IndisputableMonolith.Cryptography.KeyLengthFromPhiLadder
Module defines security level spacing on log base 2 key length ladder as phi to the power 1/2, with derived concrete lengths at 80, 128 and 256 bits. Cryptographers applying Recognition Science constants to key sizing would cite the ratio and its positivity lemmas. Structure is pure definitions plus elementary inequalities on the imported phi from Constants.
claimDefine the security level ratio $r = 2^{1/2}$ where the exponent derives from the self-similar fixed point satisfying $J(r) = r$ and $J(x) = (x + x^{-1})/2 - 1$. Then set key lengths $L_{80}$, $L_{128}$, $L_{256}$ on the ladder with doubling closure $L_{2k} = 2 L_k$.
background
Module imports Constants (fundamental RS time quantum τ₀ = 1 tick) and Cost (J-cost machinery). Recognition Science places the phi fixed point at T6 of the forcing chain after J-uniqueness at T5. The phi-ladder already governs mass rungs; this module extends the same spacing to cryptographic key lengths measured in log₂ bits. Local convention treats the ratio as the minimal multiplicative step between adjacent security levels.
proof idea
This is a definition module, no proofs. It introduces securityLevelRatio together with its positivity and greater-than-one lemmas, then instantiates the three standard key lengths and a doubling relation, plus a certificate type with inhabited instance.
why it matters in Recognition Science
Supplies the cryptographic instantiation of the phi-ladder that originates in the UnifiedForcingChain (T5–T6). No direct used_by edges appear, yet the module closes the path from physical constants to practical security parameters. It touches the open question of how RS-native units translate into discrete engineering choices such as bit lengths.
scope and limits
- Does not derive phi from the Recognition Composition Law.
- Does not prove resistance to concrete cryptanalytic attacks.
- Does not link key lengths to the eight-tick octave or spatial dimension D=3.
- Does not address variable gap(Z) or Berry threshold effects.