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[2026-04-11 09:00] ajaxdavis: (files: spectral-ecology-v2-2026-04.pdf) [2026-04-11 11:23] ajaxdavis: (files: spectral-ecology-v5-2026-04.pdf) [2026-04-11 14:47] ajaxdavis: theoretical-framework-2026-04 [2026-04-11 14:47] ajaxdavis: (files: theoretical-framework-2026-04.pdf) [2026-04-11 15:30] ajaxdavis: Bhattacharyya [2026-04-11 15:38] ajaxdavis: ``` ⏺ Major insight from v8 results! Look at the holonomy self-baseline data: - Self-curvature varies enormously: NA12889 = 1.031, NA12890 = 3.321, NA12891 = 2.288, NA12892 = 4.061 - Cross-curvature tracks self-curvature: when self-κ ≈ cross-κ, the holonomy score H is near 1.0 - The top 3 are all parent-child! Mat.GM→Mother (0.555), Mat.GF→Mother (0.552), Pat.GM→Father (0.543) - But Pat.GF→Father drops to 0.475 because NA12889 has wildly different self-κ (1.031 vs 3.9 for NA12877) The self-baseline approach works for 3/4 parent-child pairs — they cluster at the top. But NA12889 (Pat.GF) is the persistent outlier — its graph structure is fundamentally different from everyone else (1031 self-curvature vs 2288-4061 for others). ``` [2026-04-11 15:51] ajaxdavis: ``` v8 achieved something new: the top 3 scores are all parent-child pairs for the first time in any spectral method. The self-curvature baseline works — related pairs have H > 0.96 (flat connection) while unrelated have H < 0.89 (curved connection). Separation +1.62%. But the compatibility tensor approach you're describing is different from what I implemented. My v8 uses round-trip transport through triangles (holonomy). What you're proposing is a second-order relational structure — comparing relationships-between-relationships via the triple interaction Δ = ψ(i,j) + ψ(j,k) − ψ(i,k). This is a stronger formulation because: 1. It doesn't require mapping through another sample's space (avoids the kernel smoothness problem) 2. It computes curvature WITHIN each sample first, then compares curvature distributions 3. The edge compatibility ψ(i,j) can be defined intrinsically (spectral similarity, MI, role distance) rather than through cross-sample transport Want me to implement this as v9 — the constraint compatibility tensor approach? It would: 1. Define ψ(i,j) from existing patch tensors (spectral distance between patches) 2. Sample triples (i,j,k) from triangles (already have 1256-4867 per sample) 3. Compute Δ per triple → build curvature distribution per sample 4. Compare distributions between samples via EMD 5. No cross-sample field needed — purely intrinsic, then compare distributions ``` [2026-04-11 17:06] ajaxdavis: (files: spectral-ecology-v10-2026-04.pdf) [2026-04-11 20:23] ajaxdavis: https://thomasdavis.github.io/yalumba/audit terrible but history