Manuscript XV-A@1 · XV-A.tex · section · f53f3515

Lane B: ramp scalar observable with classical metric

Separate model lanes › Lane B: ramp scalar observable with classical metric · lines 735–769

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The reported sequence is

Its scope is recorded as follows XA,XB,XC,XD,record.

  1. X-A supplies a fixed-width classical coordinate and scalar prescription with plateau covariance.

  2. X-B@3 supplies scalar-only free-field admission and one normalized retarded correction, completing its stated first-order identity.

  3. X-C@3 supplies the second scalar response maps and a classical completed identity through .

  4. X-D@3 supplies a fixed-input sharp-width limit of the completed scalar tests.

The lane is scalar-quantum and metric-classical where quantum content is invoked. Its insertion tests remain actual off-shell representatives. Its classical completed identities are not automatically identities on a quotient of quantum metric kernels.

The X-D limit must retain its fixed-input qualification. A limit of completed scalar tests does not, by itself, prove joint sharp admission of a quantum metric kernel. Nor does a covariance identity at fixed commute with a sharp-width limit without a theorem establishing the needed convergence and compatibility.

Displayed formulas in this passage

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