eta_B_rung_from_chirality_eq
plain-language theorem explainer
The chirality-torsion witness for the baryon-to-photon rung evaluates to exactly -44 at three spatial dimensions. Cosmologists working within the Recognition Science framework would cite this equality when assembling the three combinatorial witnesses for the exact η_B rung. The proof is a one-line wrapper that unfolds the definitions of bitFlipCount0 and torsionGap01 then decides the arithmetic.
Claim. Let $B$ denote the chirality-torsion witness $B = -(b_0 · τ_{01})$, where $b_0 = 4$ is the Gray-code bit-flip count on axis 0 of the 3-cube and $τ_{01} = 11$ is the CW-filtration torsion gap between generations 0 and 1. Then $B = -44$.
background
In the module on η_B Rung Integer, three combinatorial witnesses realize the integer −44 that pins the baryon-to-photon ratio's φ-rung at D = 3. The chirality-torsion witness is defined as −(bitFlipCount0 × torsionGap01). Here bitFlipCount0 counts the flips of bit 0 on the Gray cycle [0,1,3,2,6,7,5,4] of the 3-cube, yielding 4. The torsionGap01 is the absolute difference |τ₁ − τ₀| = 11 drawn from the spectrum {0, 11, 17}.
proof idea
The proof is a one-line wrapper. It unfolds the definitions of eta_B_rung_from_chirality, bitFlipCount0, and torsionGap01, then applies the decide tactic to verify the arithmetic equality −(4 × 11) = −44.
why it matters
This equality supplies witness B for the certificate theorem etaBExactRungCert, which assembles the three witnesses together with agreement lemmas witnesses_AB_agree and witnesses_BC_agree. It fills the chirality-torsion reparameterization of the rung integer at D = 3, consistent with the framework's T8 forcing of three spatial dimensions. The structural unification across combinatorial settings is the content highlighted in the module documentation.
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