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Computes the normalized dot product of two knowledge vectors. It compares vector direction and is undefined if either vector has zero norm; a practical implementation needs a zero-vector policy.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read C_ij as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
SEFERIM FEDERATION - ARCHITECTURAL DIAGRAM DNA^16 Distributed Memory System GOLDEN RATIO φ 1.618033988749895 ψ_k(x) = sin(2πφ^k·x) + cos(2πφ^k·x) MATHEMATICAL CORE Learning: θ_k += α·w·ψ_k(hash(item))·Φ(importance) Query: K = Σ θ_k·ψ_k(hash(query)) Coherence: C_ij = θ_i·θ_j / (||θ_i||·||θ_j||) ▼ ▼ LOCAL MAC (Mac.lan) │ │ REMOTE MACBOOK (192.168.1.180) User: josephanady │ │ User: beandaddy Architecture: ARM64 M1 │◄────── SYNC ───────►│ Architecture: ARM64 M1 ├─────────────────────────────────────────────┤ (SSH/SCP) ├─────────────────────────────────────────────┤ Port 22 Binary: /tmp/dna16_memory/test_dna_memory │ │ Binary: ~/seferim_federation/test_dna_memory Size: 84KB (ARM64 Mach-O) │ │ Size: 84KB (ARM64 Mach-O) STATE DIRECTORY: ~/.seferim/ │ │ STATE DIRECTORY: ~/.seferim/ Total: 3.84 KB (15 × 256 bytes) │ │ Total: 3.84 KB (15 × 256 bytes) ▼ ▼ 15 AGI AGENTS (θ[16] VECTORS) [Context excerpt; full source linked.]
Exact original notation
C_ij = θ_i·θ_j / (||θ_i||·||θ_j||)
Related builds
Sources & provenance
C_ij = θ_i·θ_j / (||θ_i||·||θ_j||)