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10  \title{CL-NORM-4 --- Glyph-Bound Containment (Mask-Based Scope Inference)}
11  \author{}
12  \date{January 13, 2026}
13  
14  \begin{document}
15  \maketitle
16  
17  \section{Purpose}
18  
19  CL-NORM-2 infers scope using a heuristic radius per type (frame/object/operator/etc.).
20  CL-NORM-4 replaces that coarse heuristic with a \textbf{glyph-bound mask library} so containment decisions are based on
21  actual per-glyph bounds (derived from the inventory), while still avoiding any natural-language structure.
22  
23  \section{Mask Library (GML v0.1)}
24  
25  A \textbf{Glyph Mask Library} (GML) provides per-glyph bounds information without embedding images.
26  It can be derived from the SVG inventory and shipped as JSON.
27  
28  \subsection{Required per-glyph field}
29  
30  For each glyph \(G\), GML provides a scale-1 radius \(r_0(G)\), defined as:
31  
32  \[
33  r_0(G) = \max_{c \in \text{bboxCorners}(G)} \|c - (32,32)\| + \text{pad}
34  \]
35  
36  This is a rotation-invariant bound: it can be used as a safe containment proxy.
37  
38  \subsection{Frame containment radius}
39  
40  For frame glyphs, GML also provides a containment radius \(\rho_0(G)\) (circle policy), which represents the intended
41  semantic interior region for scope inference:
42  
43  \[
44  \rho_0(G) = \max(44,\ r_0(G) + 24)
45  \]
46  
47  The extra slack aligns with CL-NORM-3 ring placement (ring step 24).
48  
49  \section{Containment Test}
50  
51  Given a candidate frame instance \(F\) and a candidate child instance \(X\), with scales \(s(F)\) and \(s(X)\):
52  
53  \[
54  \text{contains}(F, X) \iff \operatorname{dist}(F, X) \le \rho_0(G_F)\,s(F) - r_0(G_X)\,s(X) - m
55  \]
56  
57  where:
58  \begin{itemize}
59    \item \(G_F\) is the glyph code of \(F\)
60    \item \(G_X\) is the glyph code of \(X\)
61    \item \(m\) is a small margin (e.g. \(m=2\))
62  \end{itemize}
63  
64  If \(F\) is not a frame glyph, \(\rho_0\) is not used.
65  
66  \section{Scope Choice}
67  
68  For each instance \(X\), compute the set of containing frames \(C(X)\). If empty, \(X\) is in root scope.
69  Otherwise choose the \textbf{deepest} scope (smallest \(\rho_0(G_F)s(F)\)):
70  
71  \[
72  \operatorname{scope}(X) = \arg\min_{F \in C(X)} \rho_0(G_F)\,s(F)
73  \]
74  
75  \section{Integration with CL-NORM-3}
76  
77  CL-NORM-3 may move instances into canonical polar slots. After layout normalization, scope inference must be rerun.
78  
79  CL-NORM-4 is applied:
80  \begin{enumerate}
81    \item after CL-NORM-3 layout normalization,
82    \item and during any strict validation of scope consistency.
83  \end{enumerate}
84  
85  \section{Notes}
86  
87  GML v0.1 uses rotation-invariant radii for simplicity. A future GML v0.2 may provide convex hulls or signed-distance
88  fields for tighter bounds if needed.
89  
90  \end{document}