← AMRAL · PROGRAM-CSM

Closure-Space Mathematics

Closure-Space Mathematics · Ten papers, 00–09

Unlike the other cases here, CSM does not attack any one specific conjecture — it is a methodological theory about how a long-horizon mathematics research state should itself be organized. Once research has accumulated a large body of propositions, hypotheses, proof attempts, counterexamples, obstructions, and bridges, can it be organized into a verifiable, replayable, updatable relative-global mathematical space that gives an explicit, typed determination of which regions are closed, which remain open, and which are only locally obstructed? Three core principles run through the whole series: Observed Proof Space ≠ Admissible Proof Space ≠ Mathematical Reality; Route Closure ≠ Theorem Proof; and the Globality Typing Principle — any claim of being "global" must state which axis it is global along.

The ten papers build progressively: 00 formal foundations → 01 globality typing → 02 typed closure graphs → 03 frontier geometry and exhaustion → 04 closure dynamics → 05 projection and compilation → 06 cross-domain transfer → 07 closure calculus → 08 runtime semantics → 09 instantiates the whole theory onto the Navier–Stokes research corpus, establishing "NS_GSM v0.1." Every paper draws its boundary explicitly, either with a full list of non-claims or a series of "No-Go" theorems; the one line that runs most consistently through the whole series is: without a proof-carrying certificate, there is no theorem-level mutation. For NS_GSM's concrete instantiation onto AMRAL's existing NS research lines (C1–C6, X72, DCRP, RFP, MORP, FCBP, and others), see NS Zone · NS_GSM sub-line.