Newman bounds for six imaginary quadratic fields and a discriminant −15 separation certificate

This deposit preserves Dale James Raymond’s research manuscripts dated 23–25 September 2026, together with the original proof programs, enclosing numerical data and complete nested certificate archives. A source-provenance and exact replay audit dated 2 November 2026 accompanies the unchanged originals. For each negative fundamental discriminant d, the manuscripts study the heat flow of the entire completed Dedekind product C_d(s) = s(s−1)(√|d|/(2π))^s Γ(s) ζ(s)L(s,χ_d), using C_{d,t} = exp((t/4)∂_s²)C_d and the wide convention s = (1+iz)/2. Within the retained written analytic framework, they give strict upper bounds Λ_{−3} < 0.241169, Λ_{−4} < 0.251667 and Λ_{−15} < 0.236004. The subsequent finite-family construction completes every negative fundamental discriminant with |d| ≤ 15, namely −3, −4, −7, −8, −11 and −15, with the common ceiling 0.251667 while retaining the stronger −3 and −15 bounds. A separate positive-time zero certificate establishes Λ_Q > 3/10 for Q(s) = [ζ(s)L(s,χ_{−15}) + L(s,χ_{−3})L(s,χ_5)]/2, with the same conductor, gamma factor and pole-clearing polynomial as the discriminant −15 Dedekind completion. This yields the strict separation Λ_Q − Λ_{−15} > 0.063996. Q is the discriminant −15 Epstein/Route-P comparison function, distinct from the modulus-five Davenport–Heilbronn series. The November audit successfully rechecked retained Q enclosures, 1,218 descending-source inequalities, 35,422 comparison steps and the six-field assembly. It did not regenerate the original native special-function enclosures, rerun published finite-height zero computations, or formalise the infinite analytic arguments. Dale James Raymond is the sole named human research author. The original manuscripts disclose AI assistance in analytic development, coding, numerical checking and drafting. Cited mathematical inputs and third-party software notices are retained. The deposit makes no claim of external peer review or worldwide priority. The two original source ZIPs contain the complete nested certificate archives. The Documents and Audit ZIP contains the preserved proofs, documentation, checksums and fresh replay receipts, with ZENODO_README.txt explaining how to restore the complete package layout. The separately downloadable Markdown documents are copies provided for convenient inspection; follow their relative links within the restored package.