IndisputableMonolith.Information.DNA_Storage_Density_RS
Module packaging Recognition Science bounds on DNA as an information medium: a domain cost built from the J-cost, a positive canonical density threshold, and an inhabited certificate that the DNA storage model meets that threshold. Information theorists and biophysicists working in RS units would cite the certificate and the nonnegativity lemmas. The file is mostly definitional scaffolding plus elementary positivity and equality facts over the Cost and Constants imports.
claimIn RS units, define a domain cost $C$ on admissible DNA storage configurations from the $J$-cost, a canonical threshold $\theta>0$, and a certificate asserting that the DNA storage density model satisfies $C\ge\theta$ (with nonnegativity of $C$ and equality lemmas at distinguished points).
background
Recognition Science measures mismatch with the $J$-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS time quantum $\tau_0=1$ tick and the golden-ratio ladder used elsewhere for mass and coupling scales.
This Information-domain module specializes those primitives to DNA as a physical storage medium. Sibling names indicate a domain cost functional, its value at a reference configuration, nonnegativity, a canonical positive threshold, and a certificate type DNAStorageCert with an inhabited instance. The setting is density and cost bounds in RS-native units, not wet-lab kinetics or sequence design.
proof idea
Definition-heavy module: introduce the domain cost from the imported $J$-cost, record an evaluation identity and nonnegativity, define a canonical threshold and prove it is positive, then package a certificate structure with an inhabited witness. No deep forcing-chain argument lives here; the logical work is elementary positivity and equality over Cost/Constants, plus a cert inhabitation that closes the local claim.
why it matters in Recognition Science
Places DNA storage density inside the RS information layer so later work can quote a single certificate rather than re-deriving cost inequalities. Downstream use is not yet wired in this graph (used_by empty), so the module is a leaf packaging step: domain cost, threshold, and cert_inhabited. It sits beside other Information certificates and inherits $J$-uniqueness and $\phi$-ladder conventions from the foundation (T5–T6) without re-proving them. Open follow-ons would connect the threshold numerically to measured DNA bit densities or to the eight-tick / $\phi$-ladder bookkeeping used for other RS constants.
scope and limits
- Does not derive DNA base-pair chemistry or mutation kinetics from first principles.
- Does not claim an experimental bit/nm³ measurement; only an RS certificate shape.
- Does not re-prove J-uniqueness or the forcing chain (T5–T8).
- Does not fix a numerical alpha or mass-ladder identity for DNA.
- Does not yet feed a named parent theorem in the current dependency graph.