module module high

`IndisputableMonolith.StandardModel.HiggsObservableSkeleton`

The HiggsObservableSkeleton module supplies the abstract schema for Higgs partial widths from tree-level amplitudes and phase-space factors inside the Recognition Science derivation of the Standard Model. It encodes partialWidth amp phaseSpace as phaseSpace times the squared modulus of amp, together with non-negativity constraints required for physical channels. Collider physicists reconstructing SM-like Higgs observables from RS cost geometry would cite this module. The module consists entirely of definitions and elementary non-negativity and

claimThe partial width into a channel is given by $Γ_i = Φ_i · |A_i|^2$, where $A_i$ is the real or modulus tree-level amplitude and $Φ_i$ is the kinematic phase-space factor that absorbs the Higgs mass $m_H$ and final-state masses. Both $A_i$ and $Φ_i$ are required to be non-negative.

background

This module belongs to the six-module Standard-Model Higgs effective-field-theory low-energy-limit chain. It receives the RS cost geometry to effective scalar coordinate link from the upstream HiggsEFTBridge module, whose doc-comment states that it formalises the first link in the chain RS cost geometry → effective scalar coordinate → canonical Higgs EFT. The HiggsYukawaBridge supplies the Yukawa coupling $y_f = √2 · m_f / v$, while Constants provides the fundamental RS time quantum τ₀ = 1 tick. The module itself introduces the observable skeleton by factoring each partial width into an amplitude squared multiplied by a phase-space factor.

proof idea

This is a definition module, no proofs. It introduces the partialWidth function directly as the product of phaseSpace and the squared modulus of amp, together with companion lemmas that establish non-negativity and matching to tree-level expressions.

why it matters in Recognition Science

The module completes the observable layer of the chain from RS cost geometry through the effective scalar coordinate to canonical Higgs EFT observables, as described in the HiggsEFTLowEnergyLimit master certificate. It is imported by the root IndisputableMonolith module and supplies the observable layer for the six-module Standard-Model Higgs effective-field-theory low-energy-limit chain. The schema directly supports the paper's construction of SM-like Higgs phenomenology from Recognition Science primitives.

scope and limits

Does not derive explicit amplitudes for specific decay channels.
Does not incorporate radiative corrections or higher-order effects.
Does not perform numerical evaluation of branching ratios or signal strengths.
Does not address the full electroweak symmetry breaking dynamics.

used by (2)

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

IndisputableMonolith module_import
IndisputableMonolith.StandardModel.HiggsEFTLowEnergyLimit module_import

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.StandardModel.HiggsEFTBridge module_import
IndisputableMonolith.StandardModel.HiggsYukawaBridge module_import

declarations in this module (16)

def partialWidth L58
theorem partialWidth_nonneg L61
theorem partialWidth_match L69
def totalWidth L79
theorem totalWidth_nonneg L83
def branchingRatio L103
theorem branchingRatio_nonneg L108
def signalStrength L127
theorem signalStrength_one_of_match L132
theorem signalStrength_zero_of_RS_zero L139
theorem tree_level_partial_width_match L156
theorem tree_level_total_width_match L166
theorem tree_level_branching_ratio_match L174
structure HiggsObservableSkeletonCert L194
def higgsObservableSkeletonCert L215
theorem higgsObservableSkeletonCert_inhabited L223