seferim-core · § 6.5 coherence between two θ vectors

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This relation defines § 6.5 coherence between two θ vectors in the source section “seferim-core · § 6.5 coherence between two θ vectors”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

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

1. Read § 6.5 coherence between two θ vectors as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

    for (let k = 0; k < FAMILIES; k++) K += this.theta[k] * psi(k, h);
    return K;
  }
  // § 6.3  K_norm = K / 32 + 0.5
  queryNorm(q) { return this.query(q) / (FAMILIES * 2) + 0.5; }
}

// § 6.5  coherence between two θ vectors = cosine similarity
export function coherence(a, b) {
  const n = Math.min(a.length, b.length);   // robust to mismatched dimensions
  let dot = 0, na = 0, nb = 0;
  for (let i = 0; i < n; i++) { dot += a[i] * b[i]; na += a[i] * a[i]; nb += b[i] * b[i]; }
  const denom = Math.sqrt(na) * Math.sqrt(nb);
  return denom === 0 ? 0 : dot / denom;
}

/* ============================================================ *
 * § 7. Gate5000 Binary Substrate

§ 6.5  coherence between two θ vectors = cosine similarity

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