LorentzianSectorStatus
plain-language theorem explainer
Status record for the Lorentzian-sector gap in the QG Seven-Gaps campaign. Four boolean flags track: causal tetrahedron classes defined; Wick map certified on that class; Euclideanized simplices non-degenerate on exact alpha ranges; action-level continuation still open. Downstream lorentzianSectorStatus fills three true and one open. Pure structure definition, no proof content.
Claim. A four-field status record for the Lorentzian sector: whether causal tetrahedron classes are defined; whether the Wick map is certified as an involution acting by $\alpha \mapsto -\alpha$ on that class; whether Euclideanized simplices are proved non-degenerate for $\alpha > 1/3$ (type $(3,1)$) and $\alpha > 1/2$ (type $(2,2)$); and whether Lorentzian action continuation (complex dihedral angles, sinh/boost sector, analytic continuation of the action) remains open.
background
This module opens the first certified Lorentzian layer of the discrete gravity program. Prior results were Euclidean. In 3D CDT (Ambjorn-Jurkiewicz-Loll), spatial slices are equilateral triangulations with squared edge length $a^2$. Spacetime between slices is filled by type $(3,1)$ tetrahedra (3 spacelike + 3 timelike edges) and type $(2,2)$ tetrahedra (2 spacelike + 4 timelike). Timelike squared lengths are $-\alpha a^2$ with $\alpha > 0$; Wick rotation is the sign flip $\alpha \mapsto -\alpha$ on that class.
Vertex/edge indexing follows the Cayley-Menger convention (vertices $0..3$, six edges). The module certifies combinatorial causal classes, the Wick involution, Euclidean non-degeneracy on hand-derived ranges, and a deficit-angle reality corollary at $\alpha = 1$. Action-level continuation is deliberately left open.
Sibling status patterns elsewhere (RS-native units, four-tet signed deficit, discrete Lichnerowicz) use the same boolean-flag style to mark closed versus open deliverables.
proof idea
No proof: this is a structure declaration with four Bool fields. Instantiation is by record construction (see the module-level value that sets three flags true and leaves action continuation open). Field names encode the four deliverables named in the module doc-comment.
why it matters
Gives a single typed handle for the Lorentzian-sector lane of the Seven-Gaps campaign. The sole consumer is the module status value, which reports causal classes defined, Wick certified on the class, Euclidean non-degeneracy proved, and Lorentzian action continuation still open. That open flag marks the remaining work: complex dihedral angles at timelike hinges, the sinh/boost sector of the Lorentzian Regge action, and analytic continuation of the action itself. Ties the kinematical Wick layer (classes, involution, non-degeneracy) to the broader discrete-gravity stack without claiming continuum Lorentzian dynamics or curved-background operator recovery (those remain open on the Lichnerowicz side as well).
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