/-!
# Minimum Compression Ratio for Human Neural State

**Problem:** The human brain contains ~86 billion neurons connected by
~10¹⁵ synapses. A complete snapshot of neural state requires
approximately **1 petabyte** (10⁶ GB) of storage.

**Constraint:** Practical storage and transmission systems can
accommodate at most **800 GB** per snapshot.

**Question:** What is the minimum compression ratio required?

**Answer:**
```
C_min = uncompressed_size / max_acceptable_compressed_size
C_min = 1,000,000 GB / 800 GB = 1,250×
```

**With sparsity exploitation:** Only ~15% of neurons fire at any
moment. Effective uncompressed data = 150,000 GB, giving a
sparsity-adjusted minimum of **187×**.

This file is standalone: zero imports, zero external dependencies.
-/

def uncompressedStateGb : Nat := 1000000  -- 1 PB = 10⁶ GB

def targetMinGb : Nat := 300            -- optimistic target (GB)
def targetMaxGb : Nat := 800            -- conservative target (GB)

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Minimum Compression Ratio
-- ═══════════════════════════════════════════════════════════════════════════

def minimumCompressionRatio : Nat := uncompressedStateGb / targetMaxGb

def idealCompressionRatio : Nat := uncompressedStateGb / targetMinGb

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Sparsity-Adjusted Ratio
-- ═══════════════════════════════════════════════════════════════════════════

def activeRatioPercent : Nat := 15      -- ~15% of neurons active

def effectiveUncompressedGb : Nat :=
  (uncompressedStateGb * activeRatioPercent) / 100

def effectiveMinimumRatio : Nat := effectiveUncompressedGb / targetMaxGb

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Verification Witnesses
-- ═══════════════════════════════════════════════════════════════════════════

def compressedSize (uncompressed ratio : Nat) : Nat := uncompressed / ratio

#eval minimumCompressionRatio           -- 1250
#eval idealCompressionRatio             -- 3333
#eval effectiveUncompressedGb           -- 150000
#eval effectiveMinimumRatio             -- 187
#eval compressedSize uncompressedStateGb minimumCompressionRatio  -- 800