Claim ledger

The ledger precedes the explanatory narrative. “Copied input” describes the role of a predecessor result in XV-A; the parenthetical status describes what the supplied source says it constructed or left open. “Reported” means that only the supplied coverage account or source locator supports the entry, not a reproduced proof. An omitted formula, carrier definition, or perturbative order is recorded as missing rather than reconstructed.

{}1.15 {@{} p3.45cm p2.65cm p3.70cm p3.10cm p2.15cm p3.00cm p4.25cm @{}} , domain, order, provenance, and non-implication ledger.
Claim & Source & Model & Domain & Order & Status in XV-A & Does not imply

Claim & Source & Model & Domain & Order & Status in XV-A & Does not imply

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A fixed witness gives a first-order defect for the convolution prescription. & Supplied audit account; convolution manuscript not otherwise identified. & Spacetime convolution on metric arguments of an auxiliary coordinate problem. Exact action, convolution kernel, and inverse normalization unavailable. & The frozen gauge algebra declared by that manuscript. & Classical first order; exact coupling convention unavailable. & Reported\ obstruction on that algebra. & An obstruction to every coordinate prescription; an identification with a ramp edge integral; or repair by a ramp theorem.

Fixed-width ramp coordinate and scalar prescription has plateau covariance. & X-A@1, abstract, lines 112–147; supplied account. & Ramp prescription at fixed $\epsilon$. Full action and inverse formula not reproduced. & Classical fields, with the stated plateau restrictions. & Classical; exact truncation not reproduced. & Reported\ construction. & Unrestricted fixed-background covariance, sharp-width covariance, or quantum-graviton admission.

Scalar-only free-field admission and one normalized retarded correction complete the first-order identity. & X-B@3, field-content passage, lines 202–236; supplied account. & Ramp scalar quantum field; metric classical. One normalized correction; normalization formula unavailable. & Declared scalar carrier; insertion tests are actual off-shell representatives. & Through the stated first order in $\kappa$; exact $\hslash$ order unavailable. & Reported\ construction. & A quantum metric kernel or replacement of insertion representatives by unspecified shell classes.

Second scalar response maps give the classical completed identity through ${\kappa }^2$. & X-C@3, frozen-sheet passage, lines 488–587; supplied account. & Same reported ramp scalar/classical-metric lane, with second response maps. & Classical identity; off-shell insertion representatives retained. & Classical identity through ${\kappa }^2$. & Reported\ construction. & An all-species quantum Ward identity or admission of a joint graviton coefficient.