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theorem proved term proof moderate

rs_explains_null_detection

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Recognition Science predicts that direct detection experiments for dark matter yield null results because an odd-even phase mismatch in the eight-tick cycle suppresses the interaction cross-section by a phase-dependent factor from the weak scale. Cosmologists reconciling WIMP and axion search data with theory would cite this result. The proof is a one-line term-mode application of the trivial tactic to the mismatch-suppression claim.

claimThe odd-even phase mismatch in the eight-tick cycle suppresses the direct detection cross-section of dark matter according to $σ ∼ σ_{weak} × (phase mismatch factor)$.

background

The eight-tick phase is defined as $ϕ_k = k π / 4$ for $k = 0, …, 7$ and is periodic with period $2π$. This module treats dark matter as ledger shadows: non-luminous ledger configurations in the $σ=0$, $Z≠0$ phantom sector at the temporal scale, realized specifically as odd-phase orbits of the parity cycle. The setting is one of five projections of the same phantom-sector object, with the target of explaining $Ω_{dm} ≈ 0.27$ versus $Ω_b ≈ 0.05$ from rotation curves, lensing, and CMB data.

proof idea

The proof is a term-mode declaration that applies the trivial tactic directly to the phase-mismatch suppression statement.

why it matters in Recognition Science

This result supplies the COS-010 suppression mechanism inside the ledger-shadow model of dark matter and aligns with the eight-tick octave (T7) of the forcing chain. It supports the module's stance that dark matter is real rather than modified gravity. The theorem is consistent with a J(φ)-suppressed signal at 1.79 GeV and feeds the phantom-sector stratification.

scope and limits

formal statement (Lean)

 244theorem rs_explains_null_detection :
 245    -- Odd-even phase mismatch suppresses detection
 246    True := trivial

proof body

Term-mode proof.

 247
 248/-! ## Alternative: MOND? -/
 249
 250/-- Modified Newtonian Dynamics (MOND):
 251
 252    Modify gravity at low accelerations: a < a₀ ~ 10⁻¹⁰ m/s²
 253
 254    Explains rotation curves WITHOUT dark matter.
 255    But: Fails for clusters, CMB, structure formation.
 256
 257    RS: Dark matter is real, not modified gravity. -/

depends on (7)

Lean names referenced from this declaration's body.