Manuscript VIII-C@3 · VIII-C-v3.tex · section · 3b070436

Reference-frame signature and worldline distinctions

Complete affine matching at every command boundary › Reference-frame signature and worldline distinctions · lines 383–405

VIII-C@3#eq:signature

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A chart-based primitive product is generally conjugate to $J (μ)$ . After transport back to the declared reference frame it is exactly $J (μ)$ . We use the latter convention in the persistent signature

Sig (g) = (p, μ, W_{0}, e_{0}, reference framing, [γ]_{primitive}, J (μ), collar matching) .

Its preservation does not require literal equality of every chart-based matrix.

Three different statements are kept separate:

W_{0} is a fixed ambient set, J (μ) ∣_{W_{0}} = id, P_{s} \in W_{0} may vary with s .

Fixed-packet slice advance preserves the first two, not generally the third.

Displayed formulas in this passage

VIII-C@3#eq:signature · line 388
$Sig (g) = (p, μ, W_{0}, e_{0}, reference framing, [γ]_{primitive}, J (μ), collar matching) .$
unlabeled · line 398
$W_{0} is a fixed ambient set, J (μ) ∣_{W_{0}} = id, P_{s} \in W_{0} may vary with s .$