{
  "abstract": "Zero-lag volume conduction and inter-subject baseline shift remain two primary mathematical obstacles to deploying algebraic topological data analysis (TDA) in real-time brain-computer interfaces (BCIs). While Vietoris-Rips filtration over the finite field F_2 induced by Imaginary Coherency (ImCoh) guarantees exact invariance to instantaneous volume conduction, scaling global 20-channel minimum spanning tree (MST) persistence from small homogeneous benchmarks (N=5, AUC=0.764) to heterogeneous cohorts (N=20, 1,160 epochs) causes severe accuracy degradation (AUC=0.650) and sign inversions in 20% of subjects (4/20). In this paper, we prove that this degradation stems from three mechanisms: (i) zero-lag denominator inflation under high-amplitude standing waves, (ii) sub-epoch phase cancellation across 4-second windows, and (iii) combinatorial spatial MST dilution across anterior artifact channels. We introduce the TRR 3.0 Stage 7 architecture to resolve all three bottlenecks. First, we formulate Sub-Window Rectified and Lag-Orthogonalized Imaginary Coherency (rLagImCoh), proving that it preserves exact zero-lag isolation while preventing standing-wave denominator suppression. Second, we introduce an anatomical simplicial decomposition partitioning the 10-20 montage into an 8-channel occipito-parietal complex and a 12-channel anterior reference complex, reducing 2-simplex boundary complexity by 4.13x. Third, we derive a strictly causal Post-Inversion Empirical Bayes Stein Shrinkage Fusion protocol under Leave-One-Subject-Out Cross-Validation (LOSO-CV) that prevents covariance-inversion gate cancellation. Audited across N=20 subjects (1,160 epochs) from the PhysioNet EEGBCI database, the pure F_2 topological spatial gradient elevates zero-shot (0 s) accuracy from 0.650 to 0.837 (mean within-subject AUC = 0.927) and eliminates all subject polarity inversions. Under causal prefix calibration, Pure Topological TRR scales monotonically in pooled accuracy to 0.874 at 22 s (k=10) and 0.895 at 60 s, while the Hybrid Spectral-Topological TRR architecture achieves AUC = 0.869 at zero-shot (0 s), 0.897 at 8 s, 0.928 at 22 s, and 0.954 at 60 s.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, Jerusalem, Israel"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ronen Weinberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/275czrrrt5qrw.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23504184",
  "fulltext_url": null,
  "id": "275czrrrt5qrw",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23504184",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23504184/files/TRR3_Stage7_Paper.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/275czrrrt5qrw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:38Z",
      "native_id": "23504184",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23504184"
    }
  ],
  "subjects": [],
  "title": "Regional Simplicial Decomposition and Post-Inversion Empirical Bayes Calibration for Zero-Shot and Few-Shot Topological Neurodynamics in Multichannel EEG",
  "title_text": "Regional Simplicial Decomposition and Post-Inversion Empirical Bayes Calibration for Zero-Shot and Few-Shot Topological Neurodynamics in Multichannel EEG",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:38Z",
  "url": "https://research.draconitic.com/paper/275czrrrt5qrw",
  "venue": "Zenodo",
  "versions": []
}