GalaxyRotationFalsifier
GalaxyRotationFalsifier packages three concrete observational failure modes for the ledger-shadow account of flat galaxy rotation curves into a single structure whose final field asserts logical contradiction. A cosmologist comparing Recognition Science predictions against MOND or rotation-curve surveys would cite the record when stating the conditions under which the J-cost equilibrium halo must be abandoned. The declaration is realized as a bare structure with no computational content.
claimLet $C$ assert that observed rotation curves fail to remain flat at large radii, $M$ that MOND reproduces all galactic velocities without dark matter, and $L$ that the spatial distribution of ledger entries mismatches measured halo densities. The structure asserts the conjunction of $C$, $M$, $L$ together with the implication $Clor Mto bot$.
background
The module COS-011 derives flat rotation curves from the equilibrium distribution of dark ledger entries, which Recognition Science identifies with odd-phase shadows in the eight-tick cycle. Standard Newtonian expectations give inner solid-body rise followed by Keplerian $vpropto 1/sqrt{r}$ falloff, yet data show constant velocity requiring an extended halo whose density scales as $1/r^2$. In the RS setting this halo is the J-cost minimizing arrangement of ledger shadows whose total mass exceeds the visible baryonic component by a factor of five to ten.
proof idea
The declaration is a bare structure definition containing no proof body or tactics. It directly records the three propositions named in the module documentation and packages their logical negation into the final field.
why it matters in Recognition Science
The structure supplies the explicit falsifiability criterion for the COS-011 claim that ledger distributions produce flat curves via J-cost equilibrium. It sits downstream of the eight-tick periodicity and phi-ladder mass assignments in the forcing chain, yet no later theorem currently depends on it. This leaves open whether a quantitative ledger profile can be shown to reproduce the Tully-Fisher relation without extra parameters.
scope and limits
- Does not derive an explicit density profile for the ledger halo.
- Does not compute numerical rotation velocities from a given ledger configuration.
- Does not address the core-cusp tension or other small-scale structure issues.
- Does not incorporate specific observational datasets such as Milky Way rotation measurements.
formal statement (Lean)
240structure GalaxyRotationFalsifier where
241 curves_not_flat : Prop
242 mond_works_everywhere : Prop
243 ledger_mismatch : Prop
244 falsified : curves_not_flat ∨ mond_works_everywhere → False
245
246end GalaxyRotation
247end Cosmology
248end IndisputableMonolith