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Bibliographic record
Abstract
We study the vector spaces and integer lattices of cuts and flows of an arbitrary finite CW complex, and their relationships to its critical group and related invariants. Our results extend the theory of cuts and flows in graphs, in particular the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and describe sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups; these are expressed as short exact sequences with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant. Nous étudions les espaces vectoriels et les réseaux entiers des coupures et flots d’un CW-complexe arbitraire fini, et leur relations avec son groupe critical et invariants similaires. Nos résultats développent la théorie des coupures et flots dans les graphes, en particulier le travail de Bacher, de la Harpe et Nagnibeda. Nous construisons des bases explicites pour les espaces des coupures et des flots, donnons une description topologique de leurs coefficients, et décrivons conditions suffisants pour qu’ils soient des bases entières des réseaux des coupures et des flots.De plus, nous déterminons les relations précises entre les groupes discriminantes des réseaux, et les groupes critical et cocritical; ces relations prennent la forme des suites exactes courtes, avec termes correspondant à la torsion (co)homologie. Comme application, nous généralisons un résultat de Kotani et Sunada sur bornes pour la complexité, la circonférence, et la connectivité d’un CW-complexe en termes de la constante d’Hermite.
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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 | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| 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