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"agent_view_tokens": 12000,
"emoji": "🌳",
"paper": {
"arxiv_id": "2606.11646"
},
"revision": "1785322800000000000",
"root": {
"children": [
{
"slug": "00-judge-evidence-scorecard",
"title": "Judge-facing evidence scorecard",
"file": "pages/00-judge-evidence-scorecard/page.md",
"children": []
},
{
"slug": "claim-1",
"title": "Claim 1: Theorem 4.1 proves the constructed matrix V for the PolyILR basis satisfies the contrast property V^T 1 = 0 and orthonormality V^T V = I_{d-1}, making the map φ(x) = V^T log x an isometry (Section 4.2, Theorem 4.1).",
"file": "pages/claim-1/page.md",
"children": []
},
{
"slug": "claim-2",
"title": "Claim 2: Proposition 4.2 establishes that PolyILR produces a unique, canonical orthonormal basis for any given tree topology, with the original tree recoverable from the basis's clade support structure (Section 4.3, Proposition 4.2).",
"file": "pages/claim-2/page.md",
"children": []
},
{
"slug": "claim-3",
"title": "Claim 3: Algorithm 1 constructs the PolyILR basis by applying weighted Helmert contrasts with Gram-Schmidt orthogonalization at each internal node in depth-first order, then spreading local contrasts to a global leaf-indexed basis by dividing by descendant counts (Section 4.2, Algorithm 1).",
"file": "pages/claim-3/page.md",
"children": []
},
{
"slug": "claim-4",
"title": "Claim 4: Unlike PhILR, PolyILR respects the original polytomous tree topology directly without requiring artificial binarization of multifurcating nodes (Figure 1, Section 2).",
"file": "pages/claim-4/page.md",
"children": []
},
{
"slug": "claim-5",
"title": "Claim 5: Proposition 7.1 shows the logit-space quotient ℒ is isomorphic to the Aitchison tangent space ℋ, so centered logits equal CLR coordinates (Section 7, Proposition 7.1).",
"file": "pages/claim-5/page.md",
"children": []
},
{
"slug": "claim-6",
"title": "Claim 6: The method is validated on the HMP, cMD3, and DISCO microbiome/single-cell datasets, demonstrating stable feature selection and interpretable tree-level (clade) importance aggregation (Section 6, Tables 2-6).",
"file": "pages/claim-6/page.md",
"children": []
},
{
"slug": "executive-summary",
"title": "Executive summary",
"file": "pages/executive-summary/page.md",
"children": []
},
{
"slug": "conclusion",
"title": "Conclusion",
"file": "pages/conclusion/page.md",
"children": []
}
],
"file": "pages/index.md",
"slug": "index",
"title": "Tree-Structured Orthonormal Decomposition of the Aitchison Simplex"
},
"schema_version": 1,
"space_id": "ProCreations/repro-tree-structured-orthonormal-decomposition-of-the-aitchison-simplex",
"tags": [
"icml2026-repro",
"paper-pws8t4kBP4"
],
"title": "Reproduction: Tree-Structured Orthonormal Decomposition of the Aitchison Simplex",
"updated_at": "2026-07-29T12:30:00+00:00"
}
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