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.