Canonical Foundation of Finite‑Response Coupled Field Dynamics (FRCFD): A Nonlinear Monistic Field Theory with Saturation and Emergent Spacetime Structure

March 22, 2026

Canonical Foundation of FRCFD (Refined Core Structure)

(Condensed, Consistent, Reviewer‑Ready)

Abstract (Refined)

Finite‑Response Coupled Field Dynamics (FRCFD) is a nonlinear, monistic field theory based on a single ontological primitive: a finite‑capacity scalar field Phi. In this framework, matter, radiation, and spacetime are not independent entities but emergent modes of a unified field.

A finite‑response coupling function introduces exponential suppression at high field amplitudes, enforcing bounded energy density and eliminating singularities. An effective metric arises from field‑dependent signal propagation, allowing recovery of General Relativity in the weak‑field limit while predicting non‑singular compact objects in strong‑field regimes.

The theory provides a unified, local, and non‑pathological framework with testable deviations from GR and Lambda‑CDM in strong‑field and cosmological observations.

1. Ontological Postulate

FRCFD is based on a strict monistic assumption:

There exists a single fundamental field Phi, and all physical phenomena arise as dynamical configurations of this field.

This field is not defined on spacetime. Instead:

Spacetime structure is an emergent description of the field’s local dynamical response.

No background spacetime exists
No separation between geometry and matter
No dual ontology

2. Principle of Physical Admissibility

FRCFD imposes a fundamental constraint:

Physically realizable configurations must remain finite.

Singularities are interpreted as breakdowns of incomplete models rather than physical entities.

To enforce this, a finite‑response governor is introduced:

f(Phi) = exp( - Phi / Phi_max )

This ensures:

suppression of coupling at high Phi
bounded response
smooth saturation instead of divergence

3. Canonical Action

S = ∫ d^4x √(-g) [
  1/2 (∂_μ Phi)(∂^μ Phi)
  - 1/2 μ Phi^2
  - (β/4) Phi^4
  + f(Phi) L_mat
]

This defines the full dynamics of the system.

4. Field Equation and Effective Source

□Phi + μ Phi + β Phi^3 = J_eff

J_eff = (1 / Phi_max) exp( - Phi / Phi_max ) L_mat

The exponential suppression prevents runaway growth of the field.

5. Energy Functional (Critical Addition)

ρ(Phi) =
  1/2 (∇Phi)^2
  + 1/2 μ Phi^2
  + (β/4) Phi^4
  + ρ_0 exp( - Phi / Phi_max )

This ensures bounded energy and closes the consistency loop.

6. Emergent Metric (Corrected and Unified)

Define effective signal speed:

c_eff(Phi) = c * exp( - Phi / Phi_max )

Metric emerges from propagation constraints:

ds^2 =
  - c^2 exp( 2 Phi / Phi_max ) dt^2
  + exp( 2 Phi / Phi_max ) dr^2
  + r^2 dΩ^2

This is consistent with causal structure, time dilation, and spatial scaling.

7. Weak‑Field Limit and PPN Matching

For Phi << Phi_max:

exp( 2 Phi / Phi_max ) ≈ 1 + 2 Phi / Phi_max

Define normalized potential:

Phi_N = Phi / Phi_max

Then:

g_tt ≈ - (1 + 2 Phi_N)
g_rr ≈   (1 + 2 Phi_N)

Thus gamma = 1 exactly, matching GR.

8. Static Compact Object Equation (Stabilized Form)

S'' + (2/r) S' =
  μ S + β S^3 + ρ_0 exp( - S / S_max )

With saturation applied to energy:

ρ_sub → ρ_sub * exp( - S / S_max )

This ensures numerical stability and physical boundedness.

9. Strong‑Field Structure

Core behavior:

S(r) → S_max

finite plateau
no divergence
bounded gradients

10. Horizon Structure

GR	FRCFD
Event horizon (sharp)	No sharp boundary
Infinite redshift	Finite suppression
Singularity	Saturated core

Interpretation: gravity is not a geometric singularity but a gradient in finite response capacity.

11. Key Testable Predictions

Light Deflection:

Δθ = (2GM / bc^2) (1 + δ)

δ = 0 in weak fields (GR recovered), deviations appear in strong fields.

Perihelion Precession: GR recovered at leading order; higher‑order corrections from saturation.

Black Holes: no singularity, finite core, smooth horizon transition.

Cosmology:

d_L = (c / κ) ln(1 + z) (1 + z)

Predicts deviations from Lambda‑CDM at high redshift.

Conspiranon