Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (<i>T</i>O<sub>4</sub>)<sup> <i>n</i>−</sup> tetrahedra
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Bibliographic record
Abstract
. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). The unit cell (or repeat unit) of the chain graph generates the chain graph through action of translational symmetry operators. The (infinite) chain graph is converted into a finite graph by wrapping edges that exit the unit cell such that they link to vertices within the unit cell that are translationally equivalent to the vertices to which they link in the chain graph, and the wrapped graph preserves all topological information of the chain graph. A symbolic algebra is developed that represents the degree of each vertex in the wrapped graph. The wrapped graph is represented by its adjacency matrix which is modified to indicate the direction of wrapped edges, up (+c) or down (-c) along the direction of polymerization. The symbolic algebra is used to generate all possible vertex connectivities for graphs with ≤8 vertices. This method of representing chain graphs by finite matrices may now be inverted to generate all non-isomorphic chain graphs with ≤8 vertices for all possible vertex connectivities. MatLabR2019b code is provided for computationally intensive steps of this method and ∼3000 finite graphs (and associated adjacency matrices) and ∼1500 chain graphs are generated.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it