ic002_certificate
plain-language theorem explainer
The ic002_certificate definition assembles a status string confirming that key computation limits in Recognition Science have been derived from the foundational tick and irrationality constraints. Information theorists and physicists studying fundamental bounds would cite this certificate to reference the positive status of Landauer and Bremermann limits alongside the prohibition on exact φ computation. The construction is a direct string concatenation of the verified properties listed in the module.
Claim. The IC-002 certificate is the string asserting positivity of the fundamental tick τ₀, the maximum rate 1/τ₀, irrationality of φ (preventing exact rational representation), positivity of Landauer energy k_B T ln(2) for T > 0, its monotonic increase with temperature, and positivity of the Bremermann limit 2/ℏ.
background
In the module Information.ComputationLimitsStructure the IC-002 results derive fundamental limits of computation from Recognition Science. Temporal discreteness follows from the minimum time quantum τ₀ (one tick), so the maximum bit rate equals 1/τ₀. Irrationality of φ, established by the sibling phi_minimal_polynomial, implies that φ-based states cannot be exactly represented with finite rational arithmetic.
proof idea
The definition constructs the certificate via string concatenation of fixed text lines, each corresponding to a verified property from sibling theorems such as tick_pos, max_rate_pos, no_exact_phi_computation, landauer_energy_pos, landauer_scales_with_temp, and bremermann_limit_pos. No tactics are applied beyond the literal string assembly.
why it matters
This certificate summarizes the IC-002 results on computation limits emerging from temporal discreteness and irrational constants in Recognition Science. It aligns with the module's treatment of Bremermann's limit, Landauer's bound, and the prohibition on exact φ simulation. The declaration sits at the end of the module and provides a human-readable summary of the derived bounds without feeding further theorems.
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