Exact-Root Certification of Finite-Error Ordering in Quantum Control

Audit-closure release

Version v0.3.2 adds independent audit checks around the frozen v0.3.1 exact-root certificate. It does not modify the frozen physical model, twelve exact-root boxes, manuscript, proof engines, or certified 66/66 finite-error ordering.

Added verification

• P0 — production-preconditioner regularity

  • 12/12 production Krawczyk preconditioners certified nonsingular.
  • 256-bit outward-rounded Arb Rump–Neumann verification.
  • Verified inverse-error enclosures.

• P1 — independent high-precision reconstruction

  • Operators reconstructed without importing the repository physics engine.
  • Hermitian eigendecomposition propagation.
  • 12/12 finite-error means inside full-precision certificate enclosures.
  • Complete twelve-path ordering reproduced.
  • Six closest certified pairs reproduced.
  • Three paths cross-checked with 60-digit mpmath.

• P2 — analytic and mutation-tested Krawczyk checks

  • 13/13 clean analytic assertions pass.
  • Defect-direction/sign mutation detected.
  • Correction-sign mutation detected.
  • Strict boundary-touching rejection verified.

GitHub Actions verification

• P1 independent reconstruction: https://github.com/papasop/quantum-control-geometry/actions/runs/31227414888

• Fast P0/P2 audit: https://github.com/papasop/quantum-control-geometry/actions/runs/31226380146

• Artifact checks: https://github.com/papasop/quantum-control-geometry/actions/runs/31226380241

All required workflows completed successfully using actions/checkout@v5 and actions/setup-python@v6.

Scientific scope

The formal certificate remains conditional on the serialized, finite-dimensional two-atom Hamiltonian and the declared six-axis mean finite-error functional.

This release does not certify PASQAL hardware, QPU execution, calibration, model discrepancy, open-system behavior, global fibre structure, worst-case-error ordering, or many-body scaling.

Version relationship

• v0.3.1: frozen scientific certificate.
• v0.3.2: audit-closure supplement built on the unchanged v0.3.1 result.