photonic_code_rate_rfl
plain-language theorem explainer
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.
Claim. The 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
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.
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