winding
plain-language theorem explainer
The winding definition computes the net integer winding for a ribbon word by mapping each syllable to +1 or -1 according to its direction flag and summing the results. Lattice physicists tracking topological charges on the eight-tick clock cite it when counting signed displacements in ribbon sequences. The implementation is a direct map followed by a foldl sum over the Word list.
Claim. For a word $w$ that is a list of ribbons, the winding number is defined by $winding(w) = sum_{r in w} sigma(r)$, where $sigma(r) = +1$ if the direction flag of ribbon $r$ is true and $-1$ otherwise.
background
In the mass-ribbon model a Word is an abbreviation for a list of Ribbon syllables. Each ribbon carries a direction flag whose unit vector is supplied by the dir operation from the small-angle recognition module. The map operation from the RS-native measurement core is used to transform the list before summation. The module itself is classified as a narrative scaffold whose RS derivations remain informal; downstream code consumes these definitions only as demo inputs.
proof idea
One-line wrapper that applies map to replace each ribbon by its signed integer (+1 or -1) and then folds the resulting list with addition to obtain the net winding.
why it matters
The definition supplies the integer winding count required by the global co-identity constraint theorems (gcic_global_phase_independent_of_basepoint, gcic_global_phase_unique) and by the winding-charge unification results (all_threes_unified, D_independent_charges). It therefore anchors the eight-tick octave (T7) and the D = 3 spatial structure inside the mass sector, even while the surrounding module remains a placeholder.
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