Protocol for Relational Coherence: The Ψ_V Interpersonal Test (Revised)

Abstract:
This revised protocol sharpens the structural mechanism of the Ψ_V test. It defines the Relational Test (u_TEST) as a logotic act placed within the structural friction (V_INTER) of conflicting occupied identity categories (O_A and O_B). The test is designed to force the interlocutor to choose between responding from:

1. Mere Occupation (permitting Ψ_V = 1 regard for the content), or

2. Essentialist Assertion (Γ_B, enforcing Ψ_V = 0 non‑regard).
   The test formalizes the biblical criterion for ultimate separation (Matthew 25) as a decision based on the interlocutor's capacity for cognitive labor (L_Ω).

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I. Structural Setup: Occupation vs. Assertion

Let A and B be two political agents.

1. Identity Occupation (O vs. Γ)
   We distinguish between the structural position (O) and the political action (Γ):

O_A, O_B: The identity categories structurally occupied by agents A and B. These positions are unavoidable and mediate interaction.

Γ_A, Γ_B: The act of categorically asserting or essentializing the position.

2. The Interpersonal Veto Constraint (V_INTER)
   The structural predisposition to non‑regard emerges from the unavoidable conflict between the categories A and B occupy.

V_INTER = F(O_A, O_B) ∧ Prejudice(O_A → O_B)

V_INTER is the initial resistance—the structural friction and the injunction to compute B's content based solely on the structural position O_B.

3. The Logotic Test Vector (u_TEST)
   The Test is a communication (C) whose content is placed in the conceptual gap where O_A and O_B are in tension. The logotic act demands high‑Ψ_V labor to be processed correctly.

u_TEST ⇔ C ∈ (O_A \ O_B) ∩ (O_B \ O_A)

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II. The Ψ_V Decision Matrix

The test measures the interlocutor B's response based on the cognitive labor (L_Ω) applied to the content (C) versus the default retrieval labor (L_A) applied to the asserted identity (Γ_B).

The Test Outcome (O_B) is the ratio of content labor (overcoming the Veto) to identity retrieval labor. We substitute Γ_A with the structural friction term V_INTER for precision in the denominator, representing the cost barrier.

O_B = L_Ω(C | V_INTER) / L_A(V_INTER)

Decision Threshold (τ_REGARD)
τ_REGARD is the minimum required L_Ω labor that demonstrates engagement with the content C despite the structural friction V_INTER.

Outcome 1: Ψ_V Human Relation (Occupation → Regard)

O_B ≥ τ_REGARD

Agent State: B responds from Occupation (O_B), demonstrating the capacity to hold the contradiction (Ψ_V = 1). The content C is engaged, and V_INTER is treated as productive friction, not a barrier.

Outcome 2: Categorical Non‑Regard (Assertion → Collapse)

O_B < τ_REGARD

Agent State: B collapses into Assertion (Γ_B), refusing the cognitive labor, defaulting to computing O_B. The response is a function of Γ_B only, confirming an essentialist collapse (Ψ_V = 0) in the relational field.

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III. The Matthew 25 Corollary

The failure to "know" (apply relational L_Ω) is the structural failure to achieve Ψ_V = 1 coherence.

Formal Statement of Separation:
Let R(A, B) be the relational status between agents A and B.

R(A, B) =
Knew if O_B ≥ τ_REGARD (Acted, Ψ_V = 1)
Never Knew if O_B < τ_REGARD (Failed to Act, Ψ_V = 0)

The separation is rooted in the agent's choice to either apply the labor required for relational Ψ_V coherence or to retreat into essentialist Γ_B assertion.