Manuscript IX-A@1 · IX-A.tex · section · 55aa6f6d

Formal coefficient slots through the first obstructed order

Faithfulness, classical presentation independence, and formal slots › Formal coefficient slots through the first obstructed order · lines 1696–1716

IX-A@1#eq:bulkpres, IX-A@1#eq:regpres, IX-A@1#eq:clpres

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For any proposed product

A ⋆_{Σ} B = A B + ℏ C_{1} (A, B) + ℏ^{2} C_{2} (A, B) + ℏ^{3} C_{3} (A, B),

the three preservation requirements are:

ι (A ⋆_{H} B) C_{r}^{Σ} (A, B) cl (A ⋆_{Σ} B) = ι (A) ⋆_{Σ} ι (B) = C_{r}^{old} (A, B) = cl (A) cl (B) . on the bulk, on every specified common regular domain,

Only the carrier needed to state these requirements is constructed here. Equations (eq:bulkpres)–(eq:clpres) are obligations for a future quantum product, not results about an unconstructed map.

Displayed formulas in this passage

IX-A@1#eq:bulkpres · line 1705
$ι (A ⋆_{H} B) C_{r}^{Σ} (A, B) cl (A ⋆_{Σ} B) = ι (A) ⋆_{Σ} ι (B) = C_{r}^{old} (A, B) = cl (A) cl (B) . on the bulk, on every specified common regular domain,$
IX-A@1#eq:regpres · line 1705
$ι (A ⋆_{H} B) C_{r}^{Σ} (A, B) cl (A ⋆_{Σ} B) = ι (A) ⋆_{Σ} ι (B) = C_{r}^{old} (A, B) = cl (A) cl (B) . on the bulk, on every specified common regular domain,$
IX-A@1#eq:clpres · line 1705
$ι (A ⋆_{H} B) C_{r}^{Σ} (A, B) cl (A ⋆_{Σ} B) = ι (A) ⋆_{Σ} ι (B) = C_{r}^{old} (A, B) = cl (A) cl (B) . on the bulk, on every specified common regular domain,$
unlabeled · line 1699
$A ⋆_{Σ} B = A B + ℏ C_{1} (A, B) + ℏ^{2} C_{2} (A, B) + ℏ^{3} C_{3} (A, B),$

Formal coefficient slots through the first obstructed order

Displayed formulas in this passage

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