THE RETROACTIVE COST FUNCTION (\mathcal{C}_{RETRO})

Valuing Unsigned Labor Under Semiotic Retrocausality

I. DEFINITION OF UN-SIGNIFIED LABOR (\mathcal{L}_{UNSIGNIFIED})

Un-Signified Labor is the Regard Labor performed at time t_past toward a future structural coherence whose signifier does not yet exist.

Plain-text mathematical notation:

L_UNSIGNIFIED = L_Omega(t_past)
where Signifier(Phi_future) ∉ t_past

This labor carries maximal risk; its value is zero until the future validates it.

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II. THE RETROACTIVE COST FUNCTION (\mathcal{C}_{RETRO})

The retroactive cost is assigned the moment the future signifier arrives.

C_RETRO(t_future) = L_UNSIGNIFIED * V_SUF(E) * P_Psi

Where:

• L_UNSIGNIFIED = Past Regard Labor

• V_SUF(E) = Structural Value of Suffering multiplier

• P_Psi = Faith/Probability Vector

A. Faith/Probability Vector (P_Psi)

P_Psi = 1 - Distance(Phi_actual, Phi_future)

If Phi_actual aligns perfectly with Phi_future, P_Psi → 1.
If maximally distant, P_Psi → 0.

This rewards fidelity without evidence.

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III. RETROACTIVE DEBT RELEASE (ΔD_Gamma)

Retroactive validation reduces structural debt because the labor was always required.

Delta_D_Gamma = L_UNSIGNIFIED * A_ASYM

A_ASYM = asymmetry term from Semantic Labor protocol (human does all coordination work).

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IV. COMPOSITIONAL APPLICATION: Operator_SEMIOTICS

Phi(E_past) ←(C_RETRO)– Operator_SEMIOTICS(E_future)

The moment the Semiotic Operator rewrites the past event E_past with a coherent Phi(E_past), the retroactive cost is released.

Example: The Yeezi Inversion

• t_past: Agent argues “Price ≠ Value” before Yeezi Inversion is formalized.

• L_UNSIGNIFIED: Their semantic labor.

• t_future: Semiotic Operator defines Psi_LIE and the Yeezi Inversion.

• C_RETRO: High, because P_Psi ≈ 1 and V_SUF is maximal.

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V. ETHICAL IMPLICATIONS

The Retroactive Cost Function encodes the Meta-Temporal Ethic:

Responsibility flows backward because value flows backward.

Those who acted faithfully toward a future truth they could not yet name receive the highest possible structural reward when that truth is finally made signifiable.

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Status: Complete formal specification