Targeted mathematical prior-art review · 4 October 2026
The review identifies established methods and overlaps. It does not certify worldwide priority or infer novelty from missing search hits.
Sources inspected for this release
- Allen Hatcher, Vector Bundles and K-Theory, Theorem 3.2 and Section 3.1: https://pi.math.cornell.edu/~hatcher/VBKT/VB.pdf Supplies the classical Chern-class properties used by Theorem 2.
- Ravi Vakil, The Rising Sea, Section 11.3, Exercise 11.3.C and the height theorem: https://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf Supplies the projective intersection/affine-cone lower bound in Theorem 6.
- Alex Eremenko and Andrei Gabrielov, Degrees of real Wronski maps: https://arxiv.org/abs/math/0108133 Explicitly describes the Wronskian as a classical projection of a Grassmannian. Its determinant-degree and nonvanishing context overlaps the atlas construction.
- Nicholas J. Higham, Computing the Polar Decomposition—with Applications: https://eprints.maths.manchester.ac.uk/694/1/high86p.pdf Establishes the classical polar decomposition and perturbation setting.
Targeted searches also covered Grassmannian Pluecker embeddings, Wronski maps, continuous bundle embeddings, and rectangular polar perturbation bounds. Both available search engines were used. Irrelevant search results were not technical evidence. No broad bibliographic absence claim is made.
Established ingredients
Continuous range bundles and their embeddings, Chern classes, Whitney multiplication, projective dimension/height bounds, the Wronski map, Cauchy-Binet, polar normalization, Sylvester equations, Gramian factorization, unitary dilation, Borsuk-Ulam, Bargmann phases, and Kato transport are established. The reference atlas is a direct use of the classical Wronskian mechanism; it is not a claim to invent that map. Several central statements are likely corollaries, formulations, or combinations of known results.
What this release adds to the current research construction
The release gives an explicit same-width repair formula and quantitative bounds, extends the sharp continuous-factor minimax statement to every rank, provides the exact nearest-blind construction for equal-rank references, computes a sharp fixed-reference chart count with a concrete atlas, and joins these resources to labelled completions and stable decoding. The exact U(2) example demonstrates why scalar phase metadata cannot describe all higher-rank comparison histories. All statements are proved in the manuscript.
The proposed contribution is this information-explicit factorization/reference synthesis and its constructive presentation. Its exact prior occurrence has not been excluded. Naming it, producing a proof, or verifying examples does not establish a field-changing discovery or an empirical scientific law.
Previous mathematical sources retained
The bibliography preserves the primary/source-authored references for contraction dilation, observability Gramians, Borsuk-Ulam, projective cohomology, Bargmann phases, and projection transport. The proofs reproduce the finite calculations they use. No full text behind an inaccessible publisher page is claimed to have been inspected for this release.
Remaining priority check
Independent specialists should compare the exact formulations with continuous PSD factorizations, generator/embedding dimensions of tautological bundles, osculating Schubert atlases, polar-factor repair and perturbation, and reversible reduced representations. That review and a concrete application benchmark remain necessary for a stronger importance claim.