module module high

`IndisputableMonolith.StandardModel.HiggsEFTBridge`

The module supplies the Recognition Science Higgs effective potential at canonical mass dimension four, expressed as V_RS(Λ, v, h) = Λ⁴ J(exp(h/v)). Researchers constructing the low-energy Higgs EFT from the recognition substrate cite it as the bridge step in the Standard Model chain. The module consists of a core definition together with algebraic lemmas on non-negativity, quartic expansion, and truncation error bounds.

claim$V_{RS}(\Lambda, v, h) = \Lambda^4 \cdot J(\exp(h/v))$ where $J$ denotes the recognition cost function from the Cost module.

background

The module sits inside the Standard Model Higgs effective-field-theory low-energy-limit chain. It imports the fundamental RS time quantum τ₀ = 1 tick from Constants and the recognition cost function J from Cost. The setting is the RS cost geometry that produces an effective scalar coordinate for the Higgs field, with the potential required to have canonical mass dimension four.

J satisfies the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and is realized as J(x) = cosh(log x) - 1. The potential is constructed so that its vacuum value and derivatives reproduce the required quartic structure at the electroweak scale v.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module feeds the Higgs EFT Low-Energy Limit master certificate, the Electroweak Mass Bridge, the Higgs Observable Skeleton, and Longitudinal Vector Scattering. It supplies the canonical Higgs EFT step inside the six-module Standard-Model chain cited in the root IndisputableMonolith module. The construction closes the link from RS cost geometry to the effective scalar potential used in the forcing-chain theorem surface.

scope and limits

Does not derive numerical values for the Higgs mass or vacuum expectation value.
Does not incorporate gauge couplings or loop corrections.
Does not address non-perturbative or high-energy unitarity bounds.
Does not compute partial widths or branching ratios.

used by (5)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith module_import
IndisputableMonolith.StandardModel.ElectroweakMassBridge module_import
IndisputableMonolith.StandardModel.HiggsEFTLowEnergyLimit module_import
IndisputableMonolith.StandardModel.HiggsObservableSkeleton module_import
IndisputableMonolith.StandardModel.LongitudinalVectorScattering module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (18)

def V_RS L67
theorem V_RS_eq_cosh L70
theorem V_RS_at_vacuum L76
theorem V_RS_nonneg L81
def V_RS_quartic L91
theorem exp_sub_trunc6_le L99
theorem cosh_quartic_error L115
theorem jcost_quartic_error L142
theorem V_RS_quartic_error L156
def quadratic_coefficient L176
def quartic_coefficient_canonical L179
theorem V_RS_quartic_canonical L183
def NormalizationHypothesis L201
theorem mass_term_matches_SM L206
theorem quartic_coupling_from_normalization L220
structure HiggsEFTBridgeCert L238
def higgsEFTBridgeCert L262
theorem higgsEFTBridgeCert_inhabited L271