{
  "abstract": "A signed pairwise graphlet encoding of the velocity gradient tensor $\\bm{A}$ is introduced as a minimal discrete representation of its off-diagonal structure, and its statistical relationship with the PQR topology of homogeneous isotropic turbulence is investigated using direct numerical simulation data at $Re_λ\\approx 433$. Each off-diagonal component is assigned a ternary label based on a local threshold, mapping the thresholded off-diagonal sign pattern to one of $3^6=729$ discrete states. The imbalance $Δn=n_W-n_S$ between rotation-promoting and strain-promoting pairs is shown to act as a robust proxy for the sign of $Q$: $P(Q>0\\midΔn)$ increases monotonically from $0\\%$ at $Δn\\leq-2$ to $100\\%$ at $Δn=+3$, and graphlets with a single rotation-promoting pair $(Δn=+1)$ predict the stable-focus-stretching region with probability approximately $65\\%$ -nearly double the global base rate of $36.5\\%$- despite discarding all magnitude information. This predictive power can be largely attributed to the off-diagonal contribution of $\\bm{A}$, which dominates the sign of $Q$ in a majority of flow states. The graphlet--PQR association remains statistically correlated over several Kolmogorov time scales and exhibits spatial coherence comparable to that of the $Q$ field at dissipative scales, providing a consistency check that the discrete thresholding preserves the short-range organisation inherited from the velocity-gradient field. An out-of-sample predictive log-loss test further shows that $Δn$ captures most, but not all, of the predictive content of the complete $729$-state graphlet code: the full code retains a small, reproducible gain of order $10^{-3}$ bits per observation in predicting future PQR topology beyond $Δn$ and the continuous invariants, present at finite lag and absent at zero lag.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23799",
  "author_total": 1,
  "authors": [
    {
      "name": "Radouan Boukharfane"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nmkgzwtq1eqc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23799",
  "fulltext_url": null,
  "id": "5nmkgzwtq1eqc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23799",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7214037923",
  "pdf_url": "https://arxiv.org/pdf/2609.23799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nmkgzwtq1eqc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23799"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Discrete topology sensing in turbulence via signed pairwise graphlets of the velocity gradient tensor",
  "title_text": "Discrete topology sensing in turbulence via signed pairwise graphlets of the velocity gradient tensor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/5nmkgzwtq1eqc",
  "venue": "arXiv",
  "versions": []
}