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60 lines
3.1 KiB
Text
60 lines
3.1 KiB
Text
/-!
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# Minimum Compression Ratio for Human Neural State
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**Problem:** The human brain contains ~86 billion neurons connected by
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~10¹⁵ synapses. A complete snapshot of neural state requires
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approximately **1 petabyte** (10⁶ GB) of storage.
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**Constraint:** Practical storage and transmission systems can
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accommodate at most **800 GB** per snapshot.
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**Question:** What is the minimum compression ratio required?
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**Answer:**
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```
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C_min = uncompressed_size / max_acceptable_compressed_size
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C_min = 1,000,000 GB / 800 GB = 1,250×
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```
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**With sparsity exploitation:** Only ~15% of neurons fire at any
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moment. Effective uncompressed data = 150,000 GB, giving a
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sparsity-adjusted minimum of **187×**.
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This file is standalone: zero imports, zero external dependencies.
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-/
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def uncompressedStateGb : Nat := 1000000 -- 1 PB = 10⁶ GB
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def targetMinGb : Nat := 300 -- optimistic target (GB)
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def targetMaxGb : Nat := 800 -- conservative target (GB)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Minimum Compression Ratio
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-- ═══════════════════════════════════════════════════════════════════════════
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def minimumCompressionRatio : Nat := uncompressedStateGb / targetMaxGb
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def idealCompressionRatio : Nat := uncompressedStateGb / targetMinGb
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Sparsity-Adjusted Ratio
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-- ═══════════════════════════════════════════════════════════════════════════
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def activeRatioPercent : Nat := 15 -- ~15% of neurons active
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def effectiveUncompressedGb : Nat :=
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(uncompressedStateGb * activeRatioPercent) / 100
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def effectiveMinimumRatio : Nat := effectiveUncompressedGb / targetMaxGb
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Verification Witnesses
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-- ═══════════════════════════════════════════════════════════════════════════
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def compressedSize (uncompressed ratio : Nat) : Nat := uncompressed / ratio
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#eval minimumCompressionRatio -- 1250
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#eval idealCompressionRatio -- 3333
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#eval effectiveUncompressedGb -- 150000
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#eval effectiveMinimumRatio -- 187
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#eval compressedSize uncompressedStateGb minimumCompressionRatio -- 800
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