Manuscript XVI-H@1 · XVI-H.tex · section · af895076

Provenance and proof dependencies

Provenance and proof dependencies · lines 239–304

This manuscript revises the supplied XVI-H-v3.tex. The current witness references are:

revised XVI-E.tex, “Polarized root representation and witness-level completion compatibility”;
revised XVI-F.tex, “Auxiliary/root compatibility and direct witness completion”;
current XVI-G.tex, “Frequency-dependent witness testing and resonant asymptotics.”

The supplied XVI-H-v3 reproduces additional XII-D source-kernel and root-kernel statements, and XI-G switch identities. The complete XII-D and XI-G manuscripts are not independently available here. Accordingly, those statements are formulated below as explicit inherited inputs. Their use is not represented as a full-file verification.

Item	Provenance	Role here
Prepared source coefficients	XII-D statements reproduced in XVI-H-v3	Explicit input; degree audit proved below
Diagonal completion and response	XII-D interface reproduced in revised XVI-D/E/F	Definition and domain input
Compact root and its joint kernel	XII-D statements reproduced in XVI-H-v3	Explicit kernel/support assumptions
Witness compatibility	Revised XVI-E/F and current XVI-G	Imported with matching conventions and hypotheses
Kernel construction and continuity	Present manuscript	Proved from the stated root/source inputs
Partial contraction to $j_{λ}$	Present manuscript plus current XVI-G	Proved as a distributional equality
Switch representative	XI-G identities reproduced in XVI-H-v3	Conditional consistency audit, not admission

The current XVI-G cites an earlier XVI-H only as a record of subsequent obligations, not as a premise of its witness proofs. No result of the present kernel construction is used to prove the imported witness chain. Thus witness matching below does not depend circularly on this revision.