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docs(formal-model): add weight renormalisation remark to def:agg-drift
Applies foldback from verisim-modular-experiment (FOLDBACK.adoc item 2). When a federation operates over a subset modset' ⊊ modset of modalities, aggregate-drift comparisons require per-federation weight renormalisation ŵ_{m1,m2} = w_{m1,m2} / Σ w_{m'1,m'2} over {m'1,m'2} ⊆ modset'. Without this, PROOF CONSISTENCY thresholds shift silently between full-octad and partial-octad federations. The per-octad d(·,⊥)=0 convention is sound; this remark addresses the complementary aggregate-comparison concern across federations with different modality subsets. Source: nextgen-databases/verisim-modular-experiment/docs/FOLDBACK.adoc Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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arcvix-octad-data-model.tex

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@@ -502,6 +502,30 @@ \subsection{Formal Drift Metrics}
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In practice, not all pairs have meaningful distance functions; we define
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metrics for the most important pairs.
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\begin{remark}[Per-federation weight renormalisation]\label{rem:agg-drift-renorm}
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When a federation or deployment operates over a subset
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$\modset' \subsetneq \modset$ of modalities, Definition~\ref{def:agg-drift}
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must be applied with care. The per-octad convention
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$d_{m_1, m_2}(\cdot, \bot) = 0$ from
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Definition~\ref{def:pairwise-drift} handles \emph{per-octad} absence
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soundly --- each absent modality contributes zero drift to its pairs.
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However, for aggregate-drift comparisons to remain meaningful
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\emph{across federations} with different modality subsets, the weights
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must be renormalised over the pairs actually present:
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\[
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\widehat{w}_{m_1, m_2} = \frac{w_{m_1, m_2}}{\sum_{\{m'_1, m'_2\} \subseteq \modset'} w_{m'_1, m'_2}},
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\quad \text{for } \{m_1, m_2\} \subseteq \modset',
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\]
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so that $\sum_{\{m_1, m_2\} \subseteq \modset'} \widehat{w}_{m_1, m_2} = 1$.
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Without this renormalisation, thresholds in downstream judgements (e.g.\
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\texttt{PROOF CONSISTENCY}) shift silently between full-octad and
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partial-octad federations, since absent-pair weights effectively vanish
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from the denominator. Equivalently, absent-pair weights may be treated
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as contributing to a \emph{no-drift term}; the two formulations agree
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when the $d_{m_1, m_2}(\cdot, \bot) = 0$ convention is combined with
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renormalisation over $\modset'$.
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\end{remark}
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\subsection{Modality-Pair Distance Functions}\label{sec:drift-metrics}
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\paragraph{Vector--Document drift ($d_{\mathsf{V},\mathsf{D}}$).}

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