Exact identities, proved implications and open inputs. No numerical experiment, certificate, new window or tail metric. G2 and RH remain open.
One proposition expresses the positive-weight potential through the COMPLETE corrected zero field, with finite-window pole mass I_(h,a), endpoint/trivial-zero terms and all exterior edges retained. It gives ZLD => QC_K >= κ θ² D/(2K) on the same prescribed family, and therefore QG’s growth clause when D grows. The separate source-admissible bounded-energy packet clause is not supplied.
CAE is exactly the uniform complement-floor target in these positive-weight coordinates. No new signed estimate follows. General level-measure and multiplier countermodels illustrate why value-distribution data alone do not suffice; they are not counterexamples for the actual zeta field. An excessive integer head rule makes every fixed-K cost tend to zero whether or not CAE holds. Thus QG uniformly over all head rules is false; no actual arithmetic logical nonimplication or converse for a particular natural rule is claimed.
zero_field_energy.tex: complete integrated proposition and proof.scope_review.md: independent mathematical review and corrected wording.provenance.json: source and review hashes, coordination scope.build_report.json: actual integrated build counts and artifact checks.ns39-three-inputs-2026-09-22-v1.html: versioned user-facing report.NS-38’s two missing groups were separately handled by explicit disclosure, not
recovery; see evidence/ns38_archival_disclosure/ and evidence/MISSING.md.
NS-41 and NS-42 remain separate evidence/diag_* records and are NOT proof inputs.
NS-40’s QG literature assessment is independently filed in PR #19; its fragment
is not silently included here. Neither the existing ZLD nor QG nor CAE is proved.