Theophysics Registry

ISO-006: Coherence Equation ↔ Salvation

Classification Level 3 — Isomorphism

Confidence HIGH

Version v1.0 | April 2026

⚛ ISO-006 — Coherence Equation

Logistic Growth ↔ Salvation

The Lowe Coherence Equation Maps Exactly onto Salvation and Sanctification Dynamics

"Work out your salvation with fear and trembling, for it is God who works in you." The comma in that verse IS the equation. Philippians 2:12–13 encodes dC/dt = O·G(1−C) − S·C.

The Lowe Coherence Equation

dC/dt = O·G(1−C) − S·C

                            Ceq = (O·G) / (O·G + S)
                        

Logistic-type ODE Stable equilibrium Two-variable product

Domain Specifications

⚛

Domain A — Physics

Lowe Coherence Equation

dC/dt = O·G(1−C) − S·C — a logistic-type ODE governing the time evolution of coherence. Five variables:

C = coherence (0 to 1)
O = openness / observer coupling (0 to 1)
G = grace field strength (external input, always > 0)
S = entropy / noise (always > 0)
(1−C) = capacity term (growth slows as coherence increases)

Stable equilibrium at C_eq = (O·G) / (O·G + S). Three phase regimes are determined by the coupling parameter s.

✝

Domain B — Theology

Salvation & Sanctification

Salvation and sanctification dynamics as described across the New Testament epistles. The process by which a human being moves from spiritual death toward spiritual coherence with God.

The theological tradition has split into two camps — Calvinism (grace is sovereign, not earned) and Arminianism (free will matters, you can resist). The Lowe Coherence Equation dissolves this debate: Calvinism identified G. Arminianism identified O. Both are real variables in a two-variable product O·G. Neither camp is wrong — they are each holding one factor of a product.

Three Phase Regimes

The coupling parameter s determines which regime the system occupies. Each regime maps to a distinct spiritual state with its own dynamics, trajectory, and scriptural signature.

Regime 1

Autonomous Decay

s = −1 | dC/dt = −S·C

Pure exponential collapse. No coupling to external grace. The system decays to zero with no floor.

Romans 1:24–28 — "God gave them over." Pure decay with no floor. When the observer fully decouples from the grace field, coherence collapses exponentially.

Regime 2

Performance Mode

s ≈ 0 | C_eq ≈ 1/3

Partial coupling. Effort without surrender. The equilibrium is low and the trajectory is exhausting.

Works-based religion — effort without surrender. Burnout trajectory. The system optimizes O (openness) at a fixed, low s. You can work harder, but you cannot outrun the entropy term.

Regime 3

Full Surrender

s = +1 | dC/dt = G(1−C) − S·C

Growth toward high equilibrium. Full coupling to the grace field. The capacity term (1−C) provides natural saturation.

Philippians 2:12–13 — "Work out your salvation with fear and trembling, for it is God who works in you." The comma in that verse IS the equation.

The Isomorphic Mapping

The Calvinist-Arminian resolution: Both sides are correct because both sides are holding one factor of a two-variable product. The equation does not compromise between them — it contains both as necessary terms.

Calvinism

G (Grace is sovereign)

Arminianism

O (Free will matters)

Product

O·G (Both required)

Variable Mapping Table

Physics Variable	↔	Theology Variable
C — coherence (0 to 1)	↔	Spiritual maturity / sanctification
O — openness / observer coupling	↔	Free will / human response (Arminian variable)
G — grace field strength	↔	Sovereign grace (Calvinist variable)
S — entropy / noise	↔	Sin / temptation / worldly entropy
(1−C) — capacity term	↔	Room to grow (growth slows near maturity)
s — coupling parameter	↔	Surrender coefficient (posture toward God)
C_eq — stable equilibrium	↔	Spiritual steady state (where you plateau)

Empirical Support

Cochrane Review 2020

N = 10,565. AA ≥ CBT for addiction recovery. AA changes s (the surrender coefficient). CBT optimizes O at fixed s. Changing s is categorically more powerful than optimizing O.

AA ≥ CBT (surrender > optimization)

PET Scan Data

D2 receptor downregulation in addiction maps exactly to the autonomous decay regime (s = −1). The dopaminergic system shows exponential collapse when decoupled from external coherence sources.

D2 downregulation ↔ s = −1 regime

fMRI: ACC Hyperactivity

Anterior cingulate cortex hyperactivity in performance religion maps to the s ≈ 0 regime. The brain signature of "trying harder" without surrender — effortful striving at a fixed low coupling.

ACC hyperactivity ↔ s ≈ 0 regime

Newberg Imaging

vmPFC activation in contemplative prayer maps to the s = +1 regime. The brain signature of surrender — ventromedial prefrontal cortex activation during deep prayer and meditation.

vmPFC activation ↔ s = +1 regime

Separator Tests

These four tests are the gatekeepers between Correspondence and Isomorphism. ALL FOUR must pass for Level 3 classification.

✓

Test A — Structural Preservation

The logistic-type ODE with two-variable coupling product maps directly from coherence physics to sanctification dynamics. The key structural features — coupling product O·G, capacity term (1−C), entropy opposition S·C, and stable equilibrium — are all preserved under mapping.

PASS — Structure Preserved

✓

Test B — Non-Arbitrariness

The three-regime prediction is not imposed but forced by the equation's own mathematics. The Calvinist-Arminian resolution emerges from the product structure O·G — not from theological compromise. Cochrane data independently confirms the s-change mechanism over O-optimization.

PASS — Mapping is Forced

✓

Test C — Constraint

The mapping rules things out: if O and G were the same variable, the Calvinist-Arminian resolution fails. If CBT consistently beat AA, the s-change model fails. If C = 0 were reachable with G > 0, the grace floor claim fails. The model forbids specific configurations.

PASS — Rules Out Violations

✓

Test D — Bidirectionality

Physics predicts theology: the equation requires three regimes, and Scripture independently describes exactly three spiritual states. Theology predicts physics: Philippians 2:12–13 encodes a two-variable product that the equation independently derives. Neuroimaging confirms all three predicted brain signatures.

PASS — Bidirectional Consequence

Classification & Evidence

Level 3 — Structural Isomorphism

                    Logistic-type ODE | Three-regime prediction | April 2026
                

Type

Isomorphism

Logistic growth + stable equilibrium

Confidence

HIGH

Cochrane N=10,565 + neuroimaging

Kill Conditions

6 ACTIVE

See falsification criteria below

Empirical Evidence

📊 Cochrane 2020 (N=10,565)

🧠 PET: D2 Receptor Data

🧠 fMRI: ACC Hyperactivity

🧠 Newberg: vmPFC Activation

📖 Philippians 2:12–13

📖 Romans 1:24–28

Source Articles

GTQ-03 Coherence Equation GTQ-03a Phase Regimes GTQ-03b Calvinist-Arminian Resolution GTQ-03c Empirical Validation

⚠ Falsification Criteria — 6 Kill Conditions

This claim carries its own kill conditions. If any of the following are demonstrated, the isomorphism is demoted or destroyed:

› 1. O and G collapse to one variable: If openness and grace are shown to be the SAME variable, the equation reduces and the Calvinist-Arminian resolution fails.
› 2. CBT consistently outperforms surrender-based approaches: If recovery data shows CBT consistently beating AA and similar surrender-based programs, the s-change model fails.
› 3. C = 0 reachable with G > 0: If a system with S > 0 and G > 0 can reach C = 0, the "grace floor" claim fails. The equation mathematically forbids this.
› 4. Unobserved predicted behavior: If the equation predicts a behavior not observed in any spiritual tradition, the mapping suffers empirical falsification.
› 5. Augustine's four states fail to map: If Augustine's four states of the will don't map to four parameter regions of the equation, historical theological validation fails.
› 6. Neuroimaging contradicts three-regime prediction: If brain imaging data contradicts the three predicted regimes (decay, performance, surrender), biological falsification occurs.

Calvinism identified G. Arminianism identified O. Both are real variables in a two-variable product O·G. Neither camp is wrong — they are each holding one factor of a product.

— ISO-006: Coherence Equation ↔ Salvation/Sanctification, Theophysics Registry