Recursive Resemblance: A Cross-Scale Invariant of Structural Self-Similarity in the Cascade Efficiency Continuum
Bibliographic record
Abstract
Recursive Resemblance (RR) is introduced as the third geometric invariant of the Cascade Efficiency Continuum (CEC), complementing Harmonic Reducibility (HR) and the Entropy Parabola (EP). RR formalizes cross-scale structural self-similarity across polynomial families, tensor fields, iterated dynamical systems, symbolic transformations, neural architectures, and holographic multiresolution grids.Using normalized feature embeddings, lifting/projection operators, and kernel-based similarity functions, RR defines: • The Recursive Resemblance Index• The Recursive Resemblance Curvature• The Recursive Resemblance Kernel (RRK) Experiments demonstrate that RR detects structural drift earlier than L²-error metrics or Lyapunov-based diagnostics and exhibits attractor-like behavior in stable regimes. RR offers a universal multiscale operator for engineered systems, spanning GPU-accelerated tensor pipelines, polynomial dynamics, RTNN architectures, and holographic rendering systems.
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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 | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.003 | 0.000 |
| Open science | 0.009 | 0.010 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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; both teacher heads agree on what is shown here.
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".