This paper examines the application of proto-scientific methodology in the well-documented medieval inquiry portrayed in Monty Python and the Holy Grail, specifically the “She’s a Witch!” scene. At the core of the tribunal’s reasoning lies the Duck-Weight Equivalence Principle (DWEP), which posits that any individual whose mass precisely matches that of an avian specimen (specifically, Anas platyrhynchos) must, by ancient epistemic law, consist of the same material as ducks. Since ducks float and wood floats, the DWEP formally asserts that such individuals are composed of wood, and hence, by transitive ontological inference, must be witches. This leads directly to the Lemma of Buoyant Malfeasance, though objections persist among anti-floatation theorists who deny the ontological reality of ducks.
Let $\mathbb{H}$ denote the category of peasants, $\mathbb{D}$ the space of floating waterfowl (modulo plumage), and $\mu : \mathbb{H} \sqcup \mathbb{D} \to \mathfrak{M}$ a mass-functor valued in the Medieval Reals $\mathfrak{M}$ (cf. the Holy Manual of Weighing Things).
We define the Duck-Weight Equivalence Principle (DWEP) as:
$$ \forall h \in \mathbb{H},\ \exists d \in \mathbb{D} \text{ such that } \mu(h) \sim_{\epsilon} \mu(d) \Rightarrow \mathbf{W}(h) $$where $\sim_\epsilon$ denotes approximate equivalence under the canonical Feather-Norm topology, and $\mathbf{W} : \mathbb{H} \to \mathbb{B}$ is the witch-indicator functor taking values in the Boolean topos $\mathbb{B} = \{\top, \bot\}$. The duck is assumed to be ideal, frictionless, and morally neutral.
From DWEP we derive the Compositional Parity Lemma (CPL):
$$ \mu(h) = \mu(d) \Rightarrow \mathsf{Wood}(h) $$$$ \mathsf{Wood}(h) \otimes \mathsf{Burns}(h) \Rightarrow \mathbf{W}(h) $$where $\otimes$ denotes the mob-conjunction operator (see The Standard Model of Angry Peasants), and $\mathsf{Burns}(h)$ is defined iff $h$ is subjected to $\mathcal{F}_\text{ire}$, the folklore ignition functor. Attempts to formally invert $\otimes$ remain obstructed by the Peasant Uncertainty Principle, which states that no angry mob can simultaneously know what it wants and why.
The weighing procedure is implemented via a symmetric seesaw morphism
$$ \mathcal{S} : \mathbb{H} \times \mathbb{D} \to \mathbf{Tilt} $$constrained by the Peasant Uncertainty Principle:
$$ \Delta\text{Reason} \cdot \Delta\text{Yelling} \geq \hbar_{\text{turnip}} $$Experimental results yield:
$$ \mu(h^*) \cong \mu(d^*) \mod \delta,\quad \delta < \text{bias}_{\text{duckfoot}} $$By the Witch Affirmation Theorem (WAT):
$$ \mu(h) = \mu(d) \Rightarrow \mathbf{W}(h) $$The proof of WAT is left as an exercise to the reader.
This result consolidates DWEP as a foundational principle in the broader theory of medieval verificationism. While further research is required to determine whether other small animals (e.g., badgers, newts) yield equivalent detection frameworks, the duck-based criterion remains the most parsimonious known method. Applications to legal theory, theology, and buoyancy studies are immediate and far-reaching.