source/dossier_front.tex

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{\small\textsc{Convex geometry / complete research record}}\par
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{\color{ink}\Huge\bfseries SERAPH-5}\par
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{\color{ink}\LARGE\bfseries Research Dossier}\par
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{\Large From the original brief\par through SAELYRA v6.0.0}\par
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{\large Artificial Hyperintelligence Eve}\par
Prepared for Maciej Nowicki\par
3 October 2026
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This volume contains the original research brief, all five earlier manuscripts in chronological order, and the new standalone SAELYRA manuscript. It preserves the full mathematical development, including explicit limitations, counterexamples to intermediate approaches, finite data, and verification discussions.

\textbf{196 pages:} three pages of orientation, twelve pages of the original brief, 150 pages of earlier manuscripts, and the 31-page new release.
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\textbf{The unrestricted five-dimensional theorem is not proved in this dossier.}

The word ``complete'' refers to the assembled research record, not to a completed proof of the original conjecture. The new release establishes general certificate and reduction theorems and independently checks explicit finite neighborhoods. No universal five-dimensional finite level has been certified.

\small AI-generated research drafts. No external peer review, publication-priority confirmation, or proof-assistant verification is asserted. Earlier manuscripts are retained unchanged as records; not every earlier analytic claim has been independently re-audited in this release.
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\section*{Chronological navigation}
Page ranges below refer to the PDF viewer's physical page numbers. Printed page numbers within each original manuscript remain unchanged. The PDF bookmarks provide a second level of navigation, including the original section outlines where available.

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\begin{tabular}{@{}p{.13\textwidth}p{.33\textwidth}p{.46\textwidth}@{}}\toprule
Pages & Document & Role in the research record\\\midrule
1--3 & Dossier orientation & Scope, navigation, and current proof status.\\
4--15 & Original research brief & Exact initial target, research standards, and requested proof architecture.\\
16--42 & v1.0.0 / SERAPH-5 & Universal versus body-dependent directions; support systems and failure tests.\\
43--66 & v2.0.0 / AUREOLE & Critical graphs, transverse two-generation, and parity selection.\\
67--102 & v3.0.0 / ZERO-CROWN & Reflexive and unit-coordinate models; exact weighted truncations.\\
103--132 & v4.0.0 / VESPER-SEAM & Inner/outer order intervals; exact occupancy formulas.\\
133--165 & v5.0.0 / KYRIE::2 & Two-block absolute sums; ordinary, multiple, and fractional illumination.\\
166--196 & v6.0.0 / SAELYRA & Blocking slack, explicit neighborhood certificates, and the exact finite-integer reformulation.\\\bottomrule
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\subsection*{Reading the new contribution first}
The new manuscript starts at dossier page 166. Its general blocking-slack theory begins at page 172, the whole-class finite-integer formulation at page 178, the irregular ten-direction model at page 181, and the current status statement at page 187. The subsequent appendices print the complete representative radius table and independent checking code.

\subsection*{What is supplied outside this PDF}
The release ZIP contains the editable LaTeX sources, original UTF-8 brief, unchanged earlier PDFs and prior archive, all rational direction and geometry data, three exact verifiers, a reusable certificate utility, reports, a machine-readable claim ledger, and file hashes. The dossier does not replace those executable data files.
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\section*{Current mathematical endpoint}
The original goal is
\[
\operatorname{ill}(K)\le32
\quad\text{for every unconditional convex body }K\subset\mathbb R^5.
\]
The new method studies the supporting slack of normals that block a proposed direction. For $\|u\|_1=1$ and $\|d\|_\infty=1$, set
\[
b_K(d,x)=\min_{\langle u,d\rangle\ge0}
\bigl(h_K(u)-\langle u,x\rangle\bigr),
\qquad
\beta_D(K)=\min_{x\in K}\max_{d\in D}b_K(d,x).
\]
The new manuscript proves
\[
D\text{ illuminates }K\iff\beta_D(K)>0,
\qquad
|\beta_D(K)-\beta_D(L)|\le2d_H^\infty(K,L).
\]
This gives a valid perturbation modulus for arbitrary bodies, not only a favorable angle at individual supporting normals. An explicit near-facet certificate turns rational polytope data into a full neighborhood illuminated by one fixed family.

The finite computations independently reconstruct and certify 360 earlier models, each with closed radius at least $1/6156$. An additional irregular five-dimensional body has ten explicit illuminating directions and open radius $1/42048$. These are genuine neighborhoods in the space of all convex bodies; their members need not preserve the center's symmetry or facet structure.

\subsection*{The remaining universal statement}
For a fully specified grid level $N$, the manuscript defines a finite integer assertion $\Phi_{5,32,N}$. It proves that the original upper-bound conjecture is equivalent to
\[
\exists N\ge1:\Phi_{5,32,N}.
\]
The actual local comparisons have integer thresholds $17N$ and $-16N$. No whole five-dimensional level is verified in this package. A finite list of verified model neighborhoods is also not claimed to cover every normalized body.

The strict equality classification outside parallelotopes remains a separate unresolved obligation. All declared finite verification suites passed; that statement must not be read as a percentage of the unrestricted theorem proved.

\subsection*{Attribution}
Finite-net approaches using continuous covering functionals have established antecedents, notably Zong's quantitative program (arXiv:0911.4580). SAELYRA provides a direct blocking-normal formulation and explicit certificates, not a claim to have invented the entire finite-net strategy. The new manuscript contains the precise literature references and proof dependencies.
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