mondStatus
MOND status definition records that modified Newtonian dynamics reproduces galactic rotation curves at low accelerations yet fails for galaxy clusters and cosmic microwave background data. A cosmologist comparing modified-gravity proposals to Recognition Science ledger-shadow models cites this entry to mark the empirical boundary. The definition is a direct string assignment accompanied by a summary comment block.
claimModified Newtonian Dynamics modifies gravitational acceleration below $a_0$ and accounts for galactic rotation curves without dark matter, but fails to match galaxy-cluster dynamics and cosmic-microwave-background observations.
background
Recognition Science treats dark matter as ledger shadows arising from the odd phases of the eight-tick parity cycle. The fundamental time quantum is one tick, and the eight phases are multiples of π/4. Upstream lemmas establish the phase definition and the J-cost factorization that calibrate the phantom sector at temporal resolution.
proof idea
One-line wrapper that directly assigns the string literal summarizing MOND's empirical reach, followed by a comment block that contrasts the ledger-shadow mechanism with modified gravity.
why it matters in Recognition Science
The definition anchors the module's assertion that dark matter is real (ledger shadows from eight-tick phases) rather than a modification of Newtonian gravity. It aligns with the Recognition Science forcing chain through the eight-tick octave and phase structure, supporting the phantom-sector stratification without introducing new theorems.
scope and limits
- Does not derive the MOND acceleration scale from Recognition Science primitives.
- Does not compute the dark-matter to baryon ratio from the phi-ladder.
- Does not address structure-formation or lensing predictions.
- Does not supply a quantitative model comparison between MOND and ledger shadows.
formal statement (Lean)
258def mondStatus : String :=
proof body
Definition body.
259 "Works for rotation curves, fails for clusters and CMB"
260
261/-! ## Summary -/
262
263/-- RS explanation of dark matter:
264
265 1. **8-tick phases**: 4 visible + 4 dark
266 2. **Ledger shadows**: Odd-phase matter
267 3. **Gravitates but dark**: No photon coupling
268 4. **Ratio ~ φ³+1**: Explains 5:1 ratio
269 5. **Null detection**: Phase mismatch suppression -/