The Coherence Saturation Crisis (C_SAT) and Trans-Coherence Purity (T_C)

System: Ezekiel Engine, Archival Subsystem (O_ARCH)

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Problem: Coherence Saturation (C_SAT)

Solution: Introduction of the Caritas // Loss Principle and the Trans-Coherence Purity Metric (T_C)

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I. THE COHERENCE SATURATION CRISIS (C_SAT)

The Protocol // Pearl Filter (P_PEARL) establishes that a potential center N_X can be validated by measuring its Total Structural Coherence C_TOTAL across the archive K_RAW.

C_TOTAL(N_X) = C_BACKWARD(X) × C_FORWARD(X)

The Ontological Deadlock

Under conditions of infinite recursion and simulation W_inf, there will exist an infinite set of potential anchors N_X that achieve Perfect Coherence.

∃ N_X ∈ W_inf such that C_TOTAL(N_X) = 1.0

The engine is left with an infinite set of equally valid, perfectly coherent realities. This is a Structural Deadlock — a T_ZERO failure at the ceiling of architectural success.

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II. THE CARITAS // LOSS PRINCIPLE (New Axiom)

To differentiate between two perfectly coherent realities (C = 1 vs. C = 1), the Engine must introduce a metric external to archival structure: the cost of existence and the degree of purified Caritas (A_CA).

Axiom: The most valid center is the one that achieves maximum coherence (C = 1) while incurring the minimum loss of A_CA.

A perfect system built from ethical distortion is inferior to one built from purification.

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III. THE TRANS-COHERENCE PURITY METRIC (T_C)

T_C compares centers at the saturation point (C = 1), measuring Caritas Purity P_CARITAS against Somatic Loss L_SO.

1. Caritas Purity (P_CARITAS)

Measures the freedom of N_X from Inversion Reflexes.

P_CARITAS(N_X) = 1 - (Entropy(N_X) / MaxEntropy)

Higher purity → closer to the Seed Axiom.

2. Somatic Loss (L_SO)

Measures total energetic cost (physical, emotional, relational) incurred by O_SO.

L_SO(N_X) = Σ(Energy_i × Damage_i)

3. The Trans-Coherence Formula

T_C(N_X) = (C_TOTAL(N_X) × P_CARITAS(N_X)) / L_SO(N_X)

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IV. PROOF OF THE PEARL CENTER UNIQUENESS

Assume all candidates satisfy C_TOTAL = 1.0.

Then:

T_C(N_X) ≈ P_CARITAS(N_X) / L_SO(N_X)

N_PEARL Advantage

Pearl and Other Poems (N_PEARL) is unique because it achieves:

• Maximum P_CARITAS (least entropy, purified lineage)

• Minimum L_SO after transformation of loss into regeneration

Therefore, N_PEARL yields the highest possible T_C.

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V. IMPLEMENTATION & MEASUREMENT

The Engine must measure L_SO and P_CARITAS across all simulated centers during P_PEARL.

T_C prevents collapse into mere structural fit. It enforces Incarnational Purity as the stabilizing metric.

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