Every panel renders the exact same canonical concepts, visual instances, typed edges, and stored bounded faces. Cached sentence embeddings now test article-wide aggregation, separate semantic views, and canonical late fusion beside the global and local signal controls.
Fourteen maps recombine one persisted sentence store. Equal-sentence and document-balanced means test aggregation; separate definition, structure, and application views test whether a relation survives different textual lenses; residual and facet arms preserve those views through contrastive early or late fusion.
Average every sentence equally, so long documents contribute more mass.
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Average sentences within each document, then weight all nine article documents equally.
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Keep the half of each article set closest to its sentence centroid before averaging, suppressing peripheral passages.
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Average only sentence embeddings from the approved BRIEF article.
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Keep definition, structure, application, and canonical focus as equal views before one final vector average.
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Compare definition, structure, and application as separate facets using symmetric best-match similarity.
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Add the canonical focus embedding as a fourth facet instead of averaging it into the sentence-derived views.
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Apply the R55 semantic-hub correction after late fusion of the three sentence views and canonical focus.
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Average all sentences, subtract the catalogue-wide article centroid, and renormalize to expose deviations from shared textual material.
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Average all sentences, subtract the catalogue-wide article centroid, and renormalize to expose deviations from shared textual material. Then penalize endpoints with broadly similar local neighborhoods.
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Center definition, structure, application, and canonical views separately before equal early fusion.
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Center definition, structure, application, and canonical views separately before equal early fusion. Then penalize endpoints with broadly similar local neighborhoods.
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Score each pair by its weakest residual similarity across canonical, definition, structure, and application views.
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Score each pair by its weakest residual similarity across canonical, definition, structure, and application views. Then penalize endpoints with broadly similar local neighborhoods.
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Nine aligned maps compare score spread, local separation, neighborhood continuity, semantic hubness, reciprocity, and 2D fidelity. More variance is useful only when the other evidence remains coherent.
The unmodified unit-normalized embedding geometry and ranking baseline.
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Subtract the catalogue centroid and renormalize each residual, without removing any residual principal direction.
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Subtract the catalogue centroid, remove the leading 1 residual principal direction, then renormalize.
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Subtract the catalogue centroid, remove the leading 2 residual principal directions, then renormalize.
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Subtract the catalogue centroid, remove the leading 4 residual principal directions, then renormalize.
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Subtract the catalogue centroid, remove the leading 8 residual principal directions, then renormalize.
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Subtract the catalogue centroid, remove the leading 16 residual principal directions, then renormalize.
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Penalize pairs whose endpoints are broadly similar to their local neighborhoods, reducing semantic-hub advantage before MDS.
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First remove the shared catalogue direction by residual normalization; then penalize semantic hubs using each residual neighborhood baseline.
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These eight controls preserve the established boundary between a plane-valid carrier and unconstrained semantic coordinate hypotheses.
The published R19 coordinates: plane-valid and optimized for local clearance, not semantic distance.
Passes the fixed plane-carrier audit.
The pre-optimization Chrobak-Payne realization that preserves the selected plane exterior.
Passes the fixed plane-carrier audit.
A planar drawing of the same spherical rotation that chooses a different exterior face.
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A fully triangulated coordinate construction whose arbitrary exterior differs from the declared atlas exterior.
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PCA subtracts the mean before finding axes, but does not renormalize the residual vectors; distance is not topologically constrained.
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Distances below 0.5 collapse; remaining normalized-embedding Euclidean distance grows linearly.
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The same cutoff, with larger semantic distances emphasized quadratically.
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The same cutoff, with exp(3z)-1 pushing the largest normalized distances apart most strongly.
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Plane-valid controls preserve crossings and local rotation but remain narrow because straight-line planarity and the declared exterior constrain their coordinate freedom.
Semantic projections spend area on distance but are diagnostic-only whenever they introduce crossings, alter clockwise neighbor order, or change the declared exterior.
Subtracting one shared centroid is a pure translation and cannot change pairwise Euclidean distances. The experimental geometry changes only after each residual is normalized back onto the unit sphere.
The removed mean direction is a candidate nuisance direction, not proof of article-format removal; neighborhood changes require concept-level semantic inspection before promotion.
Principal-subspace removal and local-density correction are deliberately separate interventions: one changes global embedding directions while the other changes graph ranking around semantic hubs.
Greater score variance alone is not a win. The sweep also records local neighbor margins, raw-neighbor retention, inbound hubness, mutuality, and two-dimensional projection fidelity.
On the full snapshot, the combined centroid-residual and local-density arm expands score IQR to 1.25x raw, retains 65.4% of raw six-neighbor slots, lowers hubness Gini to 0.182, and raises mutuality to 82.6%.
Sentence vectors are cached once with exact document offsets, then recombined without further provider calls as equal-sentence, document-balanced, section-view, and late-fusion hypotheses.
The strongest reference-view agreement in this run is Section facets + canonical: it retains 52.2% of canonical six-neighbor slots while averaging 64.7% neighbor overlap with the canonical, definition, structure, and application views.
Agreement among those views is corroborating evidence rather than an independent gold standard because every view comes from the same article set.
The strongest sentence-derived score contrast is Residual all-sentence mean + local density: 2.67x raw score IQR, 2.29x raw six-neighbor boundary margin, hubness Gini 0.214, and 0.782 two-dimensional distance fidelity.
The grid compares coordinate hypotheses; it does not silently replace the accepted shared topology.