photonicCodeRate
The declaration introduces the photonic code rate as the constant 7/8 in rational numbers. Researchers citing the three-substrate validation certificate for Recognition Science experiments would reference this value for the photonic qubit substrate performance. It is supplied by a direct definition without any proof obligations or lemmas.
claimIn the photonic substrate of the three-substrate validation, the code rate is given by $7/8$.
background
The ThreeSubstrateValidationCert module supplies an empirical certificate for J-cost behavior across language models, photonic qubits, and magnetized plasma. Photonic qubits are assigned code rate 7/8 (87.5%) with reported leakage 0.02%. The module imports Cost and MultiChannelJCost to ground the J-cost definitions that appear in the certificate structure, including the fixed point at x=1 where Jcost 1 = 0 and the descent property for r ≠ 1.
proof idea
The declaration is a direct definition that assigns the rational value 7/8 to photonicCodeRate. No tactics or lemmas are invoked; it functions as a named constant for subsequent use in the reflection lemma and the validation structure.
why it matters in Recognition Science
This constant populates the photonic substrate data in the ThreeSubstrateCert structure and is reflected by the photonic_code_rate_rfl lemma. It instantiates the eight-tick octave prediction from the forcing chain, where the period 2^3 yields the 7/8 rate as (2^3 - 1)/2^3. The overall certificate remains hypothesis grade, pending further formalization of the empirical results from ALEXIS Exp B.
scope and limits
- Does not derive the code rate from the J-cost functional equation or Recognition Composition Law.
- Does not model physical photonic qubit implementation or error sources.
- Does not include leakage bounds or experimental statistics.
- Does not extend the rate to language-model or plasma substrates.
formal statement (Lean)
51def photonicCodeRate : ℚ := 7/8