tree_level_partial_width_match
plain-language theorem explainer
Equal RS and SM amplitudes together with equal phase-space factors imply identical partial widths for any Higgs decay channel. A collider physicist verifying tree-level Higgs phenomenology in Recognition Science would cite the result once the EFT and Yukawa bridges close for that channel. The proof is a one-line wrapper applying the general width-matching identity.
Claim. Let $A_{RS}$, $A_{SM}$, $P_{RS}$, $P_{SM}$ be real numbers. If $A_{RS}=A_{SM}$ and $P_{RS}=P_{SM}$, then the partial decay width computed from the RS amplitude and phase-space factor equals the partial decay width computed from the SM amplitude and phase-space factor.
background
The module defines partial widths, branching ratios and signal strengths as abstract functions of an amplitude and a phase-space factor. This isolates the structural condition for RS-SM agreement without computing explicit matrix elements from scratch. The local theoretical setting is the target surface of collider observables: once the RS Higgs mass, Yukawa couplings and gauge couplings match their SM values via the canonical-normalisation map and the Yukawa map, the tree-level widths must coincide channel by channel. Upstream results supply the eight-tick phase definitions and total summation operators used in the broader amplitude constructions.
proof idea
The proof is a one-line wrapper that invokes the general partial-width matching lemma on the supplied amplitude and phase-space equalities.
why it matters
The declaration supplies the channel-by-channel tree-level match required for the total-width and branching-ratio theorems in the same module. It realises the module statement that RS reproduces SM Higgs phenomenology at tree level once the bridges are closed. Within the Recognition framework it confirms that the eight-tick octave and phi-ladder predictions propagate to identical collider observables, leaving only loop-level channels as open.
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