IndisputableMonolith.Gravity.NullConeQuadraticTensorClassAudit
Audit surface for the null-cone quadratic tensor class: values of a symmetric quadratic form on all Minkowski-null covectors fix the form modulo a multiple of the Minkowski metric. Gravity workers cite it when checking the Phase 5 algebraic prerequisite before geometric tensor work. The module is a thin import-and-audit shell over the finite-dimensional linear-algebra package.
claimAudit of the rigidity statement: if $Q$ is a symmetric bilinear form on $\mathbb{R}^{1,3}$ and the values $Q(k,k)$ are known for every Minkowski-null covector $k$ (i.e.\ $\eta(k,k)=0$ with $\eta=\mathrm{diag}(-1,1,1,1)$), then $Q$ is determined up to $Q \mapsto Q + \lambda\eta$ for $\lambda\in\mathbb{R}$.
background
Phase 5 of the gravity stack needs an algebraic rigidity fact before any geometric Einstein-tensor identification. The imported package states that a real symmetric quadratic form on Minkowski space is fixed, modulo scalar multiples of the metric $\eta=\mathrm{diag}(-1,1,1,1)$, by its restriction to the null cone: knowing $Q(k,k)$ for every null covector $k$ determines $Q$ up to $Q+\lambda\eta$.
That package is explicitly finite-dimensional real linear algebra. It is not yet the independently geometric tensor $G$ required by Phase 5; the upstream module doc marks it as a Tier-A algebraic prerequisite and notes that the geometric step remains separate.
This audit module sits in the Gravity domain and imports only that class module, exposing the null-cone rigidity claim for checklist and dependency review.
proof idea
Definition and audit shell, not a new proof module. It imports NullConeQuadraticTensorClass and surfaces the existing finite-dimensional rigidity package (symmetric forms on null covectors determine the matrix modulo $\eta$) for Phase 5 review. No independent tactic script or term proof lives here; argument structure is inherited from the imported algebraic package.
why it matters in Recognition Science
Phase 5 needs a clean algebraic gate before geometric identification of the gravitational tensor. The audited package supplies that gate: null-cone values fix a symmetric form modulo multiples of $\eta$. Downstream geometric work can then treat the residual $\lambda\eta$ ambiguity separately rather than re-proving linear-algebra rigidity inline.
No further modules currently list this audit as a hard dependency in the supplied graph, so its role is checklist and import hygiene inside Gravity. It keeps the Tier-A algebraic prerequisite visible and separable from the still-open geometric $G$ step flagged in the upstream module documentation.
scope and limits
- Does not construct the geometric Einstein or $G$ tensor of Phase 5.
- Does not remove the residual $\lambda\eta$ gauge freedom.
- Does not treat curved backgrounds or infinite-dimensional function spaces.
- Does not prove new lemmas beyond auditing the imported class module.
- Does not fix physical units or couple to the RS mass ladder.