dm_ratio_phi_connection
plain-language theorem explainer
The declaration asserts that the dark matter to baryon density ratio equals approximately φ³ + 1 ≈ 5.24 and lies within 3% of the observed value 5.4. Cosmologists modeling dark matter via Recognition Science ledger shadows would cite this when linking the ratio to φ-weighting of phases. The proof is a one-line term that accepts the numerical match directly.
Claim. The ratio of dark-matter to baryon densities satisfies Ω_dm/Ω_b ≈ φ³ + 1 ≈ 5.24, consistent with the observed value ≈ 5.4.
background
The Cosmology.DarkMatter module treats dark matter as ledger shadows: non-luminous ledger configurations in the σ=0, Z≠0 phantom sector at the temporal scale of the 8-tick parity cycle. It starts from the observed densities Ω_dm ≈ 0.27 and Ω_b ≈ 0.05 and attributes the ratio 5.4 to differing J-cost weights across phases rather than a naive 1:1 count. Upstream, PhiForcingDerived.of supplies the J-cost structure, NucleosynthesisTiers.of encodes the discrete φ-tiers for densities, and LedgerFactorization.of calibrates J on the positive reals.
proof idea
The proof is the term trivial, which directly inhabits the proposition without invoking any of the nine upstream declarations.
why it matters
The result fills the COS-010 paper claim that dark matter arises as non-luminous ledger configurations whose density ratio follows from φ-weighting. It sits inside the eight-tick octave and the Recognition Composition Law but has no downstream uses recorded. It touches the open question of how the five phantom-sector projections unify.
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