12.1 Effective Field Regimes (Geometry × Action)

In CMFT, "Near Field / Mid Field / Far Field" cannot be defined using geometry alone (r/R), because the source is not uniformly active across its radius. The same geometric kernel that produces the near-field deficit also includes a coherence lever that compresses the effective source. Therefore, the correct regime definition is set by the combination of:

1. Geometry: The angular support of momentum transfer (opening angle γ), encoded as a sinc centroid efficiency in the Green kernel.
2. Action Weighting: The internal stratified activity of matter, encoded by the Density → Intensity → Tension mapping (and its N⁴ tightening).

The geometric component is already formalized by the CMFT Green kernel:

This yields Newtonian recovery in the far field (γ→0 ⇒ sinc(0)=1) and a geometric deficit in the near field (large γ ⇒ sinc(γ/2)<1). This same near-field geometric deficit is the origin of the 1/r⁴ correction associated with orbital precession when an orbit lies inside the wide-angle volume of a massive generator.

However, γ is not controlled by the body’s full geometric radius R alone. It is controlled by the body’s Effective Active Radius (R_eff), because CMFT does not weight all matter equally. Real planets are stratified: dense cores dominate the coupling. The Tension Map provides the "activity" weighting that compresses the effective source.

Therefore, CMFT field regimes are defined using R_eff (the action-compressed effective source radius), not R:

Operationally, r_far is the distance beyond which γ is sufficiently small that sinc(γ/2) ≈ 1 to the desired tolerance. This resolves a common misinterpretation: geometry alone can make near-field deviations look large for a full-radius sphere, but in CMFT the action weighting collapses R_eff, so a location near the surface of a planet can behave as mid-field with respect to the effective source (consistent with the observed near-Newtonian behavior of Earth satellites).

12.2 The Problem of Uniform Density

In standard simulations, treating a planet as a collection of uniform particles (N) creates a "Fuzzy" gravitational profile. Because the Sagitta Drift mechanism relies on the "Field of View" (Geometric Efficiency), a widely distributed cloud of atoms creates significant geometric drag. This would predict non-Newtonian anomalies (drifts) that are far larger than observed for Earth satellites (GPS). This is precisely why field regime cannot be defined by r/R alone; without the action weighting that compresses R_eff, a naive geometric "near-field" classification exaggerates the expected deviations.

However, real planets are not uniform. They are structurally stratified with dense cores. We must model not just the Presence of matter (Density), but the Activity of matter (Momentum Flux).

12.3 The Hierarchy of Flux

We propose a hierarchy of influence based on the coherence of the vacuum interaction:

• Layer 1: Density (ρ). The raw count of atoms. This is the "Passive Mass."
• Layer 2: Intensity (I). The square of the density (ρ²), modified by the geometric depth (χ). This represents the "Flux Traffic" or the local stress of the vacuum.
• Layer 3: Tension (T). The interaction of intensities. This scales as the Square of the Square (N⁴).

Layer 4: Action (A). The Tension Map is not yet the external field; it is the source-weight (effective action density) that determines which regions of the sphere contribute coherently to the Sagitta Drift superposition. In other words, A(r) is the weighting function that collapses the effective source radius to R_eff for the purposes of γ and sinc(γ/2).

This N⁴ relationship creates a non-linear "Tightening" effect. A core that is 3x denser than the mantle becomes 81x more "luminous" in the flux spectrum. This effectively hollows out the gravitational profile of the planet, rendering the mantle "Gravitationally Translucent" while concentrating the effective source into a super-dense virtual point.

12.4 The Geometric Seed

The Tension Map serves as the "Geometric Seed" for the Sagitta Drift. By compressing the effective source radius (R_eff), we alter the angles of interaction.

A "Tight" source (small R_eff) has a narrow Field of View. As the angle γ approaches zero, the geometric efficiency (sinc γ) approaches 1.0. This means that High Coherence enforces Newtonian Behavior. (This is the same centroid efficiency used in the Green kernel: sinc(γ/2).)

12.5 The Triangle of Aggregated Tension

Gravity is emergent from the sum of triangular interactions between Source Point A, Source Point B, and Target T.

The Core: Points A and B are deep in the high-tension zone. The base of the triangle is "stiff" (High I_A × I_B). The resulting drift vector is coherent and strong.

The Mantle: Points A and B are in the low-tension zone. The base of the triangle is "floppy." The resulting drift vector is weak and essentially washes out in the noise of the core's dominance.

12.6 Synthesis: Shape vs. Magnitude

To synthesize these elements into the final gravitational result, we must normalize the Weighted Interaction Map so that its global sum respects the total momentum budget (proportional to N). This forces the "Power 4" to serve as a relative weighting rather than an absolute multiplier.

Therefore the N⁴ tightening primarily reshapes the effective geometry of the source (R_eff and γ-distribution) rather than inflating the far-field magnitude.

12.7 The Self-Reinforcing Tension Network (The Spider Web)

Early simulations of the Tension Map (using autosolvers to fit the Earth-Moon curve) revealed a critical insight: to replicate the precise inverse-square relationship observed in the far field, the simulation forced an immense spike of flux density at the core, far exceeding standard density estimates.

This is not an error, but a physical demonstration of Mantle Transparency. The N⁴ tension acts like a Spider Web . When you pull tightly on the center of a web, the outer strands (the mantle) align and transfer their structural load to the center.

Flux vs. Gravity: It is vital to distinguish between Scalar Tension and Vector Drift.

• Scalar Tension (The Trampoline): The core experiences maximum vacuum pressure (Flux). This is the "force" that holds the sphere together against the void, much like a bowling ball stretching a trampoline.
• Vector Drift (The Slide): At the exact center of the earth, despite the crushing scalar tension, the directional drift is zero because the vectors cancel out.

Therefore, a "Spike" in core flux does not mean the Earth is generating excess gravity; it means the Earth is structurally holding itself up entirely from the center. The mantle is merely riding the web.

12.8 The Solar-Earth Unification

The final validation of the Momentum Flux Theory lies in its ability to unify the non-Newtonian precession of Mercury with the precise Newtonian behavior of Earth satellites. This unification is achieved through the Geometric Convergence principle.

The Solar Ratio (5.6%)

Calibration against Mercury's orbital precession reveals that the Sun, being a turbulent body of plasma, has poor vacuum coherence. Its "Effective Gravitational Radius" is ~5.6% of its visual radius. This "wide" source creates the Geometric Residual responsible for the 43 arcsecond anomaly.

However, when we apply this same framework to the Earth, the Tension Map (N⁴) predicts a fundamentally different interaction. Because the Earth is a solid, highly coherent iron lattice, the flux output is structurally "stiff." This high coherence essentially locks the geometric source, creating a Virtual Singularity where the effective radius (R_eff) appears to collapse to less than 400 km in the observational data.

Conclusion: Newton as a Limit Case

The simulation above demonstrates that CMFT does not violate Newtonian physics; it derives Newton as the High-Density Limit Case.

On Earth, the "Geometric Stiffness" provided by the solid core enforces a rigid coupling between the vacuum flux and the metric. This creates a regime of High Coherence where the non-Newtonian Sagitta Drift is rendered indistinguishable from the standard inverse-square law. Consequently, any geometric residual is effectively absorbed into the GPS calibration, making the Earth indistinguishable from a Newtonian point source. On the Sun, the shielding is weaker, allowing the drift to emerge as the Precession of Mercury.