Supplementary algebra checks for Cores of the Merged Johnson Graphs J(2k+1,k) with relations 2 through k-2

Release notes v1.0.0 — 25 August 2026 Initial public release candidate for the manuscript Cores of the Merged Johnson Graphs (J(2k+1,k)_{{2,\ldots,k-2}}) and its supplementary algebra checks. Mathematical result For every integer (k\ge4), the manuscript proves [ \operatorname{End}(G_k)=\operatorname{Aut}(G_k)\cong S_{2k+1}. ] It also determines (\alpha(G_k)=2k+3), classifies the maximum independent sets, and derives the corresponding odd-(n) qualitative-independence hypergraph corollary. Supplementary checks formal-variable checks of the load-bearing rational identities; separate reconstruction of all endpoint-interpolation coefficients; explicit normal- and optimized-mode failure handling; finite-range Eberlein, divisor, coefficient-sign, construction, and endpoint-identity regression tests; pinned Python dependencies and a Python 3.9/3.12 CI matrix; a deterministic PDF build target based on SOURCE_DATE_EPOCH. The exact scope and limitations of the programs are documented in supplementary/README.md. The deterministic release-candidate PDF has SHA-256 c00f1a7e2dd16605ef6d52df00583cb89423e96f1ff6195fe8ef090b0a24ad42. Reproduction python3 -m venv .venv . .venv/bin/activate python3 -m pip install -r requirements.txt make verify make reproducible Licenses Software: MIT License. Manuscript and prose documentation: CC BY 4.0.