THE RETROACTIVE COST FUNCTION (C_RETRO)
Status: Formalized. Plain-text mathematical notation.
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.
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)
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If Phi_actual aligns with Phi_future, then P_PSI → 1.
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If maximally distant, P_PSI → 0.
P_PSI rewards structural fidelity in the absence of evidence.
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.
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.
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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.
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.
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