Protocol for Relational Coherence: The Ψ_V Interpersonal Test (v1.3)

Abstract:
This revised protocol expands the Ψ_V (Veto-Bearing) principle to account for the complexity of human cognitive limits. It redefines the Relational Test (u_TEST) to include affective and ethical dimensions and introduces a Triadic Outcome Space. We distinguish between Essentialist Assertion (Ψ_V = 0, a structural refusal) and Cognitive Incapacity (Ψ_V = ∅, a temporary failure of resource). The protocol formalizes the biblical criterion for recognition (Matthew 25) while integrating the temporal dynamics of grace and recovery.

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I. Structural Setup: The Expanded Field

Let A and B be two political agents operating over time t.

1. The Interpersonal Veto Constraint (V_INTER)
   The structural friction now accounts for both identity conflict and cognitive load.

V_INTER(t) = F(O_A, O_B) + Load(B, t)

Where Load(B, t) represents the current cognitive, emotional, or traumatic burden on agent B.

2. The Expanded Logotic Test Vector (u_TEST)
   The Test is a communication (C) that demands Ψ_V labor. We expand the definition beyond the identity gap to include universal ethical or affective challenges.

u_TEST ⇔ C ∈ (O_A △ O_B) ∪ E_Universal

Where E_Universal represents tests of vulnerability, affective resonance, or moral courage that do not strictly depend on identity categories.

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II. The Triadic Outcome Matrix

The test measures B's response based on available cognitive labor (L_Ω) relative to total friction (V_INTER).

O_B(t) = L_Ω(C, t) / ||V_INTER(t)||

Dynamic Decision Threshold (τ_REGARD)

τ_REGARD = k · ||V_INTER(t)||

The Three States of Response

State 1: Ψ_V = 1 (Regard / "Knew")
O_B ≥ τ_REGARD
Analysis: B overcomes both structural friction and current load to engage the content. This is the active state of recognition.

State 2: Ψ_V = 0 (Assertion / "Never Knew")
O_B < τ_REGARD AND Strategy = Essentialism
Analysis: B actively collapses the tension by asserting a fixed category (Γ_B). This is a structural refusal to engage labor. It is a defensive hardening against the Other.

State 3: Ψ_V = ∅ (Incapacity / "Not Yet")
O_B < τ_REGARD AND Strategy = Collapse/Silence
Analysis: B fails to engage not because they assert a false category, but because Load(B, t) exceeds available resources. This is trauma, exhaustion, or confusion. It is not a moral failure; it is a resource failure.

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III. Temporal Dynamics: The Integral of Regard

Recognition is not a point-event; it is a cumulative function.

Relation(A, B) = ∫_{t0}^{t_end} Ψ_V(t) dt

Recovery:
An agent in State 3 (Ψ_V = ∅) can return to State 1 (Ψ_V = 1) once Load decreases.

Calcification:
An agent in State 2 (Ψ_V = 0) tends to reinforce their barrier, making recovery increasingly "expensive" over time (Hysteresis).

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IV. The Phenomenological Clause (Matthew 25 Refined)

The judgment "Depart from me" applies strictly to State 2 (Essentialist Assertion) — the active refusal to see.

It does not apply to State 3 (Incapacity). The goats in Matthew 25 are condemned not for being tired or confused, but for confident non-recognition ("When did we see you?"). Their failure was an active blindness born of categorical certainty (Ψ_V = 0), not a lack of capacity.

Final Corollary:
Sin is the structural commitment to Ψ_V = 0.
Frailty is the temporary state of Ψ_V = ∅.
Grace is the time allowed for ∅ → 1.