Hilbert 12: Cubic Divisor Transport and Reconstruction
Komorebi P. · Companion edition · October 7, 2026
This set joins the traditional mathematical development, a reproducible Python visual guide, and a Lean companion. Editable TeX and Markdown, exact finite checks, original research checkpoints, and verification records accompany the PDFs.
Reading order
traditional/H12_Cubic_Divisor_Traditional.pdf: definitions, arithmetic and theta normalization, divisor transport, cubic growth, canonical regularization, and analytic reconstruction.visual/H12_Cubic_Divisor_Visual_Guide.pdf: eighteen Python figures, including a genuine three-dimensional integer chamber and its complex-plane image.lean/H12_Cubic_Divisor_Lean_Guide.pdf: formal statement mapping, hypotheses, compiler and axiom evidence, resource limits, and the boundary of formal coverage.verification/FINAL_VALIDATION.md: the edition's audit scope, checked artifacts, discovered failures, corrections, and remaining obligations.
Mathematical scope
The principal correction has locally finite divisor support with two-sided cubic unsigned growth. Its ungrouped absolute canonical product has genus three. The fourth logarithmic derivative, reflection identity, and period-one transition specify the cubic exponential and a branch-free formula for the special cube.
The finite-theta obstruction applies to fixed positive-definite period matrices and affine restrictions, with finite polynomial combinations and derivatives. A nowhere-zero entire factor is allowed globally. Allowing arbitrary entire exponential factors inside sums would invalidate the quadratic growth bound; that larger class is not claimed.
The original equality U_Gamma = U_alg remains open. An analytic reconstruction by an infinite canonical product does not identify its special value with a class-field unit. The exact remaining polarized reality implication, and the separate periodic descent and principal-norm obligations, are stated in the manuscripts.
Lean checks the selected finite algebraic and integer statements. Complex divisor analysis, infinite-product convergence, and the class-field comparison remain ordinary mathematical arguments or open obligations as explicitly marked. Finite computations illustrate or test their stated ranges; floating diagnostics are not directed enclosures or universal proofs.
Sources and evidence
The three publication folders are canonical for this edition. sources/ and the original ZIPs under provenance/ preserve the historical checkpoints unchanged, including wording corrected or restricted in the final manuscript. Fresh results are distinguished from inherited evidence. SOURCE_MANIFEST.json records packaged file hashes; provenance/SOURCE_INTAKE_MANIFEST.json records the protected originals.
Rebuild
With the documented TeX dependencies installed:
python3 build_release.py
Use --only traditional, --only visual, or --only lean for one PDF. The script compiles the editable canonical TeX and records output under verification/publication/rebuild/. It does not silently overwrite mathematical source sections from historical inputs.
Regenerate figures with python3 visual/generate_figures.py. Numerical replay instructions and bounded-resource records are under verification/numerical/. The Lean project provides its pinned toolchain, dependency revision, and replay runner. Compiler runtimes and dependency caches are excluded from this ZIP.
Build a new verified source archive after an intentional edit with python3 scripts/package_release.py.