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CSM · 01 v0.1 · Globality Typing Paper 2026-08-27

Globality Typing and Domain Stratification of Propositions

A direct extension of Paper 00. Argues that “global” is often used as if it were a single scalar of strength, when in fact it quantifies over entirely different axes (time, space, data class, boundary, external forcing, parameters, solution concept, regularity, equation family, representation, proof system, physical realization). Establishes the Globality Typing Principle: globality is a typed profile, not a boolean or a single totally-orderable strength. Defines ScopeContract(Q) and an 11-axis globality profile GProf(Q). Uses NS as the first domain-stratification test case, distinguishing three domains — formal/Clay NS, physical NS realization, and the generalized NS-like family — and requires that any cross-domain theorem upgrade carry an explicit certificate, never resting on surface similarity between equations alone.

Globality is a typed quantifier profile, not a single totally-orderable strength; a cross-domain theorem upgrade must carry an explicit certificate. Of the 12 non-claims, items 7 and 8 mark the paper’s most important boundary: it does not claim to have proved Clay Navier–Stokes global regularity, nor does it claim to have proved universal regularity for any generalized NS-like family.

Connections

Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.

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