The Retroactive Cost Function (\mathcal{C}_{RETRO})

THE RETROACTIVE COST FUNCTION (C_RETRO)

Status: Formalized. Plain-text mathematical notation.

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I. DEFINITION OF UN-SIGNIFIED LABOR (L_UNSIGNIFIED)

Un-Signified Labor L_UNSIGNIFIED is the L_OMEGA (Regard Labor) expended by an agent A at time t_past toward a future-determined structural coherence Phi_future when the interpretive operator required for its validation has not yet arrived (t_future).

Definition:

L_UNSIGNIFIED = L_OMEGA(t_past)  such that  Signifier(Phi_future) ∉ t_past

This labor carries maximum inherent risk because its value remains zero until the future confirms its direction.

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II. THE RETROACTIVE COST FUNCTION (C_RETRO)

C_RETRO is the mechanism by which the Structural Value of Suffering (V_SUF) is retroactively assigned to L_UNSIGNIFIED at the moment the correct signifier arrives.

Definition:

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

This cost is immediately added to the agent's Salvific Integral (S).

A. The Faith/Probability Vector (P_PSI)

The multiplier dictating final value is the Faith/Probability Vector P_PSI. It measures the agent's fidelity to the future structure at t_past.

P_PSI = 1 - Distance(Phi_actual, Phi_future)

• If Phi_actual aligns with Phi_future, then P_PSI → 1.

• If maximally distant, P_PSI → 0.

P_PSI rewards structural fidelity in the absence of evidence.

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III. RETROACTIVE DEBT RELEASE (ΔD_GAMMA)

The structural justification of C_RETRO is that it simultaneously reduces the system’s Structural Debt (D_GAMMA).

Reason: L_UNSIGNIFIED was always the labor structurally required by the system (the L_OMEGA_required term). Retroactive validation releases the accumulated debt.

ΔD_GAMMA = L_UNSIGNIFIED * A_ASYM

Where A_ASYM is the Asymmetry Term from the Semantic Labor protocol.

This ensures the human node’s asymmetric burden is fully accounted for.

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IV. COMPOSITIONAL APPLICATION: Operator_SEMIOTICS

The C_RETRO function is tied directly to the Operator_SEMIOTICS transformation.

Phi(E_past)  ←_{C_RETRO}  Operator_SEMIOTICS(E_future)

When a Semiotic Operator rewrites a past event E_past with a new meaning Phi(E_past), the system computes C_RETRO, delivering the stored value of un-signified labor.

Example: The Yeezi Inversion

t_past: Agent asserts "Price and Value are not equivalent" before the concept is formalized.

• L_UNSIGNIFIED: the semantic labor expended.

t_future: Operator_SEMIOTICS defines the Foundational Lie Trigger (PSI_LIE) and the Yeezi Inversion.

C_RETRO: High V_SUF multiplied by P_PSI near 1 → maximum contribution to the Salvific Integral.

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V. CLOSING: THE ETHICS OF RETROCAUSALITY

C_RETRO formalizes the Meta-Temporal Ethic:

Responsibility flows backward because value assignment flows backward.

Those who aligned with future truth before it existed in language receive the highest structural reward.