Manuscript IX-B@2 · IX-B-v2.tex · corollary · 8ce915d6

Corollary: Descendant conversion and scale dependence

Observation derivatives and smooth spectators · lines 895–918 · proof included or linked

IX-B@2#cor:conversion

For the same operation,

a D (u_{μ}^{ρ_{a}} - u_{μ}^{ρ_{b}}) = c_{ab} a D r, a D (u_{μ_{2}}^{ρ} - u_{μ_{1}}^{ρ}) = lo g (μ_{2} / μ_{1}) a D r .

The complete regulator difference satisfies

a D (T_{ε}^{ρ_{a}} - T_{ε}^{ρ_{b}}) ⟶ c_{ab} a D r

strongly, with the corresponding order- $64 + d$ remainder bound.

Proof. Apply $a D$ to the inherited identities (eq:parentconversion)–(eq:parentscale). For the last assertion, subtract the two estimates (eq:descendantrate); the logarithmic terms agree. The parent cocycle is inherited from VII-D, not re-derived from profile integrals here.

Displayed formulas in this passage

unlabeled · line 898
$a D (u_{μ}^{ρ_{a}} - u_{μ}^{ρ_{b}}) = c_{ab} a D r, a D (u_{μ_{2}}^{ρ} - u_{μ_{1}}^{ρ}) = lo g (μ_{2} / μ_{1}) a D r .$
unlabeled · line 904
$a D (T_{ε}^{ρ_{a}} - T_{ε}^{ρ_{b}}) ⟶ c_{ab} a D r$

Corollary: Descendant conversion and scale dependence

Displayed formulas in this passage

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