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def definition def or abbrev high

mondStatus

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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

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 -/

depends on (13)

Lean names referenced from this declaration's body.