CNRS Scientific Toolkit v0.12.1 Release date: 2026-08-04 documentation-synchronized rebuild Theme: Algebraic-curve intake, finite branch-point detection, and Problem 4 record synchronization. Added: algebraic-curve branch detection cnrs.algebraic_curve.AlgebraicCurve for accepting and validating polynomial relations P(z,w)=0. Exact construction of P_w, the resultant Res_w(P,P_w), and the polynomial discriminant where available. Detection of candidate finite branch values from resultant roots. Recovery of ramification points satisfying P=0 and P_w=0 over each candidate value. Exact root handling when SymPy supplies complete roots, with explicit numerical fallback using nroots. Ramification multiplicity, exact/numerical status, residual, and warning metadata. Convenience functions algebraic_curve(...) and finite_branch_points(...). Seven focused tests covering exact, numerical, unbranched, and repeated-component cases. Install the optional algebraic dependency with: pip install cnrs[algebraic] Problem 4 documentation synchronization The full package now identifies the canonical Problem 4 record: Donald G. Palmer, Partial Operational Completeness of a Positional Number System for Complex Numbers, Version 12, Zenodo, 2026. DOI: 10.5281/zenodo.21791909. Updated current-status files: README.md CITATION.cff RELEASE_NOTES.md docs/CLAIM_STATUS.md docs/THEOREM_ALIGNMENT.md docs/API_STATUS.md docs/TEST_STATUS.md docs/GAUSSIAN_RATIONAL_THEOREMS.md docs/CNRS_TOPOLOGY_AND_HYBRID.md docs/RESEARCH_STATUS.md docs/CNRS_P4_REFERENCE_STATUS.md (new) The documentation now distinguishes the resolved natural beta-adic completeness result from the separate open question of ordinary complex analytic convergence. Validation 1206 passed, 0 failed The suite reports 917 retained reliable-domain warnings from pre-existing scientific-workflow tests. Scope boundary The algebraic-curve detector computes finite critical values of the projection (z,w) -> z. It does not yet: analyze branch behavior at infinity; normalize singular or reducible curves; infer monodromy permutations automatically; build Puiseux charts; certify numerical roots or continuation paths. The bundled P4 records establish results only in their explicitly stated algebraic, beta-adic, coefficientwise, or formal domains. They do not identify the beta-adic completion with the ordinary complex plane and do not prove unrestricted analytic convergence of all CNRS-H series.