| # Targeted mathematical prior-art review · 4 October 2026 |
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| The review identifies established methods and overlaps. It does not certify |
| worldwide priority or infer novelty from missing search hits. |
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| ## Sources inspected for this release |
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| - 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. |
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| 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. |
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| ## Established ingredients |
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| 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. |
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| ## What this release adds to the current research construction |
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| 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. |
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| 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. |
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| ## Previous mathematical sources retained |
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| 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. |
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| ## Remaining priority check |
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| 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. |
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