IndisputableMonolith.Physics.CosmologicalConstantFromRS
Defines the RS cosmological constant Λ_RS = 8φ⁵/45 and packages positivity plus a numerical band into an audit certificate. Cosmologists and RS auditors cite it for the vacuum-energy prediction in native units. Content is definitional with elementary arithmetic lemmas on φ⁵; no deep forcing-chain work lives here.
claimThe Recognition Science cosmological constant is $\Lambda_{\mathrm{RS}} = 8\varphi^5/45$, with $\varphi$ the golden-ratio fixed point. The module records $\Lambda_{\mathrm{RS}} > 0$ and a concrete numerical band, packaged as a certificate.
background
Recognition Science fixes dimensionful constants from the self-similar scale $\varphi$ forced at T6. In RS-native units one has $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$. The same power $\varphi^5$ appears as the confining factor $Z_{\mathrm{cf}}=\varphi^5\in(11,12)$ and in the mass ladder.
This module isolates the vacuum-energy density predicted on that ladder: $\Lambda_{\mathrm{RS}}=8\varphi^5/45$. The factor 8 matches the eight-tick octave (T7); the denominator 45 is the combinatorial normalization fixed by the RS ledger. The Constants import supplies the native time quantum $\tau_0=1$ tick and the definition of $\varphi$.
proof idea
Definition module, not a deep proof development. lambdaRS is the closed form $8\varphi^5/45$. Sibling lemmas record $\varphi^5$ identities, strict positivity of $\Lambda_{\mathrm{RS}}$, and a numerical band. A certificate structure packages those facts for downstream audit; obligations reduce to elementary arithmetic on $\varphi$.
why it matters in Recognition Science
Places the cosmological-constant prediction inside the RS physics layer, parallel to the mass ladder and the fine-structure band. The formula reuses the same $\varphi^5$ that appears in $G$ and $Z_{\mathrm{cf}}$, keeping the constant count minimal. No downstream consumers are wired in the current graph; the certificate is the intended hook for global consistency audits. Observational matching and SI conversion are left open.
scope and limits
- Does not derive the 8/45 prefactor from the forcing chain inside this module.
- Does not convert Λ_RS into SI units or confront Planck/supernova data.
- Does not address dark-energy equation of state or time variation.
- Does not prove uniqueness of the expression among alternative ledger normalizations.