eMERGE IBD: Standard Relatedness vs DI Genomic Graph

Subjects 105,108 eMERGE v3 · imputed / merged

Pairwise IBD Comparisons 5.52B PLINK --genome · 5,523,793,278

Families Detected 6,048 Z0 < 0.83 ∧ Z1 > 0.1 | Z0 < 0.63

Suspect Duplicate Pairs 141 Z0 < 0.15 ∧ Z1 < 0.30

▸ Layer Controls · FamilyClusterObject_j Component Layers

Click to toggle · filters are mutually exclusive

L0 Genotype

L1 IBD

L2 Ancestry / PCA

L3 Imputation R²

L4 PRS

L5 Phenotype

L6 Clinical

L7 Admissibility

Duplicates

1st-Degree

Families

High Leakage

Depression

Dementia

Standard IBD Relatedness Graph 2D NETWORK

⬡ Standard IBD answers: "Are these individuals genetically related?"

DI Multidimensional IBD Field · FamilyClusterObject HOLOMORPHIC · 8-LAYER · v1.1

◈ DI-IBD answers: "What is the connected genomic architecture of this family cluster, and how does it constrain every downstream PRS, PheWAS, GWAS, and clinical claim?"

▸ Calculation Panel — Standard Formula vs DI Operator Form vs FamilyClusterObject Architecture

Standard IBD · PLINK

Z0 + Z1 + Z2 = 1
PI_HAT = 0.5 · Z1 + Z2

familyEdge: (Z0 < 0.83 ∧ Z1 > 0.1) ∨ Z0 < 0.63
duplicateEdge: Z0 < 0.15 ∧ Z1 < 0.30

          First-degree: PI_HAT ≥ 0.45

          Second-degree: PI_HAT ≥ 0.20

          Third-degree: PI_HAT ≥ 0.10

          Unrelated: PI_HAT < 0.10

DI Holomorphic Field · Genomic Hilbert Space

ΨG(a), ΨG(b) ∈ ℋG
Zk_DI(a,b) = ⟨ΨG(a), Πk ΨG(b)⟩ℋG
π_DI(a,b) = 0.5 · Z1_DI(a,b) + Z2_DI(a,b)

DownstreamClaim admissible iff
  IBDGraph declared
  ∧ relatedness handled
  ∧ provenance registered
  ∧ leakage risk resolved

FamilyClusterObject_j · v1.1

Subjects_j
IBDGraph_j
PRSField_j
PhenotypeField_j
AncestryContext_j
ReliabilityProfile_j
AdmissibilityState_j
ProvenanceChain_j

CompositeObject
GOG-RULE-003 applies
ODD-GENOME-001 OPEN

▸ Edge Inspector

Click any edge to inspect · EID_001 → EID_002 (default)