediction, or proof. Its meaning depends on the model, scale, units, and calibration used on that page.
rRelationship radiusHow separated or spread out the relationship is+
Plain meaning: r describes distance or separation inside the selected relationship. The exact units must be stated by the model using it.
Why it matters: a larger r makes both structural terms smaller because both divide by r².
r²Radius multiplied by itselfr × r, used in both structural terms+
Plain meaning: if r is 2, r² is 4. If r is 3, r² is 9.
Effect in this formula: as the relationship spreads out, expansion and compression are reduced by the squared distance. r can never be zero in the evaluator because division by zero is undefined.
kcExpansion strengthHow strong the outward side is+
Plain meaning: kc is the coefficient assigned to the outward or expansion response.
Exact placement: it is divided by r² only. The (1+r) bracket does not belong here.
krCompression strengthHow strong the inward side is+
Plain meaning: kr is the coefficient assigned to the inward or compression response.
Exact placement: it is divided by r²(1+r), and that completed compression amount is subtracted from the final relationship.
1+rCompression-only bracketAn extra restraint on the inward term+
Plain meaning: add 1 to r, then multiply that by r² to build the compression denominator.
Critical rule: this bracket belongs only under kr. Moving it under kc changes the formula and gives the wrong result.
ΔQThe signed changeWhat changed, including its direction+
Plain meaning: Δ means “change.” Q names the quantity being compared in that implementation. Positive and negative values keep the direction of the change.
Important: every page must define how Q is measured or derived. ΔQ by itself does not prove what caused the change.
fUFRResonance responseHow strongly the system answers the change+
Plain meaning: this factor represents how strongly the selected relationship participates in its enclosing UFR reference at that moment.
In the math: it multiplies ΔQ. If either value is near zero, the dynamic contribution is small.
tThe timestampThe one moment shared by the inputs+
Plain meaning: t says “at this time.” ΔQ(t) and fUFR(t) must refer to the same moment or to a disclosed lag-corrected moment.
Why it matters: using values from different times can create a relationship that never actually existed.
−Subtract compressionThe inward response reduces the balance+
Plain meaning: calculate the entire compression fraction first, then take that amount away from expansion.
Order matters: the minus sign does not belong inside the compression denominator.
+Add the dynamic termBring the signed change into the balance+
Plain meaning: after multiplying ΔQ by fUFR, add the signed result. Adding a negative number lowers FMEFI; adding a positive number raises it.
nodeThe system being followedMore than a dot on a screen+
Plain meaning: a node is the complete organized system chosen for the calculation. It can contain smaller member nodes and belong to a larger parent node.
Important: its boundary, scale, members, and surrounding support must be stated.
Do not overread the sign: positive does not automatically mean “good” or stable, and negative does not automatically mean “bad” or Phase D. Stability is judged from the complete nested state, its history, calibration, and what happens over time.
02 · Guided relationship path
What changes, and in what order?
Choose a stage. The explanation stays centered on one complete relationship rather than treating the coefficients as independent objects.
Load one complete nested state.
MEFI begins with the relationship, not with a disconnected coefficient. Radius, expansion response, compression response, ΔQ, UFR participation, time, parent node, and retained history must refer to the same modeled state.
03 · Layering and persistence
A pulse is a cycle, not a dot.
Each ΔQ pulse is treated as a compression–expansion wave cycle that can add another retained layer when the relationship remains supported.
The four-stage wave cycle
Select a stage to follow the modeled movement through one cycle.
The kc/r² response supports outward separation and creates the spatial-temporal opportunity for the rest of the cycle.
What can happen next?
The output is interpreted only inside the node’s complete nested support.
04 · Nested organization
The node changes with scale; the relationship logic does not.
A node is the complete organization at the selected scale. It contains internal members, participates in a parent system, and carries retained history.
Choose the modeled scale.
The same formula structure can organize a comparison at different scales, but coefficients, source measurements, units, and calibration do not transfer automatically.
Field cell
A local modeled relationship carries its own radius, field state, phase, ΔQ, and resonance response while exchanging with neighboring cells and its enclosing lattice.
05 · Evidence discipline
Measurement is not the same thing as interpretation.
Every serious MEFI comparison should preserve provenance, units, timing, transformations, uncertainty, and the boundary between observation and model output.
Native observations
Values retained as supplied by their source.
- Sensor or catalog identifier
- Native units and timestamp
- Coverage and missingness
- Uncertainty or quality flags
Derived MEFI state
Disclosed transformations aligned to one relationship time.
- Normalization and sign rules
- Lag and propagation assumptions
- kc, kr, r, ΔQ, and UFR mapping
- Calibration version and bounds
Testable model output
Results evaluated against retained observations.
- Prediction window and tolerance
- Expected location or state range
- Hit, miss, and unresolved status
- Post-window audit and revision
Continue through the framework
From explanation to formal definition.
This page shows the conceptual route. The framework page contains the full definitions, stability conditions, implementation boundaries, and falsification criteria; the formula page shows the relationship recalculating as one state.