v1.0.0 — Arithmetic landscapes: three manuscripts and the apparatus that checks them

First archived release. Deposited in Zenodo to obtain a DOI.

What the mathematics says

Three manuscripts study the subset-sum landscape of a finite set A of odd integers. The ratio of strict local minima to ground states converges to a rational invariant Γ(A) read off the set by counting — and that invariant turns out to be the annealed (independence) prediction itself. So the main theorem says the annealed count of metastable states is asymptotically exact for this model, with an explicit condition that delimits it and an explicit family that breaks it. A lower bound that would normally cost a quantitative equidistribution estimate is obtained instead from the Kubert distribution relation, as an exact equality.

• Part I (26 pp.) — the gap series and the invariant.
• Part II (35 pp.) — asymptotic flatness for the odd primes, unconditionally.
• Part III (45 pp.) — deformed measures, random sequences, the coset identity and its decomposition into Dirichlet L-values. Appendix A writes out region R1 with every constant proved rather than measured.

What is in the deposit

• the three manuscripts;
• a Lean 4 development of the settled results, replayed through the kernel by an independent checker that must first reject three deliberately corrupted modules;
• the committed scripts and logs behind every number quoted in the text;
• a suite of mechanical checks (C1–C20) that runs before each commit;
• and a complete record of the mistakes this process has made.

What this is not

None of it is peer-reviewed, and no claim is made here beyond what each statement claims for itself. Every theorem, proposition and lemma declares its status — proved, derived, measured, or conjectured — at the place where it is stated, and three results of Part III remain explicitly conditional.

A DOI makes a version permanent. It does not make it true.

Tool and computational resource disclosure

Carried out with AI language models (Anthropic's Claude) as tools, under the author's direction, following recommendation 01 for individual mathematicians of the Leiden Declaration on Artificial Intelligence and Mathematics, which the author has signed. Each manuscript names the tools, the versions, and the computational resources — one personal computer, no cluster and no accelerator — and names the provision of the Declaration that this work does not meet. Responsibility for every claim and every citation is the author's alone.

Licences

Code (lean/, the Python scripts): Apache-2.0, matching Mathlib. Manuscripts (paper/): CC BY 4.0.