IndisputableMonolith.URCAdapters.LawfulNormalizer
The LawfulNormalizer module supplies a prop-level witness that the trivial normalizer at λ=1 satisfies stationarity and scaling invariance under abstract obligations. It acts as a temporary stand-in for the concrete λ_rec bridge inside the URCAdapters layer of Recognition Science. Researchers refining the forcing chain or ethics hooks would cite it as an initial lawful case. The module structure consists of the LawfulNormalizer definition plus uniqueness statements for lambda_rec and lawful_normalizer_exists_unique.
claimA trivial normalizer $N$ at scale factor $λ=1$ satisfies stationarity ($N(x)=N(1)$ for normalized $x$) and scaling invariance ($N(λx)=λ N(x)$) under the current abstract obligations; this serves as a placeholder for the concrete $λ_{rec}$ bridge.
background
Recognition Science derives physics from a single functional equation whose solutions are constrained by the J-uniqueness relation $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$ and the self-similar fixed point φ. In the URCAdapters domain the normalizer is required to enforce stationarity and scaling invariance so that downstream mass formulas and the phi-ladder remain consistent. The module introduces LawfulNormalizer as the prop-level witness for the trivial case λ=1, standing in for the concrete λ_rec construction until the ethics alignment hook is supplied.
proof idea
This is a definition module, no proofs. It declares the LawfulNormalizer object and states the two uniqueness results lambda_rec_unique and lawful_normalizer_exists_unique as direct consequences of the abstract obligations.
why it matters in Recognition Science
The module feeds the λ_rec bridge that will later connect to the eight-tick octave and D=3 spatial dimensions in the forcing chain. It supplies the initial lawful normalizer required before the ethics alignment hook can be exposed and the concrete λ_rec implementation substituted.
scope and limits
- Does not supply the concrete λ_rec function.
- Does not incorporate the ethics alignment hook.
- Does not prove scaling invariance for λ≠1.
- Does not connect to the phi-ladder or mass formula.