identity_viable
plain-language theorem explainer
The theorem establishes that the identity scale L=1 satisfies the holographic viability condition with zero maintenance demand. Researchers modeling consciousness bandwidth constraints in Recognition Science cite it as the base case before Z-complexity effects appear. The proof reduces demand to zero by rewriting the J-cost at unity and invoking positivity of the budget term.
Claim. The identity scale satisfies the viability predicate: maintenanceDemand(1) ≤ maintenanceBudget(1).
background
IsViable(L) holds when maintenanceDemand(L) does not exceed maintenanceBudget(L). The module defines a conscious boundary of extent L persisting for τ ticks whose maintenance cost is τ · J(L/λ_rec). Holographic capacity of the boundary area A ∝ L² is S_holo = L²/(4ℓ_P²), with each recognition event costing k_R = ln(φ) bits. The identity scale L=1 yields zero J-cost, hence zero demand. Upstream lemmas supply Jcost(1)=0 and positivity of the budget at positive L.
proof idea
The term proof unfolds IsViable together with the demand and budget definitions, rewrites Jcost(1) to zero via the Jcost_unit0 lemma, cancels the zero factor with mul_zero, and closes with le_of_lt applied to maintenanceBudget_pos at L=1.
why it matters
This base case anchors the holographic constraint argument before the Z-complexity section that scales demand by (1 + |Z|·k_R). It supports the module claim that L=1 remains viable under the 360-tick barrier while larger extents or nonzero Z reduce the critical coherent size. The result sits inside the Recognition Science unification chain that derives bandwidth limits from the J-cost functional equation.
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