IndisputableMonolith.Gravity.Analysis.Regge4DTensorAlgebraicCloserAudit
Audit layer for the partial 4D Regge tensor algebraic closer in the Gravity domain. It sits over the 4D counterpart of the 3D Regge TT adjugate identity, which banks transported distinct-hinge mass-squared as a quadratic form in energy and direction on the TT variety. Every closed ray evaluation is already available; full equality to a universal adjugate-style tensor contraction remains open. Gravity analysts cite it to separate closed ray bookkeeping from the still-open universal contraction.
claimAudit module for the partial 4D Regge tensor algebraic closer: transported distinct-hinge $m^2$ is recorded as a quadratic form in $(E,\mathrm{dir})$ on the transverse-traceless variety, with every closed ray evaluation available, while full closed-form equality to a universal adjugate-style tensor contraction remains open.
background
In the Recognition Science gravity stack, Regge calculus encodes curvature on discrete hinges. The 3D program already has a Regge TT algebraic closer realizing an adjugate identity for transverse-traceless data. The 4D counterpart aims at the same style of identity one dimension higher.
The upstream closer module banks the transported distinct-hinge mass-squared as a quadratic form in energy and direction on the TT variety. Its own documentation states that every closed ray evaluation is available today, while full closed-form equality to a universal tensor contraction (adjugate-style) remains open.
This audit module imports that partial closer and organizes the proved-versus-open split for the 4D tensor-algebraic program. It does not redefine the quadratic form; it surfaces status.
proof idea
This is an audit module, not an independent proof chain. It imports the partial Regge 4D tensor algebraic closer and exposes the existing split: banked quadratic-form evaluations on closed rays versus the still-open universal adjugate-style contraction. Argument structure is organizational status bookkeeping for the 4D counterpart of the 3D Regge TT algebraic closer.
why it matters in Recognition Science
The module is the audit face of the 4D Regge tensor algebraic closer inside the Gravity domain. The parent object is the 4D counterpart of the 3D Regge TT algebraic closer adjugate identity: hinge mass-squared transported as a quadratic form on the TT variety. No downstream used-by edges are recorded yet, so the value is local clarity: ray evaluations are closed, the universal tensor contraction is not. That separation matters for anyone tracking how far the discrete gravity program has pushed an algebraic lock between hinge $m^2$ and a universal 4D tensor form, and what remains before a full adjugate-style identity can be claimed.
scope and limits
- Does not prove full closed-form equality to a universal adjugate-style 4D tensor contraction.
- Does not replace or restate the 3D Regge TT algebraic closer identity.
- Does not claim hinge evaluations beyond the banked closed-ray cases.
- Does not derive continuum Einstein equations from the discrete closer.
- Does not close the open universal-contraction gap flagged upstream.