photonic_code_rate_rfl
The declaration equates the photonic code rate to 7/8 by direct reflexivity. Researchers auditing the three-substrate validation certificate cite it to anchor the photonic qubit substrate prediction. It is realized as a one-line reflexivity that matches the upstream definition of the code rate.
claimThe photonic code rate equals $7/8$.
background
The Three-Substrate Validation Certificate module records empirical checks of J-cost uniqueness across language models, photonic qubits, and magnetized plasma. All three substrates are required to share the fixed point at x=1, descent along the J-cost gradient, and multi-channel extension. The photonic case is summarized with code rate 7/8 and leakage 0.02 percent, consistent with the eight-tick octave structure (period 2^3) in the Recognition Science forcing chain.
proof idea
The definition is a one-line reflexivity wrapper that applies rfl to the upstream photonicCodeRate definition, confirming the equality 7/8 = (2^3 - 1)/2^3 for flip variants over total states.
why it matters in Recognition Science
This definition supplies the photonic code rate value required by threeSubstrateCert. It instantiates the T7 eight-tick octave landmark inside the RS Exp B certificate, where the fraction 7/8 arises directly from the 2^3 period. The surrounding certificate remains at hypothesis grade; the Lean content only records the constant that follows from J-cost uniqueness.
scope and limits
- Does not derive the 7/8 value from the J-cost functional equation or Recognition Composition Law.
- Does not address leakage, convergence, or empirical data for the photonic substrate.
- Does not cover the language-model or plasma substrates.
- Does not elevate the certificate beyond hypothesis grade.
formal statement (Lean)
52def photonic_code_rate_rfl : photonicCodeRate = 7/8 := rfl
proof body
Definition body.
53
54/-- 7/8 = (2³ - 1)/2³ (flip variants / total). -/