The Higgs Effective Field Theory as the Low-Energy Limit of the Recognition-Cost Geometry: A Lean-Backed Map from RS Primitives to Collider Observables

The companion paper [1] argues that the 125 GeV resonance can be recovered as a feature of the local Taylor geometry of the recognition-cost functional J(x) = ½(x + x⁻¹) − 1, without postulating an independent space-filling scalar condensate. In peer review, that ontological proposal is acceptable only if it derives the Standard-Model Higgs effective field theory as its low-energy limit and reproduces collider observables, rather than bypassing them. This paper meets that burden in three steps. First, we derive the canonical Higgs effective potential as the quartic Taylor expansion of J about its minimum, with explicit dimensional analysis and a canonically normalised collider field h = vε. Second, we formalise the Standard-Model gauge-boson mass relations m²_W = g²v²/4, m²_Z = (g² + g'²)v²/4, and m_W/m_Z = cos θ_W on positive gauge couplings, and we transport the recognition-mass formula m_f = yardstick(sector) · φ^(r−8+gap(Z)) into the canonical Yukawa convention y_f = √2 m_f/v. Third, we expose the partial-width/branching-ratio/signal-strength schema under which RS reproduces the SM tree-level collider observables when the input couplings agree, and we formalise the longitudinal vector-boson scattering cancellation that protects perturbative unitarity. The full chain is bundled in the Lean library at IndisputableMonolith.StandardModel.HiggsEFTLowEnergyLimit, with six contributing modules and explicit per-claim tags (theorem, conditional theorem, tree level only, open normalization, open rung map, loop level open). We list the open subproblems honestly: the canonical-normalisation map Λ(v), the Standard-Model rung assignment from cube combinatorics, and the loop-induced channels h → γγ, h → gg, h → Zγ.