minkowski_form_zero

This module builds the zero-parameter bridge from discrete Recognition Science ledger sites to a Lorentzian continuum. The chain runs J-cost lattice → quadratic cost → Laplacian → Lorentzian interval → Minkowski flat limit, then curved metric from defect and Einstein equations. Lorentzian signature is forced by tick/voxel asymmetry; the spatial metric by $J''(1)=1$; $c=\ell_0/\tau_0$ by one voxel per tick; and $D=3$ by DimensionForcing.

The Minkowski form is the flat quadratic form $s^2(t,x,y,z)=-t^2+x^2+y^2+z^2$ on $\mathbb{R}^{1,3}$. Upstream, a ledger tick is the atomic unit of temporal progression (time advances discretely, with no background manifold). Homogeneity of degree two for this form is recorded as a sibling fact. The present statement is the evaluation of that form at the origin.

One-line tactic proof: unfold the definition of the Minkowski form, then close with ring. Substituting $(t,x,y,z)=(0,0,0,0)$ into $-t^2+x^2+y^2+z^2$ yields zero by elementary arithmetic; no external lemmas are required.

This is the trivial anchor for Part 1 of the continuum-manifold emergence module: before Lorentzian signature, causal trichotomy, and the light-cone speed limit can be stated, the quadratic form must be well-defined and vanish at the origin. The module doc lists Lorentzian signature, light cone, causal structure, and flat-space limit equal to Minkowski as unconditional proved content; this lemma is the base evaluation that those signature and trichotomy siblings sit on.

In the broader RS chain it supports the flat Minkowski limit that precedes defect-driven curvature and the Einstein equations (ZeroParameterGravity coupling $\kappa=8\phi^5$). No downstream uses are recorded yet; the immediate consumers are the sibling signature and causal-structure theorems in the same file.