IsViable
plain-language theorem explainer
A definition that marks a boundary of scale L as holographically viable exactly when its integrated J-cost demand stays at or below the holographic event capacity of its area. Researchers working on conscious extent limits within Recognition Science cite this predicate to enforce the bandwidth bound. The definition is a direct inequality between the demand and budget functions with no additional lemmas.
Claim. A real number $L$ is holographically viable when the maintenance demand over the 360-tick barrier does not exceed the holographic capacity of the boundary area, i.e., demand$(L) = 360 · J(L / λ_rec) ≤ budget(L) = L² / (4 ℓ_P² · ln φ)$.
background
The ConsciousnessBandwidth module encodes the holographic limit on conscious extent. A boundary of extent L persists for τ ticks at cost τ · J(L / λ_rec), where J is the recognition cost from the Recognition module. Holographic capacity follows from area A ∝ L² giving S_holo = L² / (4ℓ_P²) events after division by ln(φ) bits per recognition event, yielding the total budget over the 360-tick barrier period.
proof idea
One-line definition that sets IsViable L to the inequality maintenanceDemand L ≤ maintenanceBudget L. No tactics or upstream lemmas are invoked inside the body; the predicate is supplied for use by identity_viable and related results.
why it matters
This predicate supplies the central constraint for the holographic viability argument in the consciousness bandwidth model. It is invoked directly by the downstream theorem identity_viable, which verifies that the identity scale L = 1 satisfies the condition with zero demand. Within the Recognition framework it implements the bandwidth limit on coherent extent, connecting to the J-uniqueness property and the phi-ladder scaling from the forcing chain (T5–T6). It leaves open the quantitative effect of Z-complexity on the critical extent.
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