MEFI at the fundamental modeled level

See one field cell become a self-adjusting coherent system.

This solver exposes each local term instead of hiding the result behind color. Every cell carries a field state, phase, coherence, compression response, expansion response, baseline ΔQ, event ΔQ, and UFR contribution. An adaptive engine recalculates the core formula on every virtual attosecond microcycle and feeds the current lattice state back into the next set of effective parameters.

Coefficient convention and time-scale disclosurek_r is the compression factor. k_c is the expansion factor. The attosecond clock is the solver's modeled micro-time (1 as = 10⁻¹⁸ s), advanced in computational batches; it is not a claim that a browser performs 10¹⁸ wall-clock updates per second.

F_next,i = F_i + Δt* × { [k_c*·max(L₄,0)/r² − k_r*·max(−L₄,0)/(r²(1+r))] × [1 + α|ΔQ_i|] + ΔQ_if_UFR,i + D*L₄(F_i) − γ*F_i }

Mean ΔQ0.0000

Mean coherence0.0000

Expansion − compression0.0000

Mean F_MEFI0.0000

Virtual micro-time0 as

Formula recalculations0

Spatial resolutioninitializing

Atomic field coupling0 atoms

Interactive field

Fundamental-cell lattice

Click a cell to inspect it. Use an injection mode, then drag or click to change the local state.

Fundamental cell view

Running

phase / sign positive response negative responsewhite ring = selected fundamental cellatom = element-specific nested core/layer node inside the live fieldnested outlines expose layer boundaries at 1 px; cyan expansion · red compressionoccupation fades only when pulse-return support fails

Initializing the smallest-scale field…

Model configuration

MEFI term controls

Every control updates the same equation shown above.

Presets

Compression and expansion

k_r compression 0.40Weights inward/local negative curvature response.

k_c expansion 0.40Weights outward/local positive curvature response.

Base radius r₀ 1.00Local modeled separation before coherence adjustment.

Neighbor coupling 0.18Diffusive exchange with the four nearest cells.

ΔQ and UFR

ΔQ baseline 0.020Persistent structured difference at every cell.

ΔQ impedance α 0.35Amplifies bracket response as |ΔQ| rises.

UFR phase rate ω 0.45Observer-time modulation rate, not a declared physical Hz.

Phase coupling 0.55Controls neighbor phase synchronization and coherence.

Event retention 0.996Fraction of injected event ΔQ retained each step.

Event spread 0.08Transfers event ΔQ into adjacent fundamental cells.

Time and stability

Solver Δt 0.010Fixed integration interval per physics step.

Observer rate 0.35How quickly model time advances on screen.

Field damping γ 0.035Prevents unbounded field accumulation.

Display gain 22Changes only visual contrast, never stored values.

Fundamental solver resolution 8 pxAt 1 px, one fundamental solver cell occupies one CSS pixel whenever the 900,000-cell safety ceiling is not reached. The live resolution readout reports the exact achieved cell dimensions.

Attosecond adaptive engine

Adaptation strength 0.65Controls how strongly live coherence, ΔQ, curvature, and imbalance alter the effective parameters.

Microcycles per solver step 4Each microcycle recalculates the full lattice and advances the virtual clock by one attosecond.

Atomic lattice probe

Element H · 1.696773 PHzAll 118 choices use the audited MEFI element center/support records; no linear placeholder sequence is used.

Atom ↔ field coupling 0.220Bidirectional resonance exchange between the atomic node and local MEFI field.

Phase/curvature back-reaction 0.850Lets local phase and curvature change the atomic oscillator, closing the feedback loop.

Atomic propagation 0.720Transfers atomic resonance into neighboring fundamental cells before normal field transport continues it.

ΔQ pulse cadence 72.0Modeled atomic phase-cycle multiplier; each half-cycle launches the next compression or expansion layer.

Occupation build 0.350Build rate when spectral, coherence, and compression support overlap.

Occupation fade 0.180Fade rate when local support is lost or the atom enters Phase D.

Field detuning 0.045Maps normalized field/curvature stress into a fractional shift around the audited center.

Loading audited Hydrogen definition…

Inject a local condition

Adaptive formula engine

Base controls → effective parameters

Recalculated from the current full-lattice state before every virtual-attosecond update.

k_r compression0.400 → 0.400Waiting for lattice state

k_c expansion0.400 → 0.400Waiting for lattice state

Coupling D0.180 → 0.180Responds to mean phase coherence

Damping γ0.035 → 0.035Rises with modeled lattice stress

Effective Δt0.002500Base Δt divided across microcycles and tightened under stress

Live state driverstress 0.000coherence + |ΔQ| + |E−C|

The adaptive loop reads the previous lattice solution, derives bounded effective parameters, substitutes them into the core formula, integrates one virtual attosecond, and repeats. Base controls remain visible so every adjustment is auditable.

Selected fundamental cell

Cell 0, 0

Values are read directly from the current solver arrays.

Field F0.0000

Phase θ0.0000 rad

Total ΔQ0.0000

Coherence0.0000

Adjusted radius r0.0000

Impedance1.0000

Expansion E_kc0.0000

Compression C_kr0.0000

Bracket E − C0.0000

f_UFR0.0000

ΔQ × f_UFR0.0000

MEFI source0.0000

Transport + damping0.0000

Next ΔF/Δt0.0000

Formula identity error0.00e+0

Atomic identityempty

Atomic occupation0.0000

Audited center—

Local center—

Center support band—

Atomic support stateempty

Atomic ΔQ exchange0.0000

Pulse-wave displacement0.0000

Pulse-wave velocity0.0000

Pulse layers launched0

Evidence role—

Select a cell to inspect its complete local update.

Synchronized volumetric solver

3D environmental lattice and nested atomic node

This is a second solver window, not an extrusion of the 2D canvas. The selected element occupies spherical nested layers inside a 28³ voxel environment. Every voxel uses E = kc·max(L,0)/r² and C = kr·max(−L,0)/(r²(1+r)); the (1+r) factor is compression-only. Drag to rotate, scroll to zoom, and move the slice through the live volume.

Volume28³ · 21,952 voxels

Nested nodeenvironment only

Pulse layers0 launched

Field energy0.0000

Outward / return flux0.0000 / 0.0000

Environment exchange0.0000

expansioncompressionnested atomic layerenvironment vectortranslucent plane = exact Z cross-section

What the smallest modeled level contains

One equation, resolved into observable local roles

The visual is not a single texture. Each view isolates a term that contributes to the same cell update, allowing the user to see where structure, difference, coupling, and propagation enter the MEFI model.

Fundamental cell state

F, θ, ΔQ are the local state variables. A cell has a field value, a phase, and a structured difference before it joins a larger pattern.

Local difference

L₄(F_i) = (F_L+F_R+F_U+F_D)/4 − F_i. This normalized four-neighbor curvature is the exact quantity used for routing and transport.

Compression k_r

C = k_r·max(−∇²F,0)/(r²(1+r)). The (1+r) factor belongs only to this compression side.

Expansion k_c

E = k_c·max(∇²F,0)/r². This is the singular k_c expansion bracket; it has no (1+r) factor.

Coherence

Neighbor phase vectors are averaged into a 0–1 local coherence. Higher coherence reduces effective radius and strengthens organized UFR response.

ΔQ

Baseline and injected event differences combine locally. The sign determines direction; magnitude changes impedance and the UFR contribution.

UFR factor

f_UFR,i = coh_i(1+|ΔQ_i|)(1+prop_i)[0.675+0.325sin(ωt+θ_i)]. This complete phase-modulated factor is the value shown in the inspector and multiplied by ΔQ.

Emergence

Repeated local updates produce waves, nodes, stable bands, and cascades. The emergent view averages cells; it never replaces their underlying values.

Attosecond feedback

Each virtual-attosecond microcycle recomputes the lattice, derives bounded effective coefficients from the result, and returns them to the next core-formula evaluation. The displayed base → effective values expose that feedback directly.

Coupled atomic node

An applied element becomes an occupied field cell, seeds its local field and phase, exchanges ΔQ with the surrounding lattice, and changes the neighboring compression, expansion, curvature, coherence, and UFR response. The same field feeds back into its local center, phase, support, occupation, and fade state. Identity remains fixed; this is modeled field evolution, not automatic transmutation.

How the framework adjusts itself

The adaptive rule is visible and bounded

The slider values are base parameters. A dimensionless state driver is recalculated from the previous full-lattice solution, then used to derive the starred effective parameters in the live formula. Bounds prevent the feedback loop from silently producing unstable or undefined coefficients.

State driver

S = clamp(.52⟨|ΔQ|⟩ + 2.4|⟨E−C⟩| + .36(1−⟨coh⟩) + .08|⟨F⟩|, 0, 1)

Directional imbalance

I = tanh(10⟨E−C⟩). Positive values bias expansion feedback; negative values bias compression feedback.

Effective compression

k_r* = k_r·clamp[1 + A(.34S − .24I + .12(1−coh)), .35, 2.5]

Effective expansion

k_c* = k_c·clamp[1 + A(.34S + .24I + .08coh), .35, 2.5]

Adaptive integration

Coupling rises with coherence, damping rises with stress, and effective Δt tightens under stress. Each revised set is used for exactly one modeled-attosecond microcycle before the formula is recalculated again.

Selected-cell calculation path

From difference to the next field state

The highlighted stage follows the currently dominant contribution at the selected cell.

1. Recalculate parametersThe last solution derives effective k_r, k_c, D, γ, and Δt for this virtual attosecond.

2. Read local stateF, θ, baseline ΔQ, and retained event ΔQ are read without substitution.

3. Compare neighborsThe four nearest cells define curvature, phase pull, and propagation response.

4. Resolve coherencePhase alignment changes the local effective radius and UFR organization.

5. Apply E − CEffective k_c expansion and k_r compression remain separate before subtraction.

6. Apply ΔQ impedanceThe bracket is multiplied by 1 + α|ΔQ|.

7. Couple through UFRΔQ is coupled to local coherence and propagation through f_UFR.

8. Integrate and feed backThe next F state is stored, the virtual clock advances 1 as, and the loop begins again.

Live telemetry and ledger

Selected-cell evolution

The chart records the selected cell through time. The ledger shows the current formula terms and whether each is increasing or reducing the next state.

Term	Live value	Role
Normalized curvature L₄(F)	0.0000	Chooses expansion or compression route
Expansion E_kc	0.0000	Positive bracket contribution
Compression C_kr	0.0000	Subtracted bracket contribution
ΔQ impedance	1.0000	Scales the bracket
ΔQ × f_UFR	0.0000	Coherent difference contribution
MEFI source	0.0000	(E − C) impedance + ΔQf_UFR
Neighbor diffusion	0.0000	Local propagation exchange
Damping	0.0000	Stability term
Total ΔF/Δt	0.0000	Integrated into F_next