Datasets:

PureOne
/

NYRAELUNE-V

All eight verifiers below were executed on the packaged files with Python 3 and standard-library exact arithmetic. The counts are passing assertions across explicit finite instances, not counts of theorems or independent discoveries.

Verifier	Passing assertions	Coverage
`verify_coherent_repair.py`	3,991	Hodge coefficient realization for n=2..6; norm-preserving lifts and rational budget frontiers; q=2..8 jet obstructions and homogeneous derivatives; both blow-up charts; radial bounds; 72 analytic arc examples; coherence floor
`verify_cancellation_frontier.py`	2,537	Exact polynomial CP recursion versus independently enumerated ordered words; signed cancellations, protected walls, noncommuting examples, and formal Laurent/Newton leading matrices
`verify_flat_pencil.py`	31,285	Genuine zero-anchor gapped lifts for n=2,3,4; individual squares, anticommutators, ordered products and triple words; first mixed target degree; exact tensor moments through six unit sectors
`verify_frontier_api.py`	17	Dedicated marginal solver: frontier six, protected infinite frontier, moving nilpotent flag, feedback rejection, and input validation
`verify_full_feedback.py`	3,434	Exact polynomial superoperators, characteristic coefficients and recurrences across 15 models; scalar and fractional feedback; noncommuting Kraus maps; signed cycle cancellation; transient beta below b; critical ODE recurrences; logarithmic-window qualification
`verify_geometry_transport.py`	38,232	All 3,180 weighted monomials through degree seven in each of four parameter/correction cases; exact square, fourth-power and cube identities; centered binomial moments for horizons through five
`verify_feedback_api.py`	97	Self-contained public solver certificates, optional phase data, critical ODE and all-horizon test; eight hand-derived model classes; invalid inputs, CLI rejection of nonnilpotent base, exact decimal parsing, worked output reproduction
`verify_budget_resources.py`	5,579	Affine clipping and tangent/zero-radius cases; continuous varying budgets; Lipschitz and Hölder paired-point lower bounds; regularizer algebra, norm/residual bounds and exact Jacobian samples; global polynomial positivity certificates; five hand-derived stable-fiber examples
Total	85,172	Zero failures

The three genuine flat-pencil graded audits have basis sizes 462, 596, and 999. The geometry-to-transport audit has basis size 3,180. These dimensions describe explicit finite quotients. They are not numerical approximations to an infinite algebra.

The budget/resource audit has 2,244 affine clipping, 25 varying-budget boundary, 156 Lipschitz pair, 336 Hölder pair, 2,695 regularizer/Jacobian, eight global polynomial certificate, and 115 stable-fiber assertions. It distinguishes exact identities and sampled Jacobians from general analytic conclusions. The global scaled-ratio inequalities used for the derivative bound are supported by exact transformed polynomials with nonnegative coefficients.

Independent internal analytical reviews checked the finite Glaeser budget formula and its exact boundary attainment, variable budget profiles, the full feedback recurrence and spectral estimates, all three growth regimes, the arbitrary-horizon finite test and counterexample, the adaptive comparison, the graded geometry signs and invariant reduction, the sharp regularity resource law, and the noncommuting extension. The general noncommuting coupling corollary has an algebraic proof and independent review; the 38,232 computational coupling assertions concern its single-generator core.

The final two-pass LaTeX build has no unresolved references, overfull boxes, or underfull boxes. The 23 rendered pages were visually inspected, including the revised final reference page. PDF title and author metadata were checked. The figure script uses exact closed moment formulas and proved exponents; it contains no fitted empirical data.

These are internal verification records. Classical stabilization, selection, and spectral background are cited in the manuscript. Finite checks supplement the general proofs and do not establish historical novelty, external peer review, a proof-assistant certificate, or a T1–T9 ranking.