On the Structural Dependencies of Intelligence: Coherence, Preservation, and the Role of Emergence (v1.2)
Bibliographic record
Abstract
We report a structural dependency governing stable reasoning in language models: λ[C ≥ P ≥ E], where Coherence bounds Preservation, which bounds Emergence. Across 420 blind evaluations of 140 reasoning traces from 28 architectures, zero counterexamples were observed. Three non-circularity tests confirm the pattern is intrinsic to the data. The dependency is falsifiable by a single stable trace where E > P. None were found.Version 1.2. Originally published on Zenodo (DOI: 10.5281/zenodo.17858943) on December 8, 2025. No content changes from v1.1. See Version History in manuscript for full provenance.Note: The methods and frameworks described in this paper are the subject of Canadian Patent Application CA 3294110. This work is available for non-commercial research, academic study, and educational use without restriction. Commercial use may require a separate license. Contact the author for details.
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How this classification was reachedexpand
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 | 0.000 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.127 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".