Seed-Window Algebraic Instability in Dementia-Associated miRNAs: A Pilot Study

Authors: Marcelo Maciel Amaral

Journal: Gauge Freedom Field Notes (Preprint)

DOI: 10.65323/gf-lab.2026.001

Abstract

We report a pilot study of seed-window algebraic instability in dementia-associated human miRNAs. The motivating hypothesis is that disease-linked miRNAs may lie near local algebraic transition points, rather than occupying a single stable class across their seed neighborhoods. Using a presentation-first profiler based on finitely presented groups and $SL(2,\mathbb{C})$ character-variety analysis, we analyzed overlapping 6-mer, 7-mer, and 8-mer windows in the canonical seed neighborhoods of hsa-miR-124-3p, hsa-miR-29a-3p, hsa-miR-29c-3p, hsa-miR-92a-3p, hsa-miR-486-5p, hsa-let-7i-5p, and hsa-miR-15a-5p, together with preliminary comparison controls hsa-let-7a-5p and hsa-miR-16-5p. We distinguish three outcome tiers: resolved, projection-skipped-due-to-complexity, and timeout-preliminary. The clearest anchor case was hsa-miR-124-3p, for which the canonical 6-mer AAGGCA remained singular whereas the neighboring 7-mer extension AAGGCAC remained non-singular, reproducing a published regression contrast within a broader seed-neighborhood transition profile. The miR-29 family emerged as a high-scoring transition-rich family, driven primarily by confirmed free-class variation across neighboring windows, although some windows remained projection-skipped in the singularity dimension. By contrast, hsa-let-7a-5p and hsa-let-7i-5p showed no resolved singular windows and therefore provide a useful low-singularity comparison context. These results support the feasibility of quantifying seed-window algebraic transition behavior, while also showing that symbolic complexity itself becomes an interpretable part of the output. The study is exploratory and does not support diagnostic or mechanistic claims at this stage.

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Significance

  • Shifts the Paradigm in RNA Profiling: Moves the analytical focus away from assigning a single global label to an entire mature miRNA, tracking instead how local algebraic transitions shift across overlapping seed windows.
  • Transforms Computational Limits into Data: Proves that symbolic mathematical complexity (such as projection-skipped results) can be embraced as a meaningful, interpretable part of the computational boundary rather than a standard pipeline failure.
  • Novel Genomic Toolkit: Introduces a structural workflow connecting nucleotide sequence words to finitely presented groups and low-rank moduli spaces to analyze disease-linked regulatory elements.

Key Findings

  • Internal Anchor Validation: Replicated a known singular/non-singular sequence contrast (AAGGCA vs. AAGGCAC) in hsa-miR-124-3p, successfully embedding this isolated benchmark into a broader, localized neighborhood profile.
  • Family-Level Instability Signal: Identified the miR-29 family (hsa-miR-29a-3p and hsa-miR-29c-3p) as highly transition-rich, displaying prominent free-class variations across adjacent windows.
  • Low-Singularity Baselines: Established hsa-let-7a-5p and hsa-let-7i-5p as a clean reference pair containing zero resolved singular windows, providing a stark mathematical contrast to transition-dense profiles.
  • Multi-Tier Resolution System: Developed a three-tier outcome framework (resolved, projection-skipped, and timeout-preliminary) that successfully preserves high-dimensional trace-algebra data even when low-dimensional elimination scales past complexity cutoffs.

Future Outlook

  1. Expanded Cohort Validations: Moving beyond small, concept-driven cohorts to larger, statistically powered case-control panels to determine the generalizability of these algebraic profiles.
  2. Biological and Structural Bridging: Constructing a mechanistic bridge to map these abstract algebraic morphology indicators directly to real physical RNA folding structures and downstream target-network biology.
  3. Calibrating Instability Metrics: Refining the exploratory, equally weighted instability scores into a precisely calibrated mathematical classifier suitable for predictive diagnostic research.
  4. Advanced Symbolic Backends: Deploying upgraded computational configurations to systematically clear out remaining projection-skipped and timeout-preliminary windows.

How to cite

Marcelo Maciel Amaral (2026). Seed-Window Algebraic Instability in Dementia-Associated miRNAs: A Pilot Study. Gauge Freedom Field Notes. https://doi.org/10.65323/gf-lab.2026.001

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