# Verification report

## Result and limitations

The manuscript proves a continuous-time, normal, positive-orbit-generated
dilation whose GNS kernel is not shift-invariant. For each fixed m it
preserves all conditional observations at at most m times. It also proves
an exact support criterion in the commutative case. The analytic proof is
complete for this stated scope; the broader source record is not closed.

This is an originating-researcher self-audit, not independent review,
peer review or formal proof-assistant verification. Novelty searches
were bounded; absolute priority has not been certified.

## Mathematical checks

The retained self-audit tests continuity, normality, null-set conventions,
orbit generation, expectation properties, joint rather than pairwise
Gaussian independence, endpoints, the full left GNS kernel, and the
distinction from weak and strong dilation theorems.

The standard-library checker uses exact integer polynomials and rational
arithmetic. Its identical normal and optimized runs verify:

- Two denominator-cleared universal covariance/variance identities.
- 264 exterior covariances, eight residual variances and 28 cross-covariances.
- 252 support sign cases and 3024 conditional marginal cells.
- 21840 shifted sign pairs and four negative controls.

Finite sign enumeration covers m=1,...,6. Gaussian conditioning and the
written pigeonhole argument prove the infinite family, not the enumeration.
The failed initial optional-SymPy route is preserved in the research
dossier; the deliverable checker needs no third-party mathematics package.

## Source and artifact verification

Three primary-source PDFs were retained and hash-checked; eighteen complete
relevant pages were rendered and directly reviewed. The manuscript cites
the exact source and distinguishes later positive weak-dilation results.

The six manuscript pages are checked visually. The final built-in LaTeX
compile succeeds. A source-ZIP build in a clean temporary directory must
reproduce the same PDF page content and text, and both checker replays
must match before package-readiness.json can declare PASS.

The package manifest records the exact artifact hashes. Source PDFs are
not redistributed. Readiness is not publication: no DOI, Zenodo deposit,
site deployment or Hugging Face notice is asserted here.