Hubble Parameter

New clothes-radius numbers use km s⁻¹ Mpc⁻¹. That splice is the dual of — the same relation twice, not two derivations. The framework redshift is [M], with . A frozen product pays spectroscopic redshift 0. Those two sentences are not joined.

The placed splice

The Genesis splice is placed [M packaging]. At CODATA , named as , the evaluation is 68.973054 km s⁻¹ Mpc⁻¹ on codata_2022 and 68.9730537 on codata_2018 [E algebra]. The printed 68.97305 is that rounding. The clothes baseline used for new numbers stays 68.973 [P]. The emitted Hubble number and the coefficient 3/8 stay [P]. Locking is [M], not a theorem. The derivation token stays unissued.

Algebra of the placed splice

These are [E algebra] of the inserted splice, or round-sphere identities. They are not a derivation of or of . The factor is the arithmetic . It is not a new physical derivation. The Compton radius of the pair vertex is a different length from the clothes radius on this page.

• Dirac ratio .
• Clifford neck density .
• Round-sphere curvature and the lowest TT spin-2 mode .
• Trefoil winding product . A dynamical selection of that would lock stays [O residual].

What R is not

If one misreads as the FLRW spatial curvature radius, one gets . That reading is rejected: it contradicts conventional CMB curvature bounds, and it is not licensed as a Hubble-tension solution. The length itself remains an unnamed Mach length (R_eff).

If and that radius expands at , then . Divided by the quoted Müller half-width the ratio is 928 (M12). A stationary container does not write . remains an input. The conformal definition is not identified with that expansion.

Hubble tension (not resolved here)

A major crisis in modern cosmology is the "Hubble Tension": CMB measurements (Planck) infer , while local distance ladder measurements (Cepheids/Supernovae) find .

The published invert sits between Planck 67.4 and SH0ES 73. That is a [P] of the named book, not a proof that the tension is “flat ΛCDM applied to curved S³.”