Manuscript XVI-B@1 · XVI-B.tex · section · 6a0abffd
The complete-pairing specification and status ledger
The complete-pairing specification and status ledger · lines 1527–1617
The original reference to “the complete pairing of XVI-C” is a programme pointer. Since XVI-C was not supplied, this manuscript does not invent its section labels or definitions.
The following chain is a local specification of what must be checked:
A smooth root pairing or auxiliary evaluation can be a separate verification route, but an identification with this chain must be proved.
{}1.12
| Stage/object | Established or reported | Remaining check |
|---|---|---|
| Prepared source | Imported from XII-C; pure-trace witness value proved here | No full observable kernel follows from the source value |
| Witness response | Constructed in supplied XVI-D | Not automatically the completed insertion |
| Scalar completion leg | Verified in supplied XVI-D | Does not verify the coordinate leg |
| Inherited coordinate leg | Formula retained; compact-source theorem distinguished | Identification on the witness family remains unverified |
| Root pairing | Constructed in XVI-E; fixed smooth-root decay proved above | Not automatically the independently defined completion |
| Auxiliary | Constructed in XVI-F-v2; direct fixed-data decay reported | Equality with and inherited completion not verified |
| Compact class kernel | No new kernel constructed here | Exact object and free-shell comparison required |
| Class pairing | XVI-C definition not supplied | Specification, existence, and identification required |
| XI-G transfer | Proposition prop:transfer | Same-class condition not evaluated for an actual matching kernel |
The complete-pairing test must retain separately:
the bulk source and the full correction ;
forced response terms and preparation-generated homogeneous terms;
both completion legs, including derivatives of and the mass term;
the tensor contractions actually selected by the insertion;
any gauge companion and Einstein-equation term produced by the relevant complete derivation;
support, operator-domain, polarization, and complexification hypotheses at each stage;
the final comparison with the frozen observable kernel.
The gauge-fixed free-shell condition is not substituted for an Einstein-shell hypothesis. A cancellation is used only after proof. The decisive question is which preparation-dependent terms the complete observable detects, not whether the correction vanishes as an uncontracted source.
Displayed formulas in this passage
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